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Code

Documentation

Scripts

S.I. The “Checklist”

[ S.0 ] Executive summary

[ S.0.1 ] s_checklist_executive_summary

[ S.0.1.1 ] Summary

[ S.0.1.2 ] Data

[ S.0.1.3 ] Parameters

[ S.0.1.4 ] Outcomes and figures

[ S.0.1.5 ] Implementation

[ S.0.1.6 ] See also

[ S.1 ] Risk drivers identification

[ S.1.1 ] s_stock_short_horizon

[ S.1.1.1 ] Summary

[ S.1.1.2 ] Data

[ S.1.1.3 ] Parameters

[ S.1.1.4 ] Outcomes and figures

[ S.1.1.5 ] Implementation

[ S.1.2 ] s_stock_long_horizon

[ S.1.2.1 ] Summary

[ S.1.2.2 ] Data

[ S.1.2.3 ] Parameters

[ S.1.2.4 ] Outcomes and figures

[ S.1.2.5 ] Implementation

[ S.1.2.6 ] See also

[ S.1.3 ] Zero-coupon bond rolling price

[ S.1.4 ] s_yield_curve_evolution

[ S.1.4.1 ] Summary

[ S.1.4.2 ] Data

[ S.1.4.3 ] Parameters

[ S.1.4.4 ] Outcomes and figures

[ S.1.4.5 ] Implementation

[ S.1.5 ] s_analyze_rates_jgb

[ S.1.5.1 ] Summary

[ S.1.5.2 ] Data

[ S.1.5.3 ] Parameters

[ S.1.5.4 ] Outcomes and figures

[ S.1.5.5 ] Implementation

[ S.1.5.6 ] See also

[ S.1.6 ] s_fit_yield_ns

[ S.1.6.1 ] Summary

[ S.1.6.2 ] Data

[ S.1.6.3 ] Parameters

[ S.1.6.4 ] Outcomes and figures

[ S.1.6.5 ] Implementation

[ S.1.6.6 ] See also

[ S.1.7 ] Nelson-Siegel parametrization of the spread curve

[ S.1.8 ] s_implied_volatility_surface

[ S.1.8.1 ] Summary

[ S.1.8.2 ] Data

[ S.1.8.3 ] Parameters

[ S.1.8.4 ] Outcomes and figures

[ S.1.8.5 ] Implementation

[ S.1.8.6 ] See also

[ S.1.9 ] Inverse-call implied volatility

[ S.1.10 ] Market quotes in delta-moneyness coordinates

[ S.1.11 ] SVI parametrization of the implied volatility surface

[ S.1.12 ] s_fx_rates_vs_logrates

[ S.1.12.1 ] Summary

[ S.1.12.2 ] Data

[ S.1.12.3 ] Outcomes and figures

[ S.1.12.4 ] Implementation

[ S.1.13 ] s_rating_migrations

[ S.1.13.1 ] Summary

[ S.1.13.2 ] Data

[ S.1.13.3 ] Parameters

[ S.1.13.4 ] Outcomes and figures

[ S.1.13.5 ] Implementation

[ S.1.13.6 ] See also

[ S.1.14 ] s_high_freq_stock_var

[ S.1.14.1 ] Summary

[ S.1.14.2 ] Data

[ S.1.14.3 ] Parameters

[ S.1.14.4 ] Outcomes and figures

[ S.1.14.5 ] Implementation

[ S.1.14.6 ] See also

[ S.1.15 ] High frequency flow variables

[ S.1.16 ] s_high_freq_tick_time

[ S.1.16.1 ] Summary

[ S.1.16.2 ] Data

[ S.1.16.3 ] Parameters

[ S.1.16.4 ] Outcomes and figures

[ S.1.16.5 ] Implementation

[ S.1.16.6 ] See also

[ S.1.17 ] Volume time activity evolution of market microstructure

[ S.1.18 ] Vasicek fit of the yield curve

[ S.1.19 ] Heston parametrization of the implied volatility surface

[ S.1.20 ] s_checklist_scenariobased_step01

[ S.1.20.1 ] Summary

[ S.1.20.2 ] Data

[ S.1.20.3 ] Parameters

[ S.1.20.4 ] Outcomes and figures

[ S.1.20.5 ] Implementation

[ S.1.20.6 ] See also

[ S.2 ] Quest for invariance

[ S.2.1 ] s_elltest_compret

[ S.2.1.1 ] Summary

[ S.2.1.2 ] Data

[ S.2.1.3 ] Parameters

[ S.2.1.4 ] Outcomes and figures

[ S.2.1.5 ] Implementation

[ S.2.1.6 ] See also

[ S.2.2 ] s_kolmsmirn_compret

[ S.2.2.1 ] Summary

[ S.2.2.2 ] Data

[ S.2.2.3 ] Parameters

[ S.2.2.4 ] Outcomes and figures

[ S.2.2.5 ] Implementation

[ S.2.2.6 ] See also

[ S.2.3 ] Ellipsoid test for invariance on equity market variables

[ S.2.4 ] Kolmogorov-Smirnov test for invariance on equity market variables

[ S.2.5 ] Ellipsoid test for invariance on microprice increments

[ S.2.6 ] Kolmogorov-Smirnov test for invariance on microprice increments

[ S.2.7 ] s_elltest_ytm_dailychanges

[ S.2.7.1 ] Summary

[ S.2.7.2 ] Data

[ S.2.7.3 ] Parameters

[ S.2.7.4 ] Outcomes and figures

[ S.2.7.5 ] Implementation

[ S.2.7.6 ] See also

[ S.2.8 ] s_kolmsmirn_ytm

[ S.2.8.1 ] Summary

[ S.2.8.2 ] Data

[ S.2.8.3 ] Parameters

[ S.2.8.4 ] Outcomes and figures

[ S.2.8.5 ] Implementation

[ S.2.8.6 ] See also

[ S.2.9 ] s_elltest_ytm_ns

[ S.2.9.1 ] Summary

[ S.2.9.2 ] Data

[ S.2.9.3 ] Parameters

[ S.2.9.4 ] Outcomes and figures

[ S.2.9.5 ] Implementation

[ S.2.9.6 ] See also

[ S.2.10 ] s_kolmsmirn_ytm_ns

[ S.2.10.1 ] Summary

[ S.2.10.2 ] Data

[ S.2.10.3 ] Parameters

[ S.2.10.4 ] Outcomes and figures

[ S.2.10.5 ] Implementation

[ S.2.10.6 ] See also

[ S.2.11 ] Ellipsoid test for invariance on the increments of the SVI parameters

[ S.2.12 ] Kolmogorov-Smirnov test for invariance on the increments of the SVI parameters

[ S.2.13 ] Ellipsoid test for invariance in the derivatives market

[ S.2.14 ] Kolmogorov-Smirnov test for invariance in the derivatives market

[ S.2.15 ] Ellipsoid test for invariance on the waiting times in high frequency trading

[ S.2.16 ] Kolmogorov-Smirnov test for invariance on the waiting times in high frequency trading

[ S.2.17 ] Ellipsoid test for invariance on the increments of tick time in high frequency trading

[ S.2.18 ] Kolmogorov-Smirnov test for invariance on the increments of tick time in high frequency trading

[ S.2.19 ] Estimation of a quantile of a mixture I

[ S.2.20 ] Flexible combinations models

[ S.2.21 ] s_elltest_ytm_monthly

[ S.2.21.1 ] Summary

[ S.2.21.2 ] Data

[ S.2.21.3 ] Parameters

[ S.2.21.4 ] Outcomes and figures

[ S.2.21.5 ] Implementation

[ S.2.21.6 ] See also

[ S.2.22 ] s_default_merton_model

[ S.2.22.1 ] Summary

[ S.2.22.2 ] Parameters

[ S.2.22.3 ] Outcomes and figures

[ S.2.22.4 ] Implementation

[ S.2.23 ] s_fit_discrete_markov_chain

[ S.2.23.1 ] Summary

[ S.2.23.2 ] Data

[ S.2.23.3 ] Parameters

[ S.2.23.4 ] Outcomes and figures

[ S.2.23.5 ] Implementation

[ S.2.23.6 ] See also

[ S.2.24 ] Markov chain model for bid-ask spread

[ S.2.25 ] Long Memory in high frequency trading order sign

[ S.2.26 ] Long Memory in high frequency trading order sign: fractional integration processes

[ S.2.27 ] s_volatility_clustering_stock

[ S.2.27.1 ] Summary

[ S.2.27.2 ] Data

[ S.2.27.3 ] Parameters

[ S.2.27.4 ] Outcomes and figures

[ S.2.27.5 ] Implementation

[ S.2.27.6 ] See also

[ S.2.28 ] s_elltest_garchres_stock

[ S.2.28.1 ] Summary

[ S.2.28.2 ] Data

[ S.2.28.3 ] Parameters

[ S.2.28.4 ] Outcomes and figures

[ S.2.28.5 ] Implementation

[ S.2.28.6 ] See also

[ S.2.29 ] P&L realizations modeled by a GARCH(1,1): ellipsoid test for invariance on the residuals

[ S.2.30 ] Ellipsoid test for invariance on the residuals of an ACD model fitted on arrival times

[ S.2.31 ] Stochastic volatility and leverage effect

[ S.2.32 ] Implied leverage effect

[ S.2.33 ] s_fit_yields_var1

[ S.2.33.1 ] Summary

[ S.2.33.2 ] Data

[ S.2.33.3 ] Parameters

[ S.2.33.4 ] Outcomes and figures

[ S.2.33.5 ] Implementation

[ S.2.33.6 ] See also

[ S.2.34 ] Multivariate quest for invariance

[ S.2.35 ] Error correction representation of unit-root VAR(1) process: case study

[ S.2.36 ] s_fit_var1_implvol

[ S.2.36.1 ] Summary

[ S.2.36.2 ] Data

[ S.2.36.3 ] Parameters

[ S.2.36.4 ] Outcomes and figures

[ S.2.36.5 ] Implementation

[ S.2.36.6 ] See also

[ S.2.37 ] s_fit_garch_stocks

[ S.2.38 ] s_checklist_scenariobased_step02

[ S.2.38.1 ] Summary

[ S.2.38.2 ] Data

[ S.2.38.3 ] Parameters

[ S.2.38.4 ] Outcomes and figures

[ S.2.38.5 ] Implementation

[ S.2.38.6 ] See also

[ S.3 ] Estimation

[ S.3.1 ] Standard deviation estimation with backward/forward smoothing

[ S.3.2 ] s_state_crisp_fp

[ S.3.2.1 ] Summary

[ S.3.2.2 ] Data

[ S.3.2.3 ] Parameters

[ S.3.2.4 ] Outcomes and figures

[ S.3.2.5 ] Implementation

[ S.3.2.6 ] See also

[ S.3.3 ] s_exp_decay_fp

[ S.3.3.1 ] Summary

[ S.3.3.2 ] Data

[ S.3.3.3 ] Parameters

[ S.3.3.4 ] Outcomes and figures

[ S.3.3.5 ] Implementation

[ S.3.3.6 ] See also

[ S.3.4 ] s_smooth_kernel_fp

[ S.3.4.1 ] Summary

[ S.3.4.2 ] Data

[ S.3.4.3 ] Parameters

[ S.3.4.4 ] Outcomes and figures

[ S.3.4.5 ] Implementation

[ S.3.4.6 ] See also

[ S.3.5 ] s_min_entropy_fp

[ S.3.5.1 ] Summary

[ S.3.5.2 ] Data

[ S.3.5.3 ] Parameters

[ S.3.5.4 ] Outcomes and figures

[ S.3.5.5 ] Implementation

[ S.3.5.6 ] See also

[ S.3.6 ] s_glivenko_cantelli

[ S.3.6.1 ] Summary

[ S.3.6.2 ] Parameters

[ S.3.6.3 ] Outcomes and figures

[ S.3.6.4 ] Implementation

[ S.3.6.5 ] See also

[ S.3.7 ] s_glivenko_cantelli_hfp

[ S.3.7.1 ] Summary

[ S.3.7.2 ] Parameters

[ S.3.7.3 ] Outcomes and figures

[ S.3.7.4 ] Implementation

[ S.3.7.5 ] See also

[ S.3.8 ] HFP ellipsoid dependence on flexible probabilities

[ S.3.9 ] HFP quantile dependence on flexible probabilities

[ S.3.10 ] s_ens_two_scenarios

[ S.3.10.1 ] Summary

[ S.3.10.2 ] Parameters

[ S.3.10.3 ] Outcomes and figures

[ S.3.10.4 ] Implementation

[ S.3.10.5 ] See also

[ S.3.11 ] Quantile estimation: maximum likelihood vs non-parametric

[ S.3.12 ] Consistency of the maximum likelihood estimator: Student t case study

[ S.3.13 ] MLFP estimators for elliptical variables: numerical study on the Hessian matrix of Student t distribution

[ S.3.14 ] MLFP estimators for the Student t distribution. Application

[ S.3.15 ] s_mlfp_ellipsoid_convergence

[ S.3.15.1 ] Summary

[ S.3.15.2 ] Data

[ S.3.15.3 ] Parameters

[ S.3.15.4 ] Outcomes and figures

[ S.3.15.5 ] Implementation

[ S.3.15.6 ] See also

[ S.3.16 ] MLFP quantile dependence on flexible probabilities in extreme value theory

[ S.3.17 ] Quantile function tail approximation

[ S.3.18 ] Non-robustness of sample mean and sample covariance

[ S.3.19 ] Jackknife test on sample mean and covariance

[ S.3.20 ] Sample mean and sample median breakdown point

[ S.3.21 ] Minimum volume ellipsoid enclosing data

[ S.3.22 ] Farthest outlier detection

[ S.3.23 ] High breakdown point with flexible probabilities estimators

[ S.3.24 ] Robustness comparison between HFP and HBFP-estimators

[ S.3.25 ] Method of moments with flexible probabilities: reflected shifted lognormal case study

[ S.3.26 ] Generalized method of moments with flexible probabilities: Poisson distribution

[ S.3.27 ] P&L unconditional distribution

[ S.3.28 ] MLFP estimation of unconditional distribution: properties

[ S.3.29 ] MLFP estimation of unconditional distribution: skew-t fit

[ S.3.30 ] Non-synchronous data

[ S.3.31 ] Outlier detection with flexible probabilities

[ S.3.32 ] Expectation-maximization with flexible probabilities for missing values. Application

[ S.3.33 ] s_different_length_series

[ S.3.33.1 ] Summary

[ S.3.33.2 ] Data

[ S.3.33.3 ] Parameters

[ S.3.33.4 ] Outcomes and figures

[ S.3.33.5 ] Implementation

[ S.3.33.6 ] See also

[ S.3.34 ] Proxies

[ S.3.35 ] Fix non-synchroneity in HFP

[ S.3.36 ] Flexible probabilities ensemble posterior and classical equivalent

[ S.3.37 ] Hellinger distance and diversity indicator

[ S.3.38 ] Ensemble FP: curse of dimensionality?

[ S.3.39 ] Likelihood with flexible probabilities of GARCH(1,1)

[ S.3.40 ] Alternative FP specifications: bootstrap

[ S.3.41 ] Alternative FP specifications: Dirichlet distribution

[ S.3.42 ] s_estimation_copmarg_calloption

[ S.3.42.1 ] Script summary

[ S.3.42.2 ] Data

[ S.3.42.3 ] Parameters

[ S.3.42.4 ] Outcomes and figures

[ S.3.42.5 ] Implementation

[ S.3.42.6 ] See also

[ S.3.43 ] s_estimation_copmarg_ratings

[ S.3.43.1 ] Script summary

[ S.3.43.2 ] Data

[ S.3.43.3 ] Parameters

[ S.3.43.4 ] Outcomes and figures

[ S.3.43.5 ] Implementation

[ S.3.43.6 ] See also

[ S.3.44 ] Copula-marginal estimation for invariants of different asset classes

[ S.3.45 ] Standardization of invariants’ marginals into uniform realizations: case study

[ S.3.46 ] Copula-marginal distribution

[ S.3.47 ] s_dcc_fit

[ S.3.47.1 ] Summary

[ S.3.47.2 ] Data

[ S.3.47.3 ] Parameters

[ S.3.47.4 ] Outcomes and figures

[ S.3.47.5 ] Implementation

[ S.3.47.6 ] See also

[ S.3.48 ] Covariance normalization

[ S.3.49 ] EWMA: numerical example

[ S.3.50 ] Backward/forward EWMA: numerical example

[ S.3.51 ] s_shrinkage_location

[ S.3.51.1 ] Summary

[ S.3.51.2 ] Data

[ S.3.51.3 ] Parameters

[ S.3.51.4 ] Outcomes and figures

[ S.3.51.5 ] Implementation

[ S.3.52 ] s_shrinkage_factor

[ S.3.52.1 ] Summary

[ S.3.52.2 ] Data

[ S.3.52.3 ] Parameters

[ S.3.52.4 ] Outcomes and figures.

[ S.3.52.5 ] Implementation

[ S.3.52.6 ] See also

[ S.3.53 ] s_shrink_corr_clusters

[ S.3.53.1 ] Summary

[ S.3.53.2 ] Datas

[ S.3.53.3 ] Outcomes and figures

[ S.3.53.4 ] Implementation

[ S.3.54 ] Homogeneous cluster shrinkage

[ S.3.55 ] Graphical lasso estimation of the correlation and inverse correlation matrix

[ S.3.56 ] Random matrix theory: Marchenko-Pastur limit

[ S.3.57 ] Numerical integration of Marchenko-Pastur distribution

[ S.3.58 ] Spectrum of the covariance matrix: normal noise

[ S.3.59 ] Spectrum of the covariance matrix: exponential noise

[ S.3.60 ] s_shrink_spectrum_filt

[ S.3.60.1 ] Summary

[ S.3.60.2 ] Data

[ S.3.60.3 ] Parameters

[ S.3.60.4 ] Outcomes and figures

[ S.3.60.5 ] Implementation

[ S.3.60.6 ] See also

[ S.3.61 ] Sparse matrix transformation shrinkage

[ S.3.62 ] Shrinkage estimator of location: implementation

[ S.3.63 ] Sample covariance and eigenvalue dispersion

[ S.3.64 ] Shrinkage estimator of dispersion: implementation

[ S.3.65 ] Random matrix theory: Wigner semicircle law

[ S.3.66 ] Shrinkage estimators of location: assessment

[ S.3.67 ] s_bayes_prior_niw

[ S.3.67.1 ] Summary

[ S.3.67.2 ] Parameters

[ S.3.67.3 ] Outcomes and figures

[ S.3.67.4 ] Implementation

[ S.3.68 ] s_bayes_posterior_niw

[ S.3.68.1 ] Summary

[ S.3.68.2 ] Parameters

[ S.3.68.3 ] Outcomes and figures

[ S.3.68.4 ] Implementation

[ S.3.68.5 ] See also

[ S.3.69 ] s_bayesian_estimation

[ S.3.70 ] Markov chain Monte Carlo: application of Metropolis-Hastings algorithm

[ S.3.71 ] Agnostic prior on correlation

[ S.3.72 ] s_location_estimators

[ S.3.72.1 ] Summary

[ S.3.72.2 ] Parameters

[ S.3.72.3 ] Outcomes and figures

[ S.3.72.4 ] Implementation

[ S.3.72.5 ] See also

[ S.3.73 ] s_sample_mean_covariance

[ S.3.73.1 ] Summary

[ S.3.73.2 ] Parameters

[ S.3.73.3 ] Outcomes and figures

[ S.3.73.4 ] Implementation

[ S.3.73.5 ] See also

[ S.3.74 ] Estimation assessment of a moment-based functional of a mixture I

[ S.3.75 ] Estimation assessment of a moment-based functional of a mixture II

[ S.3.76 ] Estimation assessment of the quantile of a mixture I

[ S.3.77 ] Estimation assessment of the quantile of a mixture II

[ S.3.78 ] s_location_stress_error

[ S.3.78.1 ] Summary

[ S.3.78.2 ] Parameters

[ S.3.78.3 ] Outcomes and figures

[ S.3.78.4 ] Implementation

[ S.3.78.5 ] See also

[ S.3.79 ] Estimation assessment

[ S.3.80 ] Sample mean and sample covariance estimation error

[ S.3.81 ] Sample quantiles distribution

[ S.3.82 ] Distribution of conditioning variable for an aggregate of clusters

[ S.3.83 ] s_checklist_scenariobased_step03

[ S.3.83.1 ] Summary

[ S.3.83.2 ] Data

[ S.3.83.3 ] Parameters

[ S.3.83.4 ] Outcomes and figures

[ S.3.83.5 ] Implementation

[ S.3.83.6 ] See also

[ S.4 ] Projection

[ S.4.1 ] Projection of historical with flexible probabilities distribution via FFT

[ S.4.2 ] Projection of the reflected shifted lognormal distribution

[ S.4.3 ] Sum of random variables via simulation: practice

[ S.4.4 ] Empirical verification of the square-root rule

[ S.4.5 ] Projection of higher-order standardized summary statistical features

[ S.4.6 ] Projection of the GARCH process

[ S.4.7 ] s_projection_var1_yields

[ S.4.7.1 ] Summary

[ S.4.7.2 ] Data

[ S.4.7.3 ] Parameters

[ S.4.7.4 ] Outcomes and figures

[ S.4.7.5 ] Implementation

[ S.4.7.6 ] See also

[ S.4.8 ] s_projection_multiv_ratings

[ S.4.8.1 ] Summary

[ S.4.8.2 ] Data

[ S.4.8.3 ] Outcomes and figures

[ S.4.8.4 ] Implementation

[ S.4.8.5 ] See also

[ S.4.9 ] Projection of a MVOU process with non parametric invariants (historical with flexible probabilities distribution of the principal component)

[ S.4.10 ] Multivariate GARCH: fit and projection. Practice

[ S.4.11 ] Equity market: linear vs. compounded returns projection

[ S.4.12 ] s_projection_calloption

[ S.4.12.1 ] Summary

[ S.4.12.2 ] Data

[ S.4.12.3 ] Parameters

[ S.4.12.4 ] Outcomes and figures

[ S.4.12.5 ] Implementation

[ S.4.12.6 ] See also

[ S.4.13 ] Projection of cluster aggregates: case study

[ S.4.14 ] Projection of risk drivers whose invariants stem from marginal GARCH(1,1) fit and joint DCC fit: stocks case study

[ S.4.15 ] s_projection_stock_hfp

[ S.4.15.1 ] Summary

[ S.4.15.2 ] Data

[ S.4.15.3 ] Parameters

[ S.4.15.4 ] Outcomes and figures

[ S.4.15.5 ] Implementation

[ S.4.15.6 ] See also

[ S.4.16 ] s_projection_stock_bootstrap

[ S.4.16.1 ] Summary

[ S.4.16.2 ] Data

[ S.4.16.3 ] Parameters

[ S.4.16.4 ] Outcomes and figures

[ S.4.16.5 ] Implementation

[ S.4.16.6 ] See also

[ S.4.17 ] Projection via historical approach: call option risk drivers

[ S.4.18 ] Historical projection: bootstrap

[ S.4.19 ] Projection via historical bootstrapping: case study

[ S.4.20 ] Hybrid Monte Carlo-historical projection: case study

[ S.4.21 ] Hybrid historical and Monte Carlo projection: modeling default via a one-factor normal copula

[ S.4.22 ] Copula-marginal projection for risk drivers of different asset classes

[ S.4.23 ] Risk propagation in the Heston process

[ S.4.24 ] s_checklist_scenariobased_steps03_04_historical

[ S.4.24.1 ] Summary

[ S.4.24.2 ] Data

[ S.4.24.3 ] Parameters

[ S.4.24.4 ] Outcomes and figures

[ S.4.24.5 ] Implementation

[ S.4.24.6 ] See also

[ S.4.25 ] s_checklist_scenariobased_step04

[ S.4.25.1 ] Summary

[ S.4.25.2 ] Data

[ S.4.25.3 ] Parameters

[ S.4.25.4 ] Outcomes and figures

[ S.4.25.5 ] Implementation

[ S.4.25.6 ] See also

[ S.5 ] Pricing at the horizon

[ S.5.1 ] s_pricing_stock_hfp

[ S.5.1.1 ] Summary

[ S.5.1.2 ] Data

[ S.5.1.3 ] Outcomes and figures

[ S.5.1.4 ] Implementation

[ S.5.1.5 ] See also

[ S.5.2 ] Equity P&L

[ S.5.3 ] Equity P&L in base currency

[ S.5.4 ] Zero-coupon bond value

[ S.5.5 ] s_pricing_couponbond

[ S.5.5.1 ] Summary

[ S.5.5.2 ] Data

[ S.5.5.3 ] Parameters

[ S.5.5.4 ] Outcomes and figures

[ S.5.5.5 ] Implementation

[ S.5.5.6 ] See also

[ S.5.6 ] Annualized carry return of a zero-coupon bond (practice)

[ S.5.7 ] s_bond_carry

[ S.5.7.1 ] Summary

[ S.5.7.2 ] Data

[ S.5.7.3 ] Parameters

[ S.5.7.4 ] Outcomes and figures

[ S.5.7.5 ] Implementation

[ S.5.7.6 ] See also

[ S.5.8 ] Vega carry of a variance swap

[ S.5.9 ] Carry trade in currencies

[ S.5.10 ] Taylor approximation of an equity P&L

[ S.5.11 ] s_pricing_calloption

[ S.5.11.1 ] Summary

[ S.5.11.2 ] Data

[ S.5.11.3 ] Parameters

[ S.5.11.4 ] Outcomes and figures

[ S.5.11.5 ] Implementation

[ S.5.11.6 ] See also

[ S.5.12 ] s_pricing_couponbond_taylor

[ S.5.12.1 ] Summary

[ S.5.12.2 ] Data

[ S.5.12.3 ] Parameters

[ S.5.12.4 ] Outcomes and figures

[ S.5.12.5 ] Implementation

[ S.5.12.6 ] See also

[ S.5.13 ] Call option P&L Taylor approximation

[ S.5.14 ] s_pricing_zcb

[ S.5.14.1 ] Summary

[ S.5.14.2 ] Data

[ S.5.14.3 ] Parameters

[ S.5.14.4 ] Outcomes and figures

[ S.5.14.5 ] Implementation

[ S.5.14.6 ] See also

[ S.5.15 ] Exact pricing of stocks under normality

[ S.5.16 ] Decomposition of a coupon bond P&L

[ S.5.17 ] Decomposition of a call option P&L

[ S.5.18 ] Stock P&L: historical approach

[ S.5.19 ] Coupon bond with credit risk

[ S.5.20 ] Market and credit joint ex-ante P&L: scenario-based approach

[ S.5.21 ] Equity P&L’s: historical approach

[ S.5.22 ] Call option P&L: historical approach

[ S.5.23 ] s_checklist_scenariobased_step05

[ S.5.23.1 ] Summary

[ S.5.23.2 ] Data

[ S.5.23.3 ] Parameters

[ S.5.23.4 ] Outcomes and figures

[ S.5.23.5 ] Implementation

[ S.5.23.6 ] See also

[ S.6 ] Aggregation

[ S.6.1 ] s_aggregation_exante_perf

[ S.6.1.1 ] Summary

[ S.6.1.2 ] Data

[ S.6.1.3 ] Parameters

[ S.6.1.4 ] Outcomes and figures

[ S.6.1.5 ] Implementation

[ S.6.2 ] s_aggregation_scen_prob

[ S.6.2.1 ] Summary

[ S.6.2.2 ] Parameters

[ S.6.2.3 ] Outcomes and figures

[ S.6.2.4 ] Implementation

[ S.6.3 ] s_aggregation_options_hfp

[ S.6.3.1 ] Summary

[ S.6.3.2 ] Data

[ S.6.3.3 ] Parameters

[ S.6.3.4 ] Outcomes and figures

[ S.6.3.5 ] Implementation

[ S.6.3.6 ] See also

[ S.6.4 ] Ex-ante return distribution: scenario-probability distribution

[ S.6.5 ] s_aggregation_quad

[ S.6.5.1 ] Summary

[ S.6.5.2 ] Data

[ S.6.5.3 ] Parameters

[ S.6.5.4 ] Outcomes and figures

[ S.6.5.5 ] Implementation

[ S.6.5.6 ] See also

[ S.6.6 ] P&L of a large portfolio of stocks: historical approach

[ S.6.7 ] s_aggregation_norm

[ S.6.7.1 ] Summary

[ S.6.7.2 ] Data

[ S.6.7.3 ] Parameters

[ S.6.7.4 ] Outcomes and figures

[ S.6.7.5 ] Implementation

[ S.6.7.6 ] See also

[ S.6.8 ] s_aggregation_regcred

[ S.6.8.1 ] Summary

[ S.6.8.2 ] Data

[ S.6.8.3 ] Parameters

[ S.6.8.4 ] Outcomes and figures

[ S.6.8.5 ] Implementation

[ S.6.8.6 ] See also

[ S.6.9 ] s_cop_marg_stresstest

[ S.6.9.1 ] Script summary

[ S.6.9.2 ] Parameters

[ S.6.9.3 ] Outcomes and figures

[ S.6.9.4 ] Implementation

[ S.6.9.5 ] See also

[ S.6.10 ] s_checklist_scenariobased_step06

[ S.6.10.1 ] Script summary

[ S.6.10.2 ] Data

[ S.6.10.3 ] Parameters

[ S.6.10.4 ] Outcomes and figures

[ S.6.10.5 ] Implementation

[ S.6.10.6 ] See also

[ S.7 ] Ex-ante evaluation

[ S.7.1 ] s_evaluation_certainty_equiv

[ S.7.1.1 ] Summary

[ S.7.1.2 ] Data

[ S.7.1.3 ] Parameters

[ S.7.1.4 ] Outcomes and figures

[ S.7.1.5 ] Implementation

[ S.7.1.6 ] See also

[ S.7.2 ] s_evaluation_satis_scenprob

[ S.7.2.1 ] Summary

[ S.7.2.2 ] Data

[ S.7.2.3 ] Parameters

[ S.7.2.4 ] Outcomes

[ S.7.2.5 ] Implementation

[ S.7.2.6 ] Step 9

[ S.7.2.7 ] Step 11

[ S.7.2.8 ] See also

[ S.7.3 ] s_evaluation_satis_norm

[ S.7.3.1 ] Summary

[ S.7.3.2 ] Data

[ S.7.3.3 ] Parameters

[ S.7.3.4 ] Outcomes

[ S.7.3.5 ] Implementation

[ S.7.4 ] Cornish Fisher expansion: an application

[ S.7.5 ] s_evaluation_eco_cap

[ S.7.5.1 ] Summary

[ S.7.5.2 ] Data

[ S.7.5.3 ] Parameters

[ S.7.5.4 ] Outcomes

[ S.7.5.5 ] Implementation

[ S.7.5.6 ] See also

[ S.7.6 ] s_evaluation_cornishfisher_stocks

[ S.7.6.1 ] Summary

[ S.7.6.2 ] Data

[ S.7.6.3 ] Parameters

[ S.7.6.4 ] Outcomes and figures

[ S.7.6.5 ] Implementation

[ S.7.6.6 ] See also

[ S.7.7 ] The mean-lower partial moment trade-off is not co-monotonic additive: practice

[ S.7.8 ] s_checklist_scenariobased_step07

[ S.7.8.1 ] Script summary

[ S.7.8.2 ] Data

[ S.7.8.3 ] Parameters

[ S.7.8.4 ] Outcomes and figures

[ S.7.8.5 ] Implementation

[ S.7.8.6 ] See also

[ S.8a ] Ex-ante attribution: performance

[ S.8a.1 ] s_attribution_norm

[ S.8a.1.1 ] Summary

[ S.8a.1.2 ] Data

[ S.8a.1.3 ] Outcomes and figures

[ S.8a.1.4 ] Implementation

[ S.8a.1.5 ] See also

[ S.8a.2 ] s_attribution_scen_prob

[ S.8a.2.1 ] Summary

[ S.8a.2.2 ] Parameters

[ S.8a.2.3 ] Outcomes and figures

[ S.8a.2.4 ] Implementation

[ S.8a.2.5 ] See also

[ S.8a.3 ] s_attribution_hedging

[ S.8a.3.1 ] Summary

[ S.8a.3.2 ] Data

[ S.8a.3.3 ] Outcomes and figures

[ S.8a.3.4 ] Implementation

[ S.8a.3.5 ] See also

[ S.8b ] Ex-ante attribution: risk

[ S.8b.1 ] s_risk_attribution_norm

[ S.8b.1.1 ] Summary

[ S.8b.1.2 ] Data

[ S.8b.1.3 ] Parameters

[ S.8b.1.4 ] Outcomes and figures

[ S.8b.1.5 ] Implementation

[ S.8b.2 ] s_risk_attribution_scen_prob

[ S.8b.2.1 ] Summary

[ S.8b.2.2 ] Data

[ S.8b.2.3 ] Parameters

[ S.8b.2.4 ] Outcomes and figures

[ S.8b.2.5 ] Implementation

[ S.8b.2.6 ] See also

[ S.8b.3 ] s_risk_attrib_torsion

[ S.8b.3.1 ] Summary

[ S.8b.3.2 ] Data

[ S.8b.3.3 ] Parameters

[ S.8b.3.4 ] Outcomes and figures

[ S.8b.3.5 ] Implementation

[ S.8b.3.6 ] See also

[ S.8b.4 ] s_risk_attrib_variance

[ S.8b.4.1 ] Summary

[ S.8b.4.2 ] Data

[ S.8b.4.3 ] Outcomes and figures

[ S.8b.4.4 ] Implementation

[ S.8b.4.5 ] See also

[ S.8b.5 ] s_checklist_scenariobased_step08

[ S.8b.5.1 ] Script summary

[ S.8b.5.2 ] Data

[ S.8b.5.3 ] Parameters

[ S.8b.5.4 ] Outcomes and figures

[ S.8b.5.5 ] Implementation

[ S.8b.5.6 ] See also

[ S.9a ] Construction: portfolio optimization

[ S.9a.1 ] Mean-variance efficient frontier: numerical implementation

[ S.9a.2 ] Mean-variance robust efficient frontier: numerical implementation

[ S.9a.3 ] s_stock_selection

[ S.9a.3.1 ] Summary

[ S.9a.3.2 ] Data

[ S.9a.3.3 ] Parameters

[ S.9a.3.4 ] Outcomes and figures

[ S.9a.3.5 ] Implementation

[ S.9a.3.6 ] See also

[ S.9a.4 ] s_checklist_scenariobased_step09

[ S.9a.4.1 ] Script summary

[ S.9a.4.2 ] Data

[ S.9a.4.3 ] Parameters

[ S.9a.4.4 ] Outcomes and figures

[ S.9a.4.5 ] Implementation

[ S.9a.4.6 ] See also

[ S.9a.5 ] Portfolio optimization: S&P 500 stocks

[ S.9b ] Construction: estimation and model risk

[ S.9c ] Construction: cross-sectional strategies

[ S.9c.1 ] Characteristic portfolio construction (size)

[ S.9c.2 ] s_characteristic_port_rev

[ S.9c.2.1 ] Summary

[ S.9c.2.2 ] Data

[ S.9c.2.3 ] Parameters

[ S.9c.2.4 ] Outcomes and figures

[ S.9c.2.5 ] Implementation

[ S.9c.2.6 ] See also

[ S.9c.3 ] s_flexible_characteristic_port_rev

[ S.9c.3.1 ] Summary

[ S.9c.3.2 ] Data

[ S.9c.3.3 ] Parameters

[ S.9c.3.4 ] Outcomes and figures

[ S.9c.3.5 ] Implementation

[ S.9c.3.6 ] See also

[ S.9c.4 ] s_generalized_flam_toy

[ S.9d ] Construction: time series strategies

[ S.9d.1 ] s_dynamic_port_strats

[ S.9d.1.1 ] Summary

[ S.9d.1.2 ] Parameters

[ S.9d.1.3 ] Outcomes and figures

[ S.9d.1.4 ] Implementation

[ S.9d.1.5 ] See also

[ S.10 ] Execution

[ S.10.1 ] s_execution_exog_impact

[ S.10.1.1 ] Summary

[ S.10.1.2 ] Data

[ S.10.1.3 ] Parameters

[ S.10.1.4 ] Outcomes and figures

[ S.10.1.5 ] Implementation

[ S.10.1.6 ] See also

[ S.10.2 ] Monotonicity of trading trajectories in the Almgren-Chriss model (full execution requirement)

[ S.10.3 ] Non-monotone trading trajectories in the Almgren-Chriss model with null drift

[ S.10.4 ] s_execution_trading_traject

[ S.10.4.1 ] Summary

[ S.10.4.2 ] Parameters

[ S.10.4.3 ] Outcomes and figures

[ S.10.4.4 ] Implementation

[ S.10.4.5 ] See also

[ S.10.5 ] s_execution_opt_satisfaction_quantile

[ S.10.5.1 ] Summary

[ S.10.5.2 ] Parameters

[ S.10.5.3 ] Outcomes and figures

[ S.10.5.4 ] Implementation

[ S.10.6 ] Trading trajectories in the multidimensional Almgren-Chriss model

[ S.10.7 ] Liquidation trajectory and trading rate in the transient impact model with power law decay kernel

[ S.10.8 ] Liquidation trajectory and trading rate in the transient impact model with logarithmic decay kernel

[ S.10.9 ] s_execution_child_order

[ S.10.9.1 ] Summary

[ S.10.9.2 ] Data

[ S.10.9.3 ] Parameters

[ S.10.9.4 ] Outcomes and figures

[ S.10.9.5 ] Implementation

[ S.10.10 ] s_execution_sell_algorithm

[ S.10.10.1 ] Summary

[ S.10.10.2 ] Parameters

[ S.10.10.3 ] Outcomes and figures

[ S.10.10.4 ] Implementation

[ S.10.11 ] A buying algorithm

[ S.10.12 ] s_checklist_scenariobased_step10

[ S.10.12.1 ] Script summary

[ S.10.12.2 ] Data

[ S.10.12.3 ] Parameters

[ S.10.12.4 ] Outcomes and figures

[ S.10.12.5 ] Implementation

[ S.10.12.6 ] See also

S.II. Factor models and learning

[ S.11 ] Executive summary

[ S.11.1 ] s_lfm_executive_summary

[ S.11.1.1 ] Summary

[ S.11.1.2 ] Data

[ S.11.1.3 ] Parameters

[ S.11.1.4 ] Outcomes and figures

[ S.11.1.5 ] Implementation

[ S.11.1.6 ] See also

[ S.12 ] Linear factor models

[ S.12.1 ] s_normal_mean_regression

[ S.12.1.1 ] Summary

[ S.12.1.2 ] Parameters

[ S.12.1.3 ] Outcomes and figures

[ S.12.1.4 ] Implementation

[ S.12.1.5 ] See also

[ S.12.2 ] s_regression_lfm

[ S.12.2.1 ] Summary

[ S.12.2.2 ] Parameters

[ S.12.2.3 ] Outcomes and figures

[ S.12.2.4 ] Implementation

[ S.12.2.5 ] See also

[ S.12.3 ] Comparison of LFM’s

[ S.12.4 ] Symmetric regression: numerical example

[ S.12.5 ] s_principal_component_lfm

[ S.12.5.1 ] Summary

[ S.12.5.2 ] Parameters

[ S.12.5.3 ] Outcomes and figures

[ S.12.5.4 ] Implementation

[ S.12.5.5 ] See also

[ S.12.6 ] Principal-component LFM’s: joint distribution of residuals and factors

[ S.12.7 ] s_systematic_idiosyncratic_lfm

[ S.12.7.1 ] Summary

[ S.12.7.2 ] Parameters

[ S.12.7.3 ] Outcomes and figures

[ S.12.7.4 ] Implementation

[ S.12.7.5 ] See also

[ S.12.8 ] s_cross_section_lfm

[ S.12.8.1 ] Summary

[ S.12.8.2 ] Data

[ S.12.8.3 ] Parameters

[ S.12.8.4 ] Outcomes and figures

[ S.12.8.5 ] Implementation

[ S.12.9 ] s_factor_replication_logn

[ S.12.9.1 ] Summary

[ S.12.9.2 ] Parameters

[ S.12.9.3 ] Outcomes and figures

[ S.12.9.4 ] Implementation

[ S.12.9.5 ] See also

[ S.12.10 ] Factor-replicating portfolio convergence under normal factors and residuals

[ S.12.11 ] Cross-sectional LFM’s loadings versus regression LFM’s loadings

[ S.12.12 ] Cross-sectional factor extraction matrix is variance-minimizing: numerical example

[ S.12.13 ] Cross-sectional LFM’s optimal r-squared: numerical example

[ S.12.14 ] Correlation of residuals in generalized cross-sectional LFM

[ S.12.15 ] Factor extraction: numerical test

[ S.12.16 ] Hidden factors: puzzle

[ S.12.17 ] Hidden regression versus Principal-component LFM’s: numerical example

[ S.12.18 ] Correlation of residuals in generalized regression LFM’s

[ S.12.19 ] Fully observable factor model

[ S.12.20 ] Fully observable models: study of factor-residual distribution

[ S.12.21 ] Cross-sectional LFM’s: generalized cross-sectional industry factors

[ S.12.22 ] Regression LFM’s: shifted-lognormal regression II

[ S.12.23 ] s_reg_truncated_lfm

[ S.12.23.1 ] Summary

[ S.12.23.2 ] Data

[ S.12.23.3 ] Parameters

[ S.12.23.4 ] Outcomes and figures

[ S.12.23.5 ] Implementation

[ S.12.23.6 ] See also

[ S.12.24 ] s_pca_truncated_lfm

[ S.12.24.1 ] Summary

[ S.12.24.2 ] Data

[ S.12.24.3 ] Parameters

[ S.12.24.4 ] Outcomes and figures

[ S.12.24.5 ] Implementation

[ S.12.24.6 ] See also

[ S.12.25 ] s_cross_section_truncated_lfm

[ S.12.25.1 ] Summary

[ S.12.25.2 ] Data

[ S.12.25.3 ] Parameters

[ S.12.25.4 ] Outcomes and figures

[ S.12.25.5 ] Implementation

[ S.12.25.6 ] See also

[ S.12.26 ] Simulation of the distribution of statistics of regression parameters

[ S.12.27 ] Regression LFM’s: truncated estimations

[ S.12.28 ] Regression LFM’s: generalized regression industry factors

[ S.13 ] Machine learning foundations

[ S.14 ] Point machine learning models

[ S.14.1 ] s_logn_mean_regression

[ S.14.1.1 ] Summary

[ S.14.1.2 ] Parameters

[ S.14.1.3 ] Outcomes and figures

[ S.14.1.4 ] Implementation

[ S.14.1.5 ] See also

[ S.14.2 ] s_call_mean_regression

[ S.14.2.1 ] Summary

[ S.14.2.2 ] Data

[ S.14.2.3 ] Outcomes and figures

[ S.14.2.4 ] Implementation

[ S.14.2.5 ] See also

[ S.14.3 ] s_call_mean_lin_regression

[ S.14.3.1 ] Summary

[ S.14.3.2 ] Data

[ S.14.3.3 ] Outcomes and figures

[ S.14.3.4 ] Implementation

[ S.14.3.5 ] See also

[ S.14.4 ] s_logn_mean_lin_regression

[ S.14.4.1 ] Summary

[ S.14.4.2 ] Parameters

[ S.14.4.3 ] Outcomes and figures

[ S.14.4.4 ] Implementation

[ S.14.4.5 ] See also

[ S.14.5 ] s_continuum_discrete_point_pred

[ S.14.5.1 ] Summary

[ S.14.5.2 ] Parameters

[ S.14.5.3 ] Outcomes and figures

[ S.14.5.4 ] Implementation

[ S.14.5.5 ] See also

[ S.14.6 ] s_sp_anova

[ S.14.6.1 ] Summary

[ S.14.6.2 ] Data

[ S.14.6.3 ] Parameters

[ S.14.6.4 ] Outcomes and figures

[ S.14.6.5 ] Implementation

[ S.14.6.6 ] See also

[ S.14.7 ] s_interactions

[ S.14.7.1 ] Summary

[ S.14.7.2 ] Input parameters

[ S.14.7.3 ] Outcomes and figures

[ S.14.7.4 ] Implementation

[ S.14.7.5 ] See also

[ S.14.8 ] s_cart

[ S.14.8.1 ] Summary

[ S.14.8.2 ] Data

[ S.14.8.3 ] Parameters

[ S.14.8.4 ] Outcomes and figures

[ S.14.8.5 ] Implementation

[ S.14.9 ] s_ann_regression

[ S.14.9.1 ] Summary

[ S.14.9.2 ] Data

[ S.14.9.3 ] Input parameters

[ S.14.9.4 ] Outcomes and figures

[ S.14.9.5 ] Implementation

[ S.14.10 ] s_gradient_boosting

[ S.14.10.1 ] Summary

[ S.14.10.2 ] Data

[ S.14.10.3 ] Parameters

[ S.14.10.4 ] Outcomes and figures

[ S.14.10.5 ] Implementation

[ S.14.11 ] s_linclass_regression

[ S.14.12 ] s_linclass_fda

[ S.14.13 ] s_linclass_perceptron

[ S.14.14 ] s_linclass_svm

[ S.14.15 ] s_linclass_ann_svm

[ S.14.16 ] s_logn_quant_regression

[ S.14.16.1 ] Summary

[ S.14.16.2 ] Parameters

[ S.14.16.3 ] Outcomes and figures

[ S.14.16.4 ] Implementation

[ S.14.16.5 ] See also

[ S.14.17 ] s_call_quant_regression

[ S.14.17.1 ] Summary

[ S.14.17.2 ] Data

[ S.14.17.3 ] Parameters

[ S.14.17.4 ] Outcomes and figures

[ S.14.17.5 ] Implementation

[ S.14.17.6 ] See also

[ S.14.18 ] s_logn_quant_lin_regression

[ S.14.18.1 ] Summary

[ S.14.18.2 ] Parameters

[ S.14.18.3 ] Outcomes and figures

[ S.14.18.4 ] Implementation

[ S.14.18.5 ] See also

[ S.14.19 ] s_call_quant_lin_regression

[ S.14.19.1 ] Summary

[ S.14.19.2 ] Data

[ S.14.19.3 ] Parameters

[ S.14.19.4 ] Outcomes and figures

[ S.14.19.5 ] Implementation

[ S.14.19.6 ] See also

[ S.14.20 ] s_supervised_classification

[ S.14.20.1 ] Summary

[ S.14.20.2 ] Parameters

[ S.14.20.3 ] Outcomes and figures

[ S.14.20.4 ] Implementation

[ S.14.20.5 ] See also

[ S.14.21 ] s_autoencoders_kmeans

[ S.14.21.1 ] Summary

[ S.14.21.2 ] Parameters

[ S.14.21.3 ] Outcomes and figures

[ S.14.21.4 ] Implementation

[ S.14.21.5 ] See also

[ S.15 ] Probabilistic machine learning models

[ S.15.1 ] s_continuum_discrete_generative_pred

[ S.15.1.1 ] Summary

[ S.15.1.2 ] Parameters

[ S.15.1.3 ] Outcomes and figures

[ S.15.1.4 ] Implementation

[ S.15.1.5 ] See also

[ S.16 ] Generalized probabilistic inference

[ S.16.1 ] s_min_rel_ent_point_view

[ S.16.1.1 ] Summary

[ S.16.1.2 ] Parameters

[ S.16.1.3 ] Outcomes

[ S.16.1.4 ] Implementation

[ S.16.1.5 ] See also

[ S.16.2 ] s_min_rel_ent_distr_view

[ S.16.2.1 ] Summary

[ S.16.2.2 ] Parameters

[ S.16.2.3 ] Outcomes

[ S.16.2.4 ] Implementation

[ S.16.2.5 ] See also

[ S.16.3 ] s_min_rel_ent_partial_view

[ S.16.3.1 ] Summary

[ S.16.3.2 ] Parameters

[ S.16.3.3 ] Outcomes

[ S.16.3.4 ] Implementation

[ S.16.3.5 ] See also

[ S.16.4 ] s_entropy_view

[ S.16.4.1 ] Summary

[ S.16.4.2 ] Parameters

[ S.16.4.3 ] Outcomes and figures

[ S.16.4.4 ] Implementation

[ S.16.4.5 ] See also

[ S.16.5 ] s_views_linear_exp

[ S.16.5.1 ] Summary

[ S.16.5.2 ] Parameters

[ S.16.5.3 ] Outcomes

[ S.16.5.4 ] Implementation

[ S.16.5.5 ] See also

[ S.16.6 ] s_views_gen_expectations

[ S.16.6.1 ] Summary

[ S.16.6.2 ] Parameters

[ S.16.6.3 ] Outcomes

[ S.16.6.4 ] Implementation

[ S.16.6.5 ] See also

[ S.16.7 ] s_views_sorted_exp

[ S.16.7.1 ] Summary

[ S.16.7.2 ] Parameters

[ S.16.7.3 ] Outcomes

[ S.16.7.4 ] Implementation

[ S.16.7.5 ] See also

[ S.16.8 ] s_views_st_deviations

[ S.16.8.1 ] Summary

[ S.16.8.2 ] Parameters

[ S.16.8.3 ] Outcomes

[ S.16.8.4 ] Implementation

[ S.16.8.5 ] See also

[ S.16.9 ] s_views_correlations

[ S.16.9.1 ] Summary

[ S.16.9.2 ] Parameters

[ S.16.9.3 ] Outcomes

[ S.16.9.4 ] Implementation

[ S.16.9.5 ] See also

[ S.16.10 ] s_views_cond_prob

[ S.16.10.1 ] Summary

[ S.16.10.2 ] Parameters

[ S.16.10.3 ] Outcomes

[ S.16.10.4 ] Implementation

[ S.16.10.5 ] See also

[ S.16.11 ] s_views_cdf

[ S.16.11.1 ] Summary

[ S.16.11.2 ] Parameters

[ S.16.11.3 ] Outcomes

[ S.16.11.4 ] Implementation

[ S.16.11.5 ] See also

[ S.16.12 ] s_views_cond_exp

[ S.16.12.1 ] Summary

[ S.16.12.2 ] Parameters

[ S.16.12.3 ] Outcomes

[ S.16.12.4 ] Implementation

[ S.16.12.5 ] See also

[ S.16.13 ] Convexity test for relative entropy

[ S.16.14 ] Numerical verification of the gradient of entropy

[ S.16.15 ] Numerical verification of gradient of constraint function on signal

[ S.16.16 ] Numerical verification of the Hessian of entropy

[ S.16.17 ] Numerical and analytical Hessian of constraints on signal

[ S.16.18 ] Copula opinion pooling: uninformative views

[ S.17 ] Dynamic and spacial models

[ S.17.1 ] s_dyn_principal_component_var

[ S.17.1.1 ] Summary

[ S.17.1.2 ] Parameters

[ S.17.1.3 ] Outcomes and figures

[ S.17.1.4 ] Implementation

[ S.17.1.5 ] See also

[ S.17.2 ] s_kalman_filter_yield_curve

[ S.17.2.1 ] Summary

[ S.17.2.2 ] Data

[ S.17.2.3 ] Parameters

[ S.17.2.4 ] Outcomes and figures

[ S.17.2.5 ] Implementation

[ S.17.2.6 ] See also

[ S.17.3 ] s_hidden_markov_model_stocks

[ S.17.3.1 ] Summary

[ S.17.3.2 ] Data

[ S.17.3.3 ] Parameters

[ S.17.3.4 ] Outcomes and figures

[ S.17.3.5 ] Implementation

[ S.18 ] Application: probabilistic regression in the stock market

[ S.18.1 ] s_market_prediction_regression

[ S.18.2 ] s_lasso_vs_ridge

[ S.18.2.1 ] Summary

[ S.18.2.2 ] Data

[ S.18.2.3 ] Parameters

[ S.18.2.4 ] Outcomes and figures

[ S.18.2.5 ] Implementation

[ S.18.2.6 ] See also

[ S.18.3 ] Regression LFM’s: randomized least square estimates

[ S.18.4 ] s_reg_lfm_bayes_prior_niw

[ S.18.4.1 ] Summary

[ S.18.4.2 ] Parameters

[ S.18.4.3 ] Outcomes and figures

[ S.18.4.4 ] Implementation

[ S.18.5 ] s_reg_lfm_bayes_posterior_niw

[ S.18.5.1 ] Summary

[ S.18.5.2 ] Parameters

[ S.18.5.3 ] Outcomes and figures

[ S.18.5.4 ] Implementation

[ S.18.5.5 ] See also

[ S.19 ] Application: principal component analysis of the yield curve

[ S.19.1 ] Eigenvectors for Toeplitz structure

[ S.19.2 ] s_yield_change_correlation

[ S.19.2.1 ] Summary

[ S.19.2.2 ] Data

[ S.19.2.3 ] Parameters

[ S.19.2.4 ] Outcomes and figures

[ S.19.2.5 ] Implementation

[ S.19.2.6 ] See also

[ S.19.3 ] s_pca_empirical

[ S.19.3.1 ] Summary

[ S.19.3.2 ] Data

[ S.19.3.3 ] Parameters

[ S.19.3.4 ] Outcomes and figures

[ S.19.3.5 ] Implementation

[ S.19.3.6 ] See also

[ S.19.4 ] s_pca_yield

[ S.19.4.1 ] Summary

[ S.19.4.2 ] Data

[ S.19.4.3 ] Outcomes and figures

[ S.19.4.4 ] Implementation

[ S.19.5 ] Equivalent formulations of maximum likelihood with flexible probabilities estimates (numerical proof)

[ S.19.6 ] s_factors_selection

[ S.19.6.1 ] Summary

[ S.19.6.2 ] Parameters

[ S.19.6.3 ] Outcomes and figures

[ S.19.6.4 ] Implementation

[ S.19.6.5 ] See also

[ S.20 ] Application: credit default classification

[ S.20.1 ] s_default_probabilities

[ S.21 ] Application: clustering

S.III. Valuation

[ S.22 ] Executive summary

[ S.23 ] Background definitions

[ S.24 ] Linear pricing theory: core

[ S.24.1 ] s_current_values

[ S.24.1.1 ] Summary

[ S.24.1.2 ] Parameters

[ S.24.1.3 ] Outcomes and figures

[ S.24.1.4 ] Implementation

[ S.24.1.5 ] See also

[ S.24.2 ] Stochastic discount factor comparison

[ S.24.3 ] s_fund_theorem

[ S.24.3.1 ] Summary

[ S.24.3.2 ] Data

[ S.24.3.3 ] Outcomes and figures

[ S.24.3.4 ] Implementation

[ S.24.3.5 ] See also

[ S.24.4 ] s_rn_derivative_mre

[ S.24.4.1 ] Summary

[ S.24.4.2 ] Data

[ S.24.4.3 ] Outcomes and figures

[ S.24.4.4 ] Implementation

[ S.24.4.5 ] See also

[ S.24.5 ] Fundamental theorem of asset pricing with risk-neutral measure: empirical verification

[ S.24.6 ] s_risk_neutral_density

[ S.24.6.1 ] Summary

[ S.24.6.2 ] Data

[ S.24.6.3 ] Parameters

[ S.24.6.4 ] Outcomes and figures

[ S.24.6.5 ] Implementation

[ S.24.7 ] s_capm_like_identity

[ S.24.7.1 ] Summary

[ S.24.7.2 ] Parameters

[ S.24.7.3 ] Outcomes and figures

[ S.24.7.4 ] Implementation

[ S.24.7.5 ] See also

[ S.25 ] Linear pricing theory: further assumptions

[ S.25.1 ] s_simulate_call

[ S.25.1.1 ] Summary

[ S.25.1.2 ] Parameters

[ S.25.1.3 ] Outcomes and figures

[ S.25.1.4 ] Implementation

[ S.25.1.5 ] See also

[ S.25.2 ] s_simulate_payoff

[ S.25.3 ] Minimum variance factor-replicating portfolio

[ S.26 ] Non-linear pricing theory

[ S.27 ] Valuation implementation

[ S.27.1 ] Fitting implied volatility from the Black-Scholes-Merton valuation

S.IV. Performance analysis

[ S.28 ] Executive summary

[ S.29 ] Performance definitions

[ S.29.1 ] Compounded return of a portfolio

[ S.30 ] Performance attribution

S.V. Quant toolbox

[ S.31 ] Summary

[ S.32 ] Distributions

[ S.32.1 ] Conditional expectation between normal random variables

[ S.32.2 ] Innovation: the normal case, implementation

[ S.32.3 ] Innovation: the lognormal case, implementation

[ S.32.4 ] s_bivariate_normal

[ S.32.4.1 ] Summary

[ S.32.4.2 ] Parameters

[ S.32.4.3 ] Outcomes and figures

[ S.32.4.4 ] Implementation

[ S.32.5 ] s_uniform_inside_circle

[ S.32.5.1 ] Summary

[ S.32.5.2 ] Parameters

[ S.32.5.3 ] Outcomes and figures

[ S.32.5.4 ] Implementation

[ S.32.6 ] s_elliptical_uniform_radial_rep

[ S.32.6.1 ] Summary

[ S.32.6.2 ] Parameters

[ S.32.6.3 ] Outcomes and figures

[ S.32.6.4 ] Implementation

[ S.32.7 ] s_simulate_unif_in_ellipse

[ S.32.7.1 ] Summary

[ S.32.7.2 ] Parameters

[ S.32.7.3 ] Outcomes and figures

[ S.32.7.4 ] Implementation

[ S.32.7.5 ] See also

[ S.32.8 ] s_ens_exp_decay

[ S.32.8.1 ] Summary

[ S.32.8.2 ] Parameters

[ S.32.8.3 ] Outcomes and figures

[ S.32.8.4 ] Implementation

[ S.32.8.5 ] See also

[ S.32.9 ] s_display_dirac_delta

[ S.32.9.1 ] Summary

[ S.32.9.2 ] Input

[ S.32.9.3 ] Outcomes and figures

[ S.32.9.4 ] Implementation

[ S.32.9.5 ] See also

[ S.32.10 ] s_scen_prob_pdf

[ S.32.10.1 ] Summary

[ S.32.10.2 ] Parameters

[ S.32.10.3 ] Outcomes and figures

[ S.32.10.4 ] Implementation

[ S.32.10.5 ] See also

[ S.32.11 ] s_scen_prob_cdf_quantile

[ S.32.11.1 ] Summary

[ S.32.11.2 ] Input

[ S.32.11.3 ] Outcomes

[ S.32.11.4 ] Implementation

[ S.32.11.5 ] See also

[ S.32.12 ] s_generalized_expon_entropy

[ S.32.12.1 ] Summary

[ S.32.12.2 ] Parameters

[ S.32.12.3 ] Outcomes and figures

[ S.32.12.4 ] Implementation

[ S.32.12.5 ] See also

[ S.32.13 ] s_normal_exponential_family

[ S.32.13.1 ] Summary

[ S.32.13.2 ] Parameters

[ S.32.13.3 ] Outcomes

[ S.32.13.4 ] Implementation

[ S.32.13.5 ] See also

[ S.32.14 ] s_saddle_point_vs_mcfp_quadn

[ S.32.14.1 ] Summary

[ S.32.14.2 ] Parameters

[ S.32.14.3 ] Outcomes and figures

[ S.32.14.4 ] Implementation

[ S.32.14.5 ] See also

[ S.32.15 ] s_bivariate_wishart

[ S.32.15.1 ] Summary

[ S.32.15.2 ] Input

[ S.32.15.3 ] Outcomes and figures

[ S.32.15.4 ] Implementation

[ S.32.15.5 ] See also

[ S.32.16 ] s_gaussian_mixture

[ S.32.16.1 ] Summary

[ S.32.16.2 ] Parameters

[ S.32.16.3 ] Outcomes and figures

[ S.32.16.4 ] Implementation

[ S.32.16.5 ] See also

[ S.33 ] Geometry of distributions

[ S.34 ] Copulas

[ S.34.1 ] Display copula of a bivariate normal

[ S.34.2 ] s_normal_to_uniform

[ S.34.2.1 ] Summary

[ S.34.2.2 ] Parameters

[ S.34.2.3 ] Outcomes and figures

[ S.34.2.4 ] Implementation

[ S.34.2.5 ] See also

[ S.34.3 ] s_lognorm_to_uniform

[ S.34.3.1 ] Summary

[ S.34.3.2 ] Parameters

[ S.34.3.3 ] Outcomes and figures

[ S.34.3.4 ] Implementation

[ S.34.3.5 ] See also

[ S.34.4 ] s_gamma_to_uniform

[ S.34.4.1 ] Summary

[ S.34.4.2 ] Parameters

[ S.34.4.3 ] Outcomes and figures

[ S.34.4.4 ] Implementation

[ S.34.4.5 ] See also

[ S.34.5 ] s_uniform_to_normal

[ S.34.5.1 ] Summary

[ S.34.5.2 ] Parameters

[ S.34.5.3 ] Outcomes and figures

[ S.34.5.4 ] Implementation

[ S.34.5.5 ] See also

[ S.34.6 ] s_uniform_to_lognorm

[ S.34.6.1 ] Summary

[ S.34.6.2 ] Parameters

[ S.34.6.3 ] Outcomes and figures

[ S.34.6.4 ] Implementation

[ S.34.6.5 ] See also

[ S.34.7 ] s_uniform_to_gamma

[ S.34.7.1 ] Summary

[ S.34.7.2 ] Parameters

[ S.34.7.3 ] Outcomes and figures

[ S.34.7.4 ] Implementation

[ S.34.7.5 ] See also

[ S.34.8 ] Combination: from FP-copula/historical marginal to joint

[ S.34.9 ] s_display_norm_copula

[ S.34.9.1 ] Summary

[ S.34.9.2 ] Parameters

[ S.34.9.3 ] Outcomes and figures

[ S.34.9.4 ] Implementation

[ S.34.9.5 ] See also

[ S.34.10 ] s_display_t_copula

[ S.34.10.1 ] Summary

[ S.34.10.2 ] Parameters

[ S.34.10.3 ] Outcomes and figures

[ S.34.10.4 ] Implementation

[ S.34.10.5 ] See also

[ S.34.11 ] s_copula_returns

[ S.34.11.1 ] Summary

[ S.34.11.2 ] Parameters

[ S.34.11.3 ] Outcomes and figures

[ S.34.11.4 ] Implementation

[ S.34.11.5 ] See also

[ S.34.12 ] s_cop_marg_separation

[ S.34.12.1 ] Script summary

[ S.34.12.2 ] Parameters

[ S.34.12.3 ] Outcomes and figures

[ S.34.12.4 ] Implementation

[ S.34.12.5 ] See also

[ S.34.13 ] s_cop_marg_combination

[ S.34.13.1 ] Script summary

[ S.34.13.2 ] Parameters

[ S.34.13.3 ] Outcomes and figures

[ S.34.13.4 ] Implementation

[ S.34.14 ] s_t_copula_norm_marginals

[ S.34.14.1 ] Summary

[ S.34.14.2 ] Parameters

[ S.34.14.3 ] Outcomes and figures

[ S.34.14.4 ] Implementation

[ S.34.14.5 ] See also

[ S.34.15 ] Separation: from historical joint to copula/marginal

[ S.34.16 ] Display the pdf of a bivariate t-copula

[ S.35 ] Correlation and generalizations

[ S.35.1 ] s_norm_const_sw

[ S.35.1.1 ] Summary

[ S.35.1.2 ] Parameters

[ S.35.1.3 ] Outcomes and figures

[ S.35.1.4 ] Implementation

[ S.35.2 ] s_dependence_structure_call_put

[ S.35.2.1 ] Summary

[ S.35.2.2 ] Parameters

[ S.35.2.3 ] Outcomes and figures

[ S.35.2.4 ] Implementation

[ S.35.2.5 ] See also

[ S.35.3 ] Correlation between normal variables (numerical proof)

[ S.35.4 ] Correlation between lognormal variables (numerical proof)

[ S.35.5 ] Correlation between normalized Wishart marginals(numerical proof)

[ S.35.6 ] s_uncorr_no_indep

[ S.35.6.1 ] Summary

[ S.35.6.2 ] Parameters

[ S.35.6.3 ] Outcomes and figures

[ S.35.6.4 ] Implementation

[ S.35.6.5 ] See also

[ S.35.7 ] s_clt_student_t

[ S.35.7.1 ] Summary

[ S.35.7.2 ] Parameters

[ S.35.7.3 ] Outcomes and figures

[ S.35.7.4 ] Implementation

[ S.35.7.5 ] See also

[ S.35.8 ] s_full_dependence

[ S.35.8.1 ] Summary

[ S.35.8.2 ] Parameters

[ S.35.8.3 ] Outcomes and figures

[ S.35.8.4 ] Implementation

[ S.35.8.5 ] See also

[ S.35 ] Stochastic dominance

[ S.35.1 ] s_strong_dominance

[ S.35.1.1 ] Summary

[ S.35.1.2 ] Parameters

[ S.35.1.3 ] Outcomes and figures

[ S.35.1.4 ] Implementation

[ S.35.1.5 ] See also

[ S.35.2 ] s_weak_dominance

[ S.35.2.1 ] Summary

[ S.35.2.2 ] Parameters

[ S.35.2.3 ] Outcomes and figures

[ S.35.2.4 ] Implementation

[ S.35.2.5 ] See also

[ S.35.3 ] s_second_order_dominance

[ S.35.3.1 ] Summary

[ S.35.3.2 ] Parameters

[ S.35.3.3 ] Outcomes and figures

[ S.35.3.4 ] Implementation

[ S.36 ] Location and dispersion

[ S.36.1 ] s_logn_uncertainty_bands

[ S.36.1.1 ] Summary

[ S.36.1.2 ] Parameters

[ S.36.1.3 ] Outcomes and figures

[ S.36.1.4 ] Implementation

[ S.36.2 ] Different visualizations of the multivariate uncertainty band

[ S.36.3 ] s_affine_equiv_exp_cov

[ S.36.3.1 ] Summary

[ S.36.3.2 ] Parameters

[ S.36.3.3 ] Outcomes and figures

[ S.36.3.4 ] Implementation

[ S.36.3.5 ] See also

[ S.36.4 ] Ellipsoid and uncertainty band of a bivariate normal

[ S.36.5 ] s_ellipsoid_multiv_exp_cov

[ S.36.5.1 ] Summary

[ S.36.5.2 ] Parameters

[ S.36.5.3 ] Outcomes and figures

[ S.36.5.4 ] Implementation

[ S.36.5.5 ] See also

[ S.36.6 ] s_display_corr_norm_ellips

[ S.36.6.1 ] Summary

[ S.36.6.2 ] Parameters

[ S.36.6.3 ] Outcomes and figures

[ S.36.6.4 ] Implementation

[ S.36.6.5 ] See also

[ S.36.7 ] Ellipsoid and uncertainty band of a bivariate lognormal

[ S.36.8 ] Ellipsoid and uncertainty band of normalized Wishart marginals

[ S.36.9 ] s_affine_equiv_mode_mod_disp

[ S.36.9.1 ] Summary

[ S.36.9.2 ] Parameters

[ S.36.9.3 ] Outcomes and figures

[ S.36.9.4 ] Implementation

[ S.36.9.5 ] See also

[ S.36.10 ] Iso-contour of a lognormal bivariate distribution

[ S.36.11 ] s_chebyshev_ineq

[ S.36.11.1 ] Summary

[ S.36.11.2 ] Parameters

[ S.36.11.3 ] Outcomes and figures

[ S.36.11.4 ] Implementation

[ S.36.11.5 ] See also

[ S.36.12 ] Expectation-covariance as minimum volume ellipsoid

[ S.36.13 ] R-squared: numerical example

[ S.36.14 ] Euclidean vectors of joint normal variables

[ S.36.15 ] Euclidean vectors of joint lognormal variables

[ S.36.16 ] Orthogonality of principal directions

[ S.36.17 ] Euclidean vectors via linear transformation and Riccati root

[ S.37 ] Decision theory with model uncertainty

[ S.38 ] Estimation techniques

[ S.38.1 ] Maximum likelihood estimation

[ S.39 ] Estimation and assessment

[ S.39.1 ] s_bias_vs_variance_lognormal

[ S.39.2 ] Predictive distribution assessment

[ S.41 ] Estimation and regularization

[ S.41.1 ] s_bias_vs_variance_normal

[ S.41.2 ] s_encoding

[ S.42 ] Hypothesis testing

[ S.43 ] Stochastic processes cheat sheet

[ S.44 ] Invariance tests

[ S.44.1 ] s_elltest_normal

[ S.44.1.1 ] Summary

[ S.44.1.2 ] Parameters

[ S.44.1.3 ] Outcomes and figures

[ S.44.1.4 ] Implementation

[ S.44.1.5 ] See also

[ S.44.2 ] Kolmogorov-Smirnov test for invariance on simulations

[ S.44.3 ] Copula based tests for invariance on simulations

[ S.44.4 ] Invariance tests on realized time series

[ S.45 ] Continuous time processes

[ S.45.1 ] s_projection_brownian_motion

[ S.45.1.1 ] Summary

[ S.45.1.2 ] Data

[ S.45.1.3 ] Parameters

[ S.45.1.4 ] Outcomes and figures

[ S.45.1.5 ] Implementation

[ S.45.1.6 ] See also

[ S.45.2 ] s_projection_univ_rating

[ S.45.2.1 ] Summary

[ S.45.2.2 ] Data

[ S.45.2.3 ] Outcomes and figures

[ S.45.2.4 ] Implementation

[ S.45.2.5 ] See also

[ S.45.3 ] Projection of Poisson process

[ S.45.4 ] Simulate compound Poisson processes

[ S.45.5 ] Projection of a Compound Poisson Process

[ S.45.6 ] Projection of Cauchy distribution

[ S.45.7 ] Projection of the variance gamma distribution

[ S.45.8 ] Simulate the NIG and VG processes

[ S.45.9 ] Simulation of the variance gamma process by subordination

[ S.45.10 ] Projection of the Student t distribution

[ S.45.11 ] Projection of the uniform distribution

[ S.45.12 ] Projection of fractional Brownian motion

[ S.45.13 ] Projection of the Heston process

[ S.45.14 ] Simulation of the Heston process by Time Change

[ S.45.15 ] Simulation of a Ornstein-Uhlenbeck process

[ S.45.16 ] MVOU change of coordinates

[ S.45.17 ] Projection of conditional mean and covariance of the MVOU process

[ S.46 ] Covariance stationary processes

[ S.46.1 ] s_autocov_spec_dens_ar1

[ S.46.1.1 ] Summary

[ S.46.1.2 ] Parameters

[ S.46.1.3 ] Outcomes and figures

[ S.46.1.4 ] Implementation

[ S.46.2 ] s_spectral_representation

[ S.46.2.1 ] Summary

[ S.46.2.2 ] Parameters

[ S.46.2.3 ] Outcomes and figures

[ S.46.2.4 ] Implementation

[ S.46.2.5 ] Tips

[ S.46.2.6 ] See also

[ S.46.3 ] s_toeplitz_spectral

[ S.46.3.1 ] Summary

[ S.46.3.2 ] Parameters

[ S.46.3.3 ] Outcomes and figures

[ S.46.3.4 ] Implementation

[ S.46.3.5 ] See also

[ S.46.4 ] Bandpass filter applied to AR(1) processes

[ S.46.4.1 ] Summary

[ S.46.4.2 ] Parameters

[ S.46.4.3 ] Outcomes and figures

[ S.46.4.4 ] Implementation

[ S.46.4.5 ] See also

[ S.47 ] Signals

[ S.47.1 ] s_cointegration_detection

[ S.47.1.1 ] Summary

[ S.47.1.2 ] Data

[ S.47.1.3 ] Parameters

[ S.47.1.4 ] Outcomes and figures

[ S.47.1.5 ] Implementation

[ S.47.1.6 ] See also

[ S.47.2 ] s_cointegration_signal

[ S.47.2.1 ] Summary

[ S.47.2.2 ] Data

[ S.47.2.3 ] Parameters

[ S.47.2.4 ] Outcomes and figures

[ S.47.2.5 ] Implementation

[ S.47.2.6 ] See also

[ S.47.3 ] s_trade_autocorr_signal

[ S.47.3.1 ] Summary

[ S.47.3.2 ] Data

[ S.47.3.3 ] Parameters

[ S.47.3.4 ] Outcomes and figures

[ S.47.3.5 ] Implementation

[ S.47.3.6 ] See also

[ S.47.4 ] s_order_imbal_signal

[ S.47.4.1 ] Summary

[ S.47.4.2 ] Data

[ S.47.4.3 ] Parameters

[ S.47.4.4 ] Outcomes and figures

[ S.47.4.5 ] Implementation

[ S.47.4.6 ] See also

[ S.47.5 ] s_price_pred_signal

[ S.47.5.1 ] Summary

[ S.47.5.2 ] Data

[ S.47.5.3 ] Parameters

[ S.47.5.4 ] Outcomes and figures

[ S.47.5.5 ] Implementation

[ S.47.5.6 ] See also

[ S.47.6 ] s_volume_cluster_signal

[ S.47.6.1 ] Summary

[ S.47.6.2 ] Data

[ S.47.6.3 ] Parameters

[ S.47.6.4 ] Outcomes and figures

[ S.47.6.5 ] Implementation

[ S.47.6.6 ] See also

[ S.47.7 ] s_momentum_signals

[ S.47.7.1 ] Summary

[ S.47.7.2 ] Data

[ S.47.7.3 ] Parameters

[ S.47.7.4 ] Outcomes and figures

[ S.47.7.5 ] Implementation

[ S.47.7.6 ] See also

[ S.47.8 ] Signal filtering for systematic strategy (size)

[ S.48 ] Black-Litterman

[ S.48.1 ] s_bl_equilibrium_ret

[ S.48.1.1 ] Summary

[ S.48.1.2 ] Data

[ S.48.1.3 ] Parameters

[ S.48.1.4 ] Outcomes

[ S.48.1.5 ] Implementation

[ S.48.1.6 ] See also

[ S.48.2 ] s_info_processing_comparison

[ S.48.2.1 ] Summary

[ S.48.2.2 ] Data

[ S.48.2.3 ] Parameters

[ S.48.2.4 ] Outcomes and figures

[ S.48.2.5 ] Implementation

[ S.48.2.6 ] See also

[ S.49 ] Optimization primer

[ S.49.1 ] s_convex_programming

[ S.49.1.1 ] Summary

[ S.49.1.2 ] Implementation

[ S.49.1.3 ] See also

[ S.49.2 ] s_selection_toy

[ S.49.2.1 ] Summary

[ S.49.2.2 ] Parameters

[ S.49.2.3 ] Outcomes and figures

[ S.49.2.4 ] Implementation

[ S.49.2.5 ] See also

[ S.50 ] Useful algorithms

[ S.50.1 ] Cholesky decomposition of the covariance (numerical proof)

[ S.50.2 ] Numerical proof

[ S.50.3 ] s_cpca_vs_pca

[ S.50.3.1 ] Script summary

[ S.50.3.2 ] Parameters

[ S.50.3.3 ] Outcomes and figures

[ S.50.3.4 ] Implementation

[ S.50.3.5 ] See also

[ S.50.4 ] s_factor_analysis_algos

[ S.50.4.1 ] Summary

[ S.50.4.2 ] Parameters

[ S.50.4.3 ] Outcomes and figures

[ S.50.4.4 ] Implementation

[ S.50.4.5 ] See also

[ S.50.5 ] Transpose-square-root of a symmetric positive (semi)definite matrix

[ S.51 ] Linear algebra primer

[ S.51.1 ] s_vector_representation

[ S.51.1.1 ] Summary

[ S.51.1.2 ] Parameters

[ S.51.1.3 ] Outcomes and figures

[ S.51.2 ] s_vector_operations

[ S.51.2.1 ] Summary

[ S.51.2.2 ] Parameters

[ S.51.2.3 ] Outcomes and figures

[ S.51.2.4 ] Implementation

[ S.51.3 ] s_vector_subspaces

[ S.51.3.1 ] Summary

[ S.51.3.2 ] Parameters

[ S.51.3.3 ] Outcomes and figures

[ S.51.4 ] s_linear_transformations

[ S.51.4.1 ] Summary

[ S.51.4.2 ] Parameters

[ S.51.4.3 ] Outcomes and figures

[ S.51.4.4 ] Implementation

[ S.51.5 ] s_positive_definite_matrix

[ S.51.5.1 ] Summary

[ S.51.5.2 ] Parameters

[ S.51.5.3 ] Outcomes and figures

[ S.51.5.4 ] Implementation

[ S.51.6 ] s_spectral_theorem

[ S.51.6.1 ] Summary

[ S.51.6.2 ] Parameters

[ S.51.6.3 ] Outcomes and figures

[ S.51.6.4 ] Implementation

[ S.51.6.5 ] See also

[ S.52 ] Calculus primer

[ S.52.1 ] s_univariate_derivatives

[ S.52.1.1 ] Summary

[ S.52.1.2 ] Parameters

[ S.52.1.3 ] Outcomes and figures

[ S.52.1.4 ] Implementation

[ S.52.2 ] s_multivariate_derivatives

[ S.52.2.1 ] Summary

[ S.52.2.2 ] Parameters

[ S.52.2.3 ] Outcomes and figures

[ S.52.2.4 ] Implementation

[ S.52.3 ] s_riemann_integration_univariate

[ S.52.3.1 ] Summary

[ S.52.3.2 ] Parameters

[ S.52.3.3 ] Outcomes and figures

[ S.52.3.4 ] Implementation

[ S.52.4 ] s_riemann_integration_multivariate

[ S.52.4.1 ] Summary

[ S.52.4.2 ] Parameters

[ S.52.4.3 ] Outcomes and figures

[ S.52.4.4 ] Implementation

F.I. Functions

Functions

[ F.1 ] Estimation

[ F.1.1 ] cointegration_fp

[ F.1.1.1 ] Summary

[ F.1.1.2 ] Input

[ F.1.1.3 ] Output

[ F.1.1.4 ] Implementation

[ F.1.1.5 ] Example

[ F.1.1.6 ] Case studies

[ F.1.1.7 ] See also

[ F.1.2 ] conditional_fp

[ F.1.2.1 ] Summary

[ F.1.2.2 ] Input

[ F.1.2.3 ] Output

[ F.1.2.4 ] Implementation

[ F.1.2.5 ] Example

[ F.1.2.6 ] Case studies

[ F.1.2.7 ] References

[ F.1.3.4 ] Implementation

[ F.1.3.5 ] Example

[ F.1.3.6 ] Case studies

[ F.1.3.7 ] References

[ F.1.4.4 ] Implementation

[ F.1.4.5 ] Example

[ F.1.4.6 ] Case studies

[ F.1.4.7 ] References

[ F.1.4.8 ] See also

[ F.1.5 ] effective_num_scenarios

[ F.1.5.1 ] Summary

[ F.1.5.2 ] Input

[ F.1.5.3 ] Output

[ F.1.5.4 ] Implementation

[ F.1.5.5 ] Example

[ F.1.5.6 ] Case studies

[ F.1.5.7 ] References

[ F.1.6.3 ] Implementation

[ F.1.6.4 ] Example

[ F.1.6.5 ] Case studies

[ F.1.7 ] exp_decay_fp

[ F.1.7.1 ] Summary

[ F.1.7.2 ] Input

[ F.1.7.3 ] Output

[ F.1.7.4 ] Implementation

[ F.1.7.5 ] Example

[ F.1.7.6 ] Case studies

[ F.1.8 ] factor_analysis_mlf

[ F.1.8.1 ] Summary

[ F.1.8.2 ] Input

[ F.1.8.3 ] Output

[ F.1.8.4 ] Implementation

[ F.1.8.5 ] Example

[ F.1.8.6 ] Case studies

[ F.1.8.7 ] References

[ F.1.8.8 ] See also

[ F.1.9 ] factor_analysis_paf

[ F.1.9.1 ] Summary

[ F.1.9.2 ] Input

[ F.1.9.3 ] Output

[ F.1.9.4 ] Implementation

[ F.1.9.5 ] Example

[ F.1.9.6 ] Case studies

[ F.1.9.7 ] References

[ F.1.10.4 ] Implementation

[ F.1.10.5 ] Example

[ F.1.10.6 ] Case studies

[ F.1.10.7 ] See also

[ F.1.11 ] fit_factor_analysis

[ F.1.11.1 ] Summary

[ F.1.11.2 ] Input

[ F.1.11.3 ] Output

[ F.1.11.4 ] Implementation

[ F.1.11.5 ] Tips

[ F.1.11.6 ] Example

[ F.1.11.7 ] References

[ F.1.11.8 ] See also

[ F.1.12 ] fit_garch_fp

[ F.1.12.1 ] Summary

[ F.1.12.2 ] Input

[ F.1.12.3 ] Output

[ F.1.12.4 ] Implementation

[ F.1.12.5 ] Tips

[ F.1.12.6 ] Example

[ F.1.12.7 ] Case studies

[ F.1.12.8 ] See also

[ F.1.13 ] fit_lfm_lasso

[ F.1.13.1 ] Summary

[ F.1.13.2 ] Input

[ F.1.13.3 ] Output

[ F.1.13.4 ] Implementation

[ F.1.13.5 ] Example

[ F.1.13.6 ] See also

[ F.1.14 ] fit_lfm_lasso_path

[ F.1.14.1 ] Example

[ F.1.15 ] fit_lfm_mlfp

[ F.1.15.1 ] Summary

[ F.1.15.2 ] Input

[ F.1.15.3 ] Output

[ F.1.15.4 ] Implementation

[ F.1.15.5 ] Example

[ F.1.15.6 ] Case studies

[ F.1.15.7 ] See also

[ F.1.16 ] fit_lfm_ols

[ F.1.16.1 ] Summary

[ F.1.16.2 ] Input

[ F.1.16.3 ] Output

[ F.1.16.4 ] Implementation

[ F.1.16.5 ] Example

[ F.1.16.6 ] Case studies

[ F.1.16.7 ] References

[ F.1.16.8 ] See also

[ F.1.17 ] fit_lfm_pcfp

[ F.1.17.1 ] Example

[ F.1.18 ] fit_lfm_ridge

[ F.1.18.1 ] Example

[ F.1.19 ] fit_lfm_ridge_path

[ F.1.19.1 ] Example

[ F.1.20 ] fit_lfm_roblasso

[ F.1.20.1 ] Example

[ F.1.21 ] fit_locdisp_mlfp

[ F.1.21.1 ] Summary

[ F.1.21.2 ] Input

[ F.1.21.3 ] Output

[ F.1.21.4 ] Implementation

[ F.1.21.5 ] Example

[ F.1.21.6 ] Case studies

[ F.1.21.7 ] See also

[ F.1.22 ] fit_locdisp_mlfp_difflength

[ F.1.22.1 ] Summary

[ F.1.22.2 ] Input

[ F.1.22.3 ] Output

[ F.1.22.4 ] Implementation

[ F.1.22.5 ] Tips

[ F.1.22.6 ] Example

[ F.1.22.7 ] Case studies

[ F.1.22.8 ] References

[ F.1.22.9 ] See also

[ F.1.23 ] fit_ratings_markov_chain

[ F.1.23.1 ] Summary

[ F.1.23.2 ] Input

[ F.1.23.3 ] Output

[ F.1.23.4 ] Implementation

[ F.1.23.5 ] Tips

[ F.1.23.6 ] Example

[ F.1.23.7 ] Case studies

[ F.1.24 ] fit_state_space

[ F.1.24.1 ] Summary

[ F.1.24.2 ] Input

[ F.1.24.3 ] Output

[ F.1.24.4 ] Implementation

[ F.1.24.5 ] Example

[ F.1.24.6 ] Case studies

[ F.1.24.7 ] References

[ F.1.24.8 ] See also

[ F.1.27.4 ] Implementation

[ F.1.27.5 ] Example

[ F.1.27.6 ] Case studies

[ F.1.27.7 ] See also

[ F.1.28 ] markov_network

[ F.1.28.1 ] Example

[ F.1.29 ] min_corr_toeplitz

[ F.1.29.1 ] Summary

[ F.1.29.2 ] Input

[ F.1.29.3 ] Output

[ F.1.29.4 ] Implementation

[ F.1.29.5 ] Example

[ F.1.29.6 ] Case studies

[ F.1.29.7 ] References

[ F.1.30 ] smooth_kernel_fp

[ F.1.30.1 ] Summary

[ F.1.30.2 ] Input

[ F.1.30.3 ] Output

[ F.1.30.4 ] Implementation

[ F.1.30.5 ] Example

[ F.1.30.6 ] Case studies

[ F.1.30.7 ] References

[ F.1.30.8 ] See also

[ F.1.31 ] spectrum_shrink

[ F.1.32.4 ] Implementation

[ F.1.32.5 ] Tips

[ F.1.32.6 ] Example

[ F.1.32.7 ] Case studies

[ F.1.32.8 ] References

[ F.1.33 ] Generate FP profiles via multivariate Gaussian kernel: function implementation

[ F.1.34 ] Expectation Maximization algorithm with flexible probabilities for Missing Values. Routine

[ F.1.35 ] Homogeneous correlation cluster shrinkage

[ F.1.36 ] Iterated generalized method of moments with flexible probabilities for the Poisson distribution

[ F.1.37 ] Minimum volume ellipsoid enclosing data. Routine

[ F.1.38 ] Farthest Outlier Detection. Routine

[ F.1.39 ] High breakdown point with flexible probabilities. Routine

[ F.1.40 ] Outlier detection with flexible probabilities. Routine

[ F.1.41 ] SMTCovariance

[ F.1.42 ] FitFractionalIntegration

[ F.1.43 ] FitGenParetoMLFP

[ F.1.44 ] NormalMixtureFit

[ F.1.45 ] FitSkewtMLFP

[ F.1.46 ] FitVar_ATMSVI

[ F.1.47 ] GarchResiduals

[ F.1.48 ] MMFP

[ F.1.49 ] kMeansClustering

[ F.1.50 ] QuantileGenParetoMLFP

[ F.1.51 ] ObjectiveToeplitz

[ F.2 ] Portfolio

[ F.2.1 ] almgren_chriss

[ F.2.1.1 ] Example

[ F.2.2 ] char_portfolio

[ F.2.2.1 ] Example

[ F.2.3 ] effective_num_bets

[ F.2.4 ] minimum_torsion

[ F.2.5 ] obj_tracking_err

[ F.2.5.1 ] Summary

[ F.2.5.2 ] Input

[ F.2.5.3 ] Output

[ F.2.5.4 ] Implementation

[ F.2.5.5 ] Example

[ F.2.5.6 ] Case studies

[ F.2.5.7 ] References

[ F.2.6 ] opt_trade_meanvar

[ F.2.6.1 ] Example

[ F.2.7 ] spectral_index

[ F.2.7.1 ] Summary

[ F.2.7.2 ] Input

[ F.2.7.3 ] Output

[ F.2.7.4 ] Implementation

[ F.2.7.5 ] Example

[ F.2.7.6 ] Case studies

[ F.2.7.7 ] References

[ F.2.8 ] Profit-and-loss statistical features: function implementation

[ F.2.9 ] EwmaIncludingStartingDays

[ F.2.10 ] SolveGarleanuPedersen

[ F.2.11 ] Leverage

[ F.2.12 ] MomentumStrategy

[ F.3.1.4 ] Implementation

[ F.3.1.5 ] Example

[ F.3.1.6 ] Case studies

[ F.3.1.7 ] References

[ F.3.1.8 ] See also

[ F.3.2 ] bootstrap_nelson_siegel

[ F.3.2.1 ] Summary

[ F.3.2.2 ] Input

[ F.3.2.3 ] Output

[ F.3.2.4 ] Implementation

[ F.3.2.5 ] Example

[ F.3.2.6 ] Case studies

[ F.3.2.7 ] References

[ F.3.2.8 ] See also

[ F.3.3 ] bsm_function

[ F.3.3.1 ] Summary

[ F.3.3.2 ] Input

[ F.3.3.3 ] Output

[ F.3.3.4 ] Implementation

[ F.3.3.5 ] Tips

[ F.3.3.6 ] Example

[ F.3.3.7 ] Case studies

[ F.3.3.8 ] References

[ F.3.4 ] call_option_value

[ F.3.4.1 ] Summary

[ F.3.4.2 ] Input

[ F.3.4.3 ] Output

[ F.3.4.4 ] Implementation

[ F.3.4.5 ] Tips

[ F.3.4.6 ] Example

[ F.3.4.7 ] Case studies

[ F.3.4.8 ] References

[ F.3.4.9 ] See also

[ F.3.5 ] cash_flow_reinv

[ F.3.5.1 ] Summary

[ F.3.5.2 ] Input

[ F.3.5.3 ] Output

[ F.3.5.4 ] Implementation

[ F.3.5.5 ] Tips

[ F.3.5.6 ] Example

[ F.3.5.7 ] Case studies

[ F.3.5.8 ] References

[ F.3.6 ] fit_nelson_siegel_bonds

[ F.3.6.1 ] Summary

[ F.3.6.2 ] Input

[ F.3.6.3 ] Output

[ F.3.6.4 ] Implementation

[ F.3.6.5 ] Tips

[ F.3.6.6 ] Example

[ F.3.6.7 ] References

[ F.3.6.8 ] See also

[ F.3.7 ] fit_nelson_siegel_yield

[ F.3.7.1 ] Summary

[ F.3.7.2 ] Input

[ F.3.7.3 ] Output

[ F.3.7.4 ] Implementation

[ F.3.7.5 ] Tips

[ F.3.7.6 ] Example

[ F.3.7.7 ] Case studies

[ F.3.7.8 ] References

[ F.3.7.9 ] See also

[ F.3.8 ] implvol_delta2m_moneyness

[ F.3.8.1 ] Summary

[ F.3.8.2 ] Input

[ F.3.8.3 ] Output

[ F.3.8.4 ] Implementation

[ F.3.8.5 ] Example

[ F.3.8.6 ] Case studies

[ F.3.8.7 ] References

[ F.3.9 ] ytm_shadowrates

[ F.3.9.1 ] Summary

[ F.3.9.2 ] Input

[ F.3.9.3 ] Output

[ F.3.9.4 ] Implementation

[ F.3.9.5 ] Example

[ F.3.9.6 ] Case studies

[ F.3.9.7 ] References

[ F.3.10 ] nelson_siegel_yield

[ F.3.10.1 ] Summary

[ F.3.10.2 ] Input

[ F.3.10.3 ] Output

[ F.3.10.4 ] Implementation

[ F.3.10.5 ] Example

[ F.3.10.6 ] Case studies

[ F.3.10.7 ] References

[ F.3.11 ] shadowrates_ytm

[ F.3.11.1 ] Summary

[ F.3.11.2 ] Input

[ F.3.11.3 ] Output

[ F.3.11.4 ] Implementation

[ F.3.11.5 ] Example

[ F.3.11.6 ] Case studies

[ F.3.11.7 ] References

[ F.3.12 ] numeraire_mre

[ F.3.12.1 ] Summary

[ F.3.12.2 ] Input

[ F.3.12.3 ] Output

[ F.3.12.4 ] Implementation

[ F.3.12.5 ] Tips

[ F.3.12.6 ] Example

[ F.3.12.7 ] Case studies

[ F.3.12.8 ] References

[ F.3.12.9 ] See also

[ F.3.13.4 ] Implementation

[ F.3.13.5 ] Example

[ F.3.13.6 ] Case studies

[ F.3.13.7 ] References

[ F.3.13.8 ] See also

[ F.3.14 ] Vasicek yield curve

[ F.3.15 ] regularized_payoff

[ F.3.15.5 ] Case studies

[ F.3.16 ] Stochastic discount factor and kernel space: implementation

[ F.3.17 ] BachelierCallPrice

[ F.3.18 ] BondPriceNelSieg

[ F.3.19 ] blsimpv

[ F.3.20 ] FilterStochasticVolatility

[ F.3.21 ] FitCIR_FP

[ F.3.22 ] FitHeston

[ F.3.23 ] FitStochasticVolatilityModel

[ F.3.24 ] FitSigmaSVI

[ F.3.25 ] FitVasicek

[ F.3.26 ] HestonChFun

[ F.3.27 ] CallPriceHestonFFT

[ F.3.28 ] MapSVIparams

[ F.3.29 ] SigmaSVI

[ F.3.30 ] StochTime

[ F.3.31 ] RollPrices2Prices

[ F.3.32 ] ZCBondPriceVasicek

[ F.4 ] Statistics

[ F.4.1 ] bootstrap_hfp

[ F.4.1.1 ] Summary

[ F.4.1.2 ] Input

[ F.4.1.3 ] Output

[ F.4.1.4 ] Implementation

[ F.4.1.5 ] Example

[ F.4.1.6 ] Case studies

[ F.4.1.7 ] References

[ F.4.2.4 ] Implementation

[ F.4.2.5 ] Example

[ F.4.2.6 ] Case studies

[ F.4.2.7 ] References

[ F.4.3 ] cop_marg_comb

[ F.4.3.1 ] Summary

[ F.4.3.2 ] Input

[ F.4.3.3 ] Output

[ F.4.3.4 ] Implementation

[ F.4.3.5 ] Example

[ F.4.3.6 ] References

[ F.4.3.7 ] See also

[ F.4.4 ] cop_marg_sep

[ F.4.4.1 ] Summary

[ F.4.4.2 ] Input

[ F.4.4.3 ] Output

[ F.4.4.4 ] Implementation

[ F.4.4.5 ] Example

[ F.4.4.6 ] References

[ F.4.4.7 ] See also

[ F.4.5 ] cornish_fisher

[ F.4.5.1 ] Summary

[ F.4.5.2 ] Input

[ F.4.5.3 ] Output

[ F.4.5.4 ] Implementation

[ F.4.5.5 ] Example

[ F.4.5.6 ] Case studies

[ F.4.6 ] ewm_meancov

[ F.4.6.1 ] Summary

[ F.4.6.2 ] Input

[ F.4.6.3 ] Output

[ F.4.6.4 ] Implementation

[ F.4.6.5 ] Example

[ F.4.6.6 ] References

[ F.4.6.7 ] See also

[ F.4.7 ] gaussian_kernel

[ F.4.7.1 ] Summary

[ F.4.7.2 ] Input

[ F.4.7.3 ] Output

[ F.4.7.4 ] Implementation

[ F.4.7.5 ] Example

[ F.4.7.6 ] Case studies

[ F.4.7.7 ] References

[ F.4.8 ] invariance_test_copula

[ F.4.8.1 ] Summary

[ F.4.8.2 ] Input

[ F.4.8.3 ] Output

[ F.4.8.4 ] Implementation

[ F.4.8.5 ] Example

[ F.4.8.6 ] Case studies

[ F.4.8.7 ] See also

[ F.4.9 ] invariance_test_ellipsoid

[ F.4.9.1 ] Summary

[ F.4.9.2 ] Input

[ F.4.9.3 ] Output

[ F.4.9.4 ] Implementation

[ F.4.9.5 ] Tips

[ F.4.9.6 ] Example

[ F.4.9.7 ] Case studies

[ F.4.9.8 ] References

[ F.4.9.9 ] See also

[ F.4.10 ] invariance_test_ks

[ F.4.10.1 ] Summary

[ F.4.10.2 ] Input

[ F.4.10.3 ] Output

[ F.4.10.4 ] Implementation

[ F.4.10.5 ] Example

[ F.4.10.6 ] References

[ F.4.10.7 ] See also

[ F.4.11 ] kalman_filter

[ F.4.11.1 ] Example

[ F.4.11.2 ] References

[ F.4.12 ] marchenko_pastur

[ F.4.12.1 ] Example

[ F.4.13 ] meancov_sp

[ F.4.13.1 ] Summary

[ F.4.13.2 ] Input

[ F.4.13.3 ] Output

[ F.4.13.4 ] Implementation

[ F.4.13.5 ] Tips

[ F.4.13.6 ] Example

[ F.4.13.7 ] Case studies

[ F.4.13.8 ] References

[ F.4.14 ] meancov_inverse_wishart

[ F.4.14.1 ] Summary

[ F.4.14.2 ] Input

[ F.4.14.3 ] Output

[ F.4.14.4 ] Implementation

[ F.4.14.5 ] Example

[ F.4.14.6 ] Case studies

[ F.4.14.7 ] References

[ F.4.15 ] meancov_wishart

[ F.4.15.1 ] Summary

[ F.4.15.2 ] Input

[ F.4.15.3 ] Output

[ F.4.15.4 ] Implementation

[ F.4.15.5 ] Example

[ F.4.15.6 ] Case studies

[ F.4.15.7 ] References

[ F.4.16 ] moments_logn

[ F.4.17 ] moments_mvou

[ F.4.17.1 ] Summary

[ F.4.17.2 ] Input

[ F.4.17.3 ] Output

[ F.4.17.4 ] Implementation

[ F.4.17.5 ] Example

[ F.4.17.6 ] Case studies

[ F.4.17.7 ] References

[ F.4.18.4 ] Implementation

[ F.4.18.5 ] Example

[ F.4.18.6 ] See also

[ F.4.19.4 ] Implementation

[ F.4.19.5 ] Example

[ F.4.19.6 ] Case studies

[ F.4.19.7 ] References

[ F.4.20 ] mvt_logpdf

[ F.4.20.1 ] Summary

[ F.4.20.2 ] Input

[ F.4.20.3 ] Output

[ F.4.20.4 ] Implementation

[ F.4.20.5 ] Example

[ F.4.20.6 ] References

[ F.4.21 ] normal_canonical

[ F.4.21.1 ] Summary

[ F.4.21.2 ] Input

[ F.4.21.3 ] Output

[ F.4.21.4 ] Implementation

[ F.4.21.5 ] Example

[ F.4.21.6 ] Case studies

[ F.4.21.7 ] References

[ F.4.22 ] objective_r2

[ F.4.22.1 ] Summary

[ F.4.22.2 ] Input

[ F.4.22.3 ] Output

[ F.4.22.4 ] Implementation

[ F.4.22.5 ] Example

[ F.4.22.6 ] Case studies

[ F.4.22.7 ] See also

[ F.4.23 ] perceptron_fp

[ F.4.23.1 ] Summary

[ F.4.24 ] plot_kstest

[ F.4.25.4 ] Implementation

[ F.4.25.5 ] Example

[ F.4.25.6 ] Case studies

[ F.4.25.7 ] References

[ F.4.26 ] project_trans_matrix

[ F.4.26.1 ] Summary

[ F.4.26.2 ] Input

[ F.4.26.3 ] Output

[ F.4.26.4 ] Implementation

[ F.4.26.5 ] Example

[ F.4.26.6 ] Case studies

[ F.4.27 ] quantile_sp

[ F.4.27.1 ] Summary

[ F.4.27.2 ] Input

[ F.4.27.3 ] Output

[ F.4.27.4 ] Implementation

[ F.4.27.5 ] Example

[ F.4.27.6 ] Case studies

[ F.4.27.7 ] References

[ F.4.28 ] saddle_point_quadn

[ F.4.28.1 ] Summary

[ F.4.28.2 ] Input

[ F.4.28.3 ] Output

[ F.4.28.4 ] Implementation

[ F.4.28.5 ] Tips

[ F.4.28.6 ] Example

[ F.4.28.7 ] Case studies

[ F.4.28.8 ] References

[ F.4.28.9 ] See also

[ F.4.29 ] schweizer_wolff

[ F.4.29.1 ] Summary

[ F.4.29.2 ] Input

[ F.4.29.3 ] Output

[ F.4.29.4 ] Implementation

[ F.4.29.5 ] Example

[ F.4.29.6 ] Case studies

[ F.4.29.7 ] See also

[ F.4.30.4 ] Implementation

[ F.4.30.5 ] Example

[ F.4.30.6 ] Case studies

[ F.4.30.7 ] References

[ F.4.30.8 ] See also

[ F.4.31 ] simulate_garch

[ F.4.31.1 ] Summary

[ F.4.31.2 ] Input

[ F.4.31.3 ] Output

[ F.4.31.4 ] Implementation

[ F.4.31.5 ] Example

[ F.4.31.6 ] See also

[ F.4.32 ] simulate_niw

[ F.4.32.1 ] Example

[ F.4.33 ] simulate_bm

[ F.4.33.1 ] Summary

[ F.4.33.2 ] Input

[ F.4.33.3 ] Output

[ F.4.33.4 ] Implementation

[ F.4.33.5 ] Example

[ F.4.33.6 ] Case studies

[ F.4.33.7 ] References

[ F.4.33.8 ] See also

[ F.4.34 ] simulate_markov_chain_univ

[ F.4.34.1 ] Summary

[ F.4.34.2 ] Input

[ F.4.34.3 ] Output

[ F.4.34.4 ] Implementation

[ F.4.34.5 ] Example

[ F.4.34.6 ] Case studies

[ F.4.34.7 ] References

[ F.4.34.8 ] See also

[ F.4.35 ] simulate_markov_chain_multiv

[ F.4.35.1 ] Summary

[ F.4.35.2 ] Input

[ F.4.35.3 ] Output

[ F.4.35.4 ] Implementation

[ F.4.35.5 ] Example

[ F.4.35.6 ] Case studies

[ F.4.35.7 ] References

[ F.4.35.8 ] See also

[ F.4.36 ] simulate_mvou

[ F.4.36.1 ] Summary

[ F.4.36.2 ] Input

[ F.4.36.3 ] Output

[ F.4.36.4 ] Implementation

[ F.4.36.5 ] Tips

[ F.4.36.6 ] Example

[ F.4.36.7 ] Case studies

[ F.4.36.8 ] References

[ F.4.36.9 ] See also

[ F.4.37 ] simulate_normal

[ F.4.37.1 ] Summary

[ F.4.37.2 ] Input

[ F.4.37.3 ] Output

[ F.4.37.4 ] Implementation

[ F.4.37.5 ] Tips

[ F.4.37.6 ] Example

[ F.4.37.7 ] Case studies

[ F.4.37.8 ] References

[ F.4.37.9 ] See also

[ F.4.38 ] simulate_normal_dimred

[ F.4.38.1 ] Example

[ F.4.39 ] simulate_quadn

[ F.4.39.1 ] Summary

[ F.4.39.2 ] Input

[ F.4.39.3 ] Output

[ F.4.39.4 ] Implementation

[ F.4.39.5 ] Example

[ F.4.39.6 ] Case studies

[ F.4.39.7 ] References

[ F.4.39.8 ] See also

[ F.4.40 ] simulate_rw_hfp

[ F.4.40.1 ] Summary

[ F.4.40.2 ] Input

[ F.4.40.3 ] Output

[ F.4.40.4 ] Implementation

[ F.4.40.5 ] Example

[ F.4.40.6 ] Case studies

[ F.4.40.7 ] References

[ F.4.40.8 ] See also

[ F.4.41 ] simulate_t

[ F.4.41.1 ] Summary

[ F.4.41.2 ] Input

[ F.4.41.3 ] Output

[ F.4.41.4 ] Implementation

[ F.4.41.5 ] Tips

[ F.4.41.6 ] Example

[ F.4.41.7 ] References

[ F.4.41.8 ] See also

[ F.4.42 ] simulate_unif_in_ellips

[ F.4.42.1 ] Summary

[ F.4.42.2 ] Input

[ F.4.42.3 ] Output

[ F.4.42.4 ] Implementation

[ F.4.42.5 ] Tips

[ F.4.42.6 ] Example

[ F.4.42.7 ] Case studies

[ F.4.42.8 ] References

[ F.4.42.9 ] See also

[ F.4.43 ] simulate_var1

[ F.4.43.1 ] Summary

[ F.4.43.2 ] Input

[ F.4.43.3 ] Output

[ F.4.43.4 ] Implementation

[ F.4.43.5 ] Example

[ F.4.43.6 ] Case studies

[ F.4.43.7 ] References

[ F.4.43.8 ] See also

[ F.4.44 ] simulate_wishart

[ F.4.44.1 ] Summary

[ F.4.44.2 ] Input

[ F.4.44.3 ] Output

[ F.4.44.4 ] Implementation

[ F.4.44.5 ] Example

[ F.4.44.6 ] Case studies

[ F.4.44.7 ] References

[ F.4.44.8 ] See also

[ F.4.45.4 ] Implementation

[ F.4.45.5 ] Example

[ F.4.45.6 ] Case studies

[ F.4.45.7 ] References

[ F.4.45.8 ] See also

[ F.4.46 ] twist_prob_mom_match

[ F.4.46.1 ] Summary

[ F.4.46.2 ] Input

[ F.4.46.3 ] Output

[ F.4.46.4 ] Implementation

[ F.4.46.5 ] Tips

[ F.4.46.6 ] Example

[ F.4.46.7 ] Case studies

[ F.4.46.8 ] References

[ F.4.46.9 ] See also

[ F.4.47 ] twist_scenarios_mom_match

[ F.4.47.1 ] Summary

[ F.4.47.2 ] Input

[ F.4.47.3 ] Output

[ F.4.47.4 ] Implementation

[ F.4.47.5 ] Example

[ F.4.47.6 ] Case studies

[ F.4.47.7 ] References

[ F.4.47.8 ] See also

[ F.4.48 ] Flexible probabilities and scenarios of panic distribution

[ F.4.49 ] norm_cop_pdf

[ F.4.49.1 ] Summary

[ F.4.49.2 ] Input

[ F.4.49.3 ] Output

[ F.4.49.4 ] Implementation

[ F.4.49.5 ] Example

[ F.4.49.6 ] Case studies

[ F.4.50.4 ] Implementation

[ F.4.50.5 ] Example

[ F.4.50.6 ] Case studies

[ F.4.51 ] Elliptical Copula Scenarios via dimension reduction function

[ F.4.52 ] Normalized empirical histogram of scenario-probability distribution: function implementation

[ F.4.53 ] Metropolis-Hastings algorithm: implementation

[ F.4.54 ] Projection to horizon of central moments. Routine

[ F.4.55 ] Normal innovation function

[ F.4.56 ] Projection of the pdf via DFT: function implementation

[ F.4.57 ] GHCalibration

[ F.4.58 ] Stats

[ F.4.59 ] Raw2Cumul

[ F.4.60 ] PnlVolatility_ewma

[ F.4.61 ] ffgn

[ F.4.62 ] Central2Raw

[ F.4.63 ] CentralAndStandardizedStatistics

[ F.4.64 ] Schout2ConTank

[ F.4.65 ] ProjectionStudentT

[ F.4.66 ] QuantileMixture

[ F.4.67 ] ScoringAssessmentFP

[ F.4.68 ] SharpeRatio

[ F.4.69 ] PathsCauchy

[ F.4.70 ] SimulateCompPoisson

[ F.4.71 ] JumpDiffusionKou

[ F.4.72 ] JumpDiffusionMerton

[ F.4.73 ] NIG

[ F.4.74 ] VGpdf

[ F.4.75 ] SmoothStep

[ F.4.76 ] SpinOutlier

[ F.4.77 ] ShiftedVGMoments

[ F.4.78 ] ParamChangeVG

[ F.4.79 ] VG

[ F.5 ] Views

[ F.5.1 ] black_litterman

[ F.5.1.1 ] Example

[ F.5.2 ] min_rel_entropy_normal

[ F.5.2.1 ] Example

[ F.5.3 ] min_rel_entropy_sp

[ F.5.3.1 ] Summary

[ F.5.3.2 ] Input

[ F.5.3.3 ] Output

[ F.5.3.4 ] Implementation

[ F.5.3.5 ] Example

[ F.5.3.6 ] Case studies

[ F.5.3.7 ] References

[ F.5.3.8 ] See also

[ F.5.4 ] rel_entropy_normal

[ F.5.4.1 ] Summary

[ F.5.4.2 ] Input

[ F.5.4.3 ] Output

[ F.5.4.4 ] Implementation

[ F.5.4.5 ] Tips

[ F.5.4.6 ] Example

[ F.5.4.7 ] Case studies

[ F.5.4.8 ] References

[ F.5.5 ] Relative entropy function

[ F.5.6 ] Signal-to-noise constraint function

[ F.5.7 ] Copula opinion pooling function

[ F.6 ] Tools

[ F.6.1 ] adjusted_value

[ F.6.1.1 ] Summary

[ F.6.1.2 ] Input

[ F.6.1.3 ] Output

[ F.6.1.4 ] Implementation

[ F.6.1.5 ] Tips

[ F.6.1.6 ] Example

[ F.6.1.7 ] Case studies

[ F.6.1.8 ] References

[ F.6.2 ] aggregate_rating_migrations

[ F.6.2.1 ] Summary

[ F.6.2.2 ] Input

[ F.6.2.3 ] Output

[ F.6.2.4 ] Implementation

[ F.6.2.5 ] Example

[ F.6.2.6 ] Case studies

[ F.6.3 ] backward_selection

[ F.6.3.1 ] Summary

[ F.6.3.2 ] Input

[ F.6.3.3 ] Output

[ F.6.3.4 ] Implementation

[ F.6.3.5 ] Example

[ F.6.3.6 ] Case studies

[ F.6.4 ] colormap_fp

[ F.6.5.4 ] Implementation

[ F.6.5.5 ] Tips

[ F.6.5.6 ] Example

[ F.6.5.7 ] Case studies

[ F.6.5.8 ] References

[ F.6.5.9 ] See also

[ F.6.6 ] enet_selection

[ F.6.6.1 ] Summary

[ F.6.6.2 ] Input

[ F.6.6.3 ] Output

[ F.6.6.4 ] Implementation

[ F.6.6.5 ] Example

[ F.6.6.6 ] Case studies

[ F.6.6.7 ] See also

[ F.6.7 ] forward_selection

[ F.6.7.1 ] Summary

[ F.6.7.2 ] Input

[ F.6.7.3 ] Output

[ F.6.7.4 ] Implementation

[ F.6.7.5 ] Example

[ F.6.7.6 ] Case studies

[ F.6.8 ] gram_schmidt

[ F.6.8.1 ] Summary

[ F.6.8.2 ] Input

[ F.6.8.3 ] Output

[ F.6.8.4 ] Implementation

[ F.6.8.5 ] Example

[ F.6.8.6 ] References

[ F.6.9 ] histogram_sp

[ F.6.9.1 ] Summary

[ F.6.9.2 ] Input

[ F.6.9.3 ] Output

[ F.6.9.4 ] Implementation

[ F.6.9.5 ] Example

[ F.6.9.6 ] Case studies

[ F.6.9.7 ] References

[ F.6.10 ] histogram2d_sp

[ F.6.10.1 ] Summary

[ F.6.10.2 ] Input

[ F.6.10.3 ] Output

[ F.6.10.4 ] Implementation

[ F.6.10.5 ] Example

[ F.6.10.6 ] Case studies

[ F.6.11 ] mahalanobis_dist

[ F.6.11.1 ] Summary

[ F.6.11.2 ] Input

[ F.6.11.3 ] Output

[ F.6.11.4 ] Implementation

[ F.6.11.5 ] Example

[ F.6.11.6 ] Case studies

[ F.6.11.7 ] References

[ F.6.12 ] naive_selection

[ F.6.12.1 ] Summary

[ F.6.12.2 ] Input

[ F.6.12.3 ] Output

[ F.6.12.4 ] Implementation

[ F.6.12.5 ] Example

[ F.6.12.6 ] Case studies

[ F.6.13.4 ] Implementation

[ F.6.13.5 ] Example

[ F.6.13.6 ] Case studies

[ F.6.13.7 ] See also

[ F.6.14 ] plot_dynamic_strats

[ F.6.14.1 ] Example

[ F.6.15 ] plot_ellipse

[ F.6.15.1 ] Summary

[ F.6.15.2 ] Input

[ F.6.15.3 ] Output

[ F.6.15.4 ] Implementation

[ F.6.15.5 ] Example

[ F.6.15.6 ] Case studies

[ F.6.15.7 ] References

[ F.6.15.8 ] See also

[ F.6.16 ] plot_ellipsoid

[ F.6.16.1 ] Example

[ F.6.16.2 ] Case studies

[ F.6.16.3 ] See also

[ F.6.17 ] quad_prog

[ F.6.17.1 ] Example

[ F.6.18 ] sector_select

[ F.6.18.1 ] Example

[ F.6.19 ] smart_solve

[ F.6.20.4 ] Implementation

[ F.6.20.5 ] Example

[ F.6.21 ] softplus_inverse

[ F.6.21.1 ] Summary

[ F.6.21.2 ] Input

[ F.6.21.3 ] Output

[ F.6.21.4 ] Implementation

[ F.6.21.5 ] Example

[ F.6.22 ] trade_quote_processing

[ F.6.22.1 ] Example

[ F.6.23 ] trade_quote_spreading

[ F.6.23.1 ] Example

[ F.6.24 ] transpose_square_root

[ F.6.24.1 ] Summar