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S.I. The “Checklist”

[ S.0 ] Executive summary

[ S.0.1 ] s_checklist_executive_summary

[ S.0.1.1 ] Summary

[ S.0.1.2 ] Parameters

[ S.0.1.3 ] Outcomes and figures

[ S.0.1.4 ] Implementation

[ S.0.1.5 ] 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 ] Log-yield representation

[ S.1.6 ] s_analyze_rates_jgb

[ 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 ] Shadow rates evolution

[ S.1.8 ] Nelson-Siegel parametrization of the yield curve

[ S.1.9 ] Nelson-Siegel parametrization of the spread curve

[ S.1.10 ] s_implied_volatility_surface

[ S.1.10.1 ] Summary

[ S.1.10.2 ] Data

[ S.1.10.3 ] Parameters

[ S.1.10.4 ] Outcomes and figures

[ S.1.10.5 ] Implementation

[ S.1.10.6 ] See also

[ S.1.11 ] Log-implied volatility

[ S.1.12 ] Inverse-call implied volatility

[ S.1.13 ] Market quotes in delta-moneyness coordinates

[ S.1.14 ] SVI parametrization of the implied volatility surface

[ S.1.15 ] s_fx_rates_vs_logrates

[ S.1.15.1 ] Summary

[ S.1.15.2 ] Data

[ S.1.15.3 ] Outcomes and figures

[ S.1.15.4 ] Implementation

[ S.1.16 ] Cumulative number of rating migrations

[ S.1.17 ] s_default_merton_model

[ S.1.17.1 ] Summary

[ S.1.17.2 ] Parameters

[ S.1.17.3 ] Outcomes and figures

[ S.1.17.4 ] Implementation

[ S.1.18 ] s_high_freq_stock_var

[ S.1.18.1 ] Summary

[ S.1.18.2 ] Data

[ S.1.18.3 ] Parameters

[ S.1.18.4 ] Outcomes and figures

[ S.1.18.5 ] Implementation

[ S.1.18.6 ] See also

[ S.1.19 ] High frequency flow variables

[ S.1.20 ] s_high_freq_tick_time

[ 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.1.21 ] Volume time activity evolution of market microstructure

[ S.1.22 ] Vasicek fit of the yield curve

[ S.1.23 ] Heston parametrization of the implied volatility surface

[ S.1.24 ] Rating thresholds and Merton model

[ S.1.25 ] s_checklist_scenariobased_step01

[ S.2 ] Quest for invariance

[ S.2.1 ] Ellipsoid test for invariance on compounded returns

[ S.2.2 ] Kolmogorov-Smirnov test for invariance on compounded returns

[ 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 ] Kolmogorov-Smirnov test for invariance on zero swap rates

[ S.2.9 ] Ellipsoid test for invariance on the parameters of Nelson-Siegel model

[ S.2.10 ] Kolmogorov-Smirnov test for invariance on the parameters of Nelson-Siegel model

[ 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 ] Markov chain model for bid-ask spread

[ S.2.23 ] Next-step function for Markov chains

[ S.2.24 ] Long Memory in high frequency trading order sign

[ S.2.25 ] Long Memory in high frequency trading order sign: fractional integration processes

[ S.2.26 ] Volatility clustering in the stock market

[ S.2.27 ] Volatility Clustering in the stock market: GARCH(1,1) model

[ S.2.28 ] P&L realizations modeled by a GARCH(1,1): ellipsoid test for invariance on the residuals

[ S.2.29 ] Ellipsoid test for invariance on the residuals of an ACD model fitted on arrival times

[ S.2.30 ] Stochastic volatility and leverage effect

[ S.2.31 ] Implied leverage effect

[ S.2.32 ] s_fit_yields_var1

[ S.2.32.1 ] Summary

[ S.2.32.2 ] Data

[ S.2.32.3 ] Parameters

[ S.2.32.4 ] Outcomes and figures

[ S.2.32.5 ] Implementation

[ S.2.32.6 ] See also

[ S.2.33 ] Multivariate quest for invariance

[ S.2.34 ] Error correction representation of unit-root VAR(1) process: case study

[ S.2.35 ] s_fit_var1_implvol

[ S.2.35.1 ] Summary

[ S.2.35.2 ] Data

[ S.2.35.3 ] Parameters

[ S.2.35.4 ] Outcomes and figures

[ S.2.35.5 ] Implementation

[ S.2.35.6 ] See also

[ S.2.36 ] s_fit_garch_stocks

[ S.2.37 ] s_checklist_scenariobased_step02

[ 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 ] s_default_probabilities

[ S.3.33 ] Expectation-maximization with flexible probabilities for missing values. Application

[ S.3.34 ] s_different_length_series

[ S.3.34.1 ] Summary

[ S.3.34.2 ] Data

[ S.3.34.3 ] Parameters

[ S.3.34.4 ] Outcomes and figures

[ S.3.34.5 ] Implementation

[ S.3.34.6 ] See also

[ S.3.35 ] Proxies

[ S.3.36 ] Fix non-synchroneity in HFP

[ S.3.37 ] Flexible probabilities ensemble posterior and classical equivalent

[ S.3.38 ] Hellinger distance and diversity indicator

[ S.3.39 ] Ensemble FP: curse of dimensionality?

[ S.3.40 ] Likelihood with flexible probabilities of GARCH(1,1)

[ S.3.41 ] Alternative FP specifications: bootstrap

[ S.3.42 ] Alternative FP specifications: Dirichlet distribution

[ S.3.43 ] Copula-marginal estimation for the invariants of a call option

[ 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 ] Credit migrations as time homogeneous Markov chain

[ S.3.50 ] EWMA: numerical example

[ S.3.51 ] Backward/forward EWMA: numerical example

[ S.3.52 ] s_shrinkage_location

[ 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.3.53 ] s_shrinkage_factor

[ S.3.53.1 ] Summary

[ S.3.53.2 ] Data

[ S.3.53.3 ] Parameters

[ S.3.53.4 ] Outcomes and figures.

[ S.3.53.5 ] Implementation

[ S.3.53.6 ] See also

[ S.3.54 ] s_shrink_corr_clusters

[ S.3.54.1 ] Summary

[ S.3.54.2 ] Datas

[ S.3.54.3 ] Outcomes and figures

[ S.3.54.4 ] Implementation

[ S.3.55 ] Homogeneous cluster shrinkage

[ S.3.56 ] Graphical lasso estimation of the correlation and inverse correlation matrix

[ S.3.57 ] Random matrix theory: Marchenko-Pastur limit

[ S.3.58 ] Numerical integration of Marchenko-Pastur distribution

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

[ S.3.60 ] Spectrum of the covariance matrix: exponential noise

[ S.3.61 ] s_shrink_spectrum_filt

[ S.3.61.1 ] Summary

[ S.3.61.2 ] Data

[ S.3.61.3 ] Parameters

[ S.3.61.4 ] Outcomes and figures

[ S.3.61.5 ] Implementation

[ S.3.61.6 ] See also

[ S.3.62 ] Sparse matrix transformation shrinkage

[ S.3.63 ] Shrinkage estimator of location: implementation

[ S.3.64 ] Sample covariance and eigenvalue dispersion

[ S.3.65 ] Shrinkage estimator of dispersion: implementation

[ S.3.66 ] Random matrix theory: Wigner semicircle law

[ S.3.67 ] Shrinkage estimators of location: assessment

[ S.3.68 ] s_bayes_prior_niw

[ S.3.68.1 ] Summary

[ S.3.68.2 ] Parameters

[ S.3.68.3 ] Outcomes and figures

[ S.3.68.4 ] Implementation

[ S.3.69 ] s_bayes_posterior_niw

[ S.3.69.1 ] Summary

[ S.3.69.2 ] Parameters

[ S.3.69.3 ] Outcomes and figures

[ S.3.69.4 ] Implementation

[ S.3.69.5 ] See also

[ S.3.70 ] s_bayesian_estimation

[ S.3.71 ] Markov chain Monte Carlo: application of Metropolis-Hastings algorithm

[ S.3.72 ] Agnostic prior on correlation

[ S.3.73 ] s_location_estimators

[ 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 ] s_sample_mean_covariance

[ S.3.74.1 ] Summary

[ S.3.74.2 ] Parameters

[ S.3.74.3 ] Outcomes and figures

[ S.3.74.4 ] Implementation

[ S.3.74.5 ] See also

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

[ S.3.76 ] Estimation assessment of a moment-based functional of a mixture II

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

[ S.3.78 ] Estimation assessment of the quantile of a mixture II

[ S.3.79 ] s_location_stress_error

[ S.3.79.1 ] Summary

[ S.3.79.2 ] Parameters

[ S.3.79.3 ] Outcomes and figures

[ S.3.79.4 ] Implementation

[ S.3.79.5 ] See also

[ S.3.80 ] Estimation assessment

[ S.3.81 ] Sample mean and sample covariance estimation error

[ S.3.82 ] Sample quantiles distribution

[ S.3.83 ] Distribution of conditioning variable for an aggregate of clusters

[ S.3.84 ] s_checklist_scenariobased_steps03_04_historical

[ S.3.85 ] s_checklist_scenariobased_step03

[ 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 ] Projecting the credit structural Merton’s model

[ S.4.9 ] s_projection_multiv_ratings

[ S.4.9.1 ] Summary

[ S.4.9.2 ] Data

[ S.4.9.3 ] Outcomes and figures

[ S.4.9.4 ] Implementation

[ S.4.9.5 ] See also

[ S.4.10 ] Hybrid historical and Monte Carlo projection: modeling default via a one-factor t-copula

[ S.4.11 ] Projection of a MVOU process with non parametric invariants (historical with flexible probabilities distribution of the principal component)

[ S.4.12 ] Multivariate GARCH: fit and projection. Practice

[ S.4.13 ] Equity market: linear vs. compounded returns projection

[ S.4.14 ] Projection of shadow rates via Monte Carlo approach

[ S.4.15 ] Projection of cluster aggregates: case study

[ S.4.16 ] Projection of risk drivers whose invariants stem from marginal GARCH(1,1) fit and joint DCC fit: stocks case study

[ S.4.17 ] s_projection_stock_hfp

[ S.4.17.1 ] Summary

[ S.4.17.2 ] Data

[ S.4.17.3 ] Parameters

[ S.4.17.4 ] Outcomes and figures

[ S.4.17.5 ] Implementation

[ S.4.17.6 ] See also

[ S.4.18 ] s_projection_stock_bootstrap

[ S.4.18.1 ] Summary

[ S.4.18.2 ] Data

[ S.4.18.3 ] Parameters

[ S.4.18.4 ] Outcomes and figures

[ S.4.18.5 ] Implementation

[ S.4.18.6 ] See also

[ S.4.19 ] Projection via historical approach: call option risk drivers

[ S.4.20 ] Historical projection: bootstrap

[ S.4.21 ] Projection via historical bootstrapping: case study

[ S.4.22 ] Hybrid Monte Carlo-historical projection: case study

[ S.4.23 ] Hybrid historical and Monte Carlo projection: modeling default via a one-factor normal copula

[ S.4.24 ] Copula-marginal projection for risk drivers of different asset classes

[ S.4.25 ] Risk propagation in the Heston process

[ S.4.26 ] s_checklist_scenariobased_steps03_04_historical

[ S.4.27 ] s_checklist_scenariobased_step04

[ S.5 ] Pricing at the horizon

[ S.5.1 ] s_pricing_stocks_hfp

[ 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 ] Call option value: parametric projection

[ 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.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 ] Aggregate return in the scenario approach: application

[ 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 ] Outcomes and figures

[ S.6.7.4 ] Implementation

[ S.6.7.5 ] 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.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 ] Satisfaction measures: scenario-probability distribution (historical case)

[ S.7.3 ] s_evaluation_satis_scenprob

[ 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.7.3.6 ] See also

[ S.7.4 ] s_evaluation_satis_norm

[ S.7.4.1 ] Summary

[ S.7.4.2 ] Data

[ S.7.4.3 ] Parameters

[ S.7.4.4 ] Outcomes

[ S.7.4.5 ] Implementation

[ S.7.5 ] Cornish Fisher expansion: an application

[ S.7.6 ] s_evaluation_eco_cap

[ S.7.6.1 ] Summary

[ S.7.6.2 ] Data

[ S.7.6.3 ] Parameters

[ S.7.6.4 ] Outcomes

[ S.7.6.5 ] Implementation

[ S.7.6.6 ] See also

[ S.7.7 ] s_evaluation_cornishfisher_stocks

[ S.7.7.1 ] Summary

[ S.7.7.2 ] Data

[ S.7.7.3 ] Parameters

[ S.7.7.4 ] Outcomes and figures

[ S.7.7.5 ] Implementation

[ S.7.7.6 ] See also

[ S.7.8 ] The mean-lower partial moment trade-off is not co-monotonic additive: practice

[ S.7.9 ] s_checklist_scenariobased_step07

[ 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 ] Top-down and bottom-up exposures relationship

[ S.8a.4 ] s_attribution_hedging

[ S.8a.4.1 ] Summary

[ S.8a.4.2 ] Data

[ S.8a.4.3 ] Outcomes and figures

[ S.8a.4.4 ] Implementation

[ S.8a.4.5 ] See also

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

[ 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_checklist_scenariobased_step09

[ S.9a.4 ] Portfolio optimization: S&P 500 stocks

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

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

[ S.9b.2 ] s_characteristic_port_rev

[ S.9b.2.1 ] Summary

[ S.9b.2.2 ] Data

[ S.9b.2.3 ] Parameters

[ S.9b.2.4 ] Outcomes and figures

[ S.9b.2.5 ] Implementation

[ S.9b.2.6 ] See also

[ S.9b.3 ] s_flexible_characteristic_port_rev

[ S.9b.3.1 ] Summary

[ S.9b.3.2 ] Data

[ S.9b.3.3 ] Parameters

[ S.9b.3.4 ] Outcomes and figures

[ S.9b.3.5 ] Implementation

[ S.9b.3.6 ] See also

[ S.9b.4 ] s_generalized_flam_toy

[ S.9c ] Construction: time series strategies

[ S.9c.1 ] s_dynamic_port_strats

[ S.9c.1.1 ] Summary

[ S.9c.1.2 ] Parameters

[ S.9c.1.3 ] Outcomes and figures

[ S.9c.1.4 ] Implementation

[ S.9c.1.5 ] See also

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

[ 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.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 ] Parameters

[ S.11.1.3 ] Outcomes and figures

[ S.11.1.4 ] Implementation

[ S.11.1.5 ] See also

[ S.12 ] Linear factor models: theory

[ S.12.1 ] Fully observable factor model

[ S.12.2 ] Fully observable models: study of factor-residual distribution

[ S.12.3 ] s_regression_lfm

[ S.12.3.1 ] Summary

[ S.12.3.2 ] Parameters

[ S.12.3.3 ] Outcomes and figures

[ S.12.3.4 ] Implementation

[ S.12.3.5 ] See also

[ S.12.4 ] s_normal_mean_regression

[ S.12.4.1 ] Summary

[ S.12.4.2 ] Parameters

[ S.12.4.3 ] Outcomes and figures

[ S.12.4.4 ] Implementation

[ S.12.4.5 ] See also

[ S.12.5 ] Regression LFM’s linear formulation: numerical proof

[ S.12.6 ] s_display_corr_norm_ellips

[ S.12.6.1 ] Summary

[ S.12.6.2 ] Parameters

[ S.12.6.3 ] Outcomes and figures

[ S.12.6.4 ] Implementation

[ S.12.6.5 ] See also

[ S.12.7 ] s_principal_component_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 ] Principal-component LFM’s: joint distribution of residuals and factors

[ S.12.9 ] s_systematic_idiosyncratic_lfm

[ 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 ] s_cross_section_lfm

[ S.12.10.1 ] Summary

[ S.12.10.2 ] Parameters

[ S.12.10.3 ] Outcomes and figures

[ S.12.10.4 ] Implementation

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

[ S.12.15 ] s_factor_replication_logn

[ S.12.15.1 ] Summary

[ S.12.15.2 ] Parameters

[ S.12.15.3 ] Outcomes and figures

[ S.12.15.4 ] Implementation

[ S.12.15.5 ] See also

[ S.12.16 ] Factor extraction: numerical test

[ S.12.17 ] Comparison between observable and hidden factors

[ S.12.18 ] s_cross_section_truncated_lfm

[ S.12.18.1 ] Summary

[ S.12.18.2 ] Data

[ S.12.18.3 ] Parameters

[ S.12.18.4 ] Outcomes and figures

[ S.12.18.5 ] Implementation

[ S.12.18.6 ] See also

[ S.12.19 ] Comparison of LFM’s

[ S.12.20 ] Correlation of residuals in generalized regression LFM’s

[ S.12.21 ] Correlation of residuals in generalized cross-sectional LFM

[ S.12.22 ] Hidden regression versus Principal-component LFM’s: numerical example

[ S.12.23 ] Symmetric regression: numerical example

[ S.12.24 ] Hidden factors: puzzle

[ S.13 ] Linear factor models: estimation

[ S.13.1 ] s_reg_truncated_lfm

[ S.13.1.1 ] Summary

[ S.13.1.2 ] Data

[ S.13.1.3 ] Parameters

[ S.13.1.4 ] Outcomes and figures

[ S.13.1.5 ] Implementation

[ S.13.1.6 ] See also

[ S.13.2 ] Simulation of the distribution of statistics of regression parameters

[ S.13.3 ] Regression LFM’s: truncated estimations

[ S.13.4 ] Regression LFM’s: generalized regression industry factors

[ S.13.5 ] s_pca_truncated_lfm

[ S.13.5.1 ] Summary

[ S.13.5.2 ] Data

[ S.13.5.3 ] Parameters

[ S.13.5.4 ] Outcomes and figures

[ S.13.5.5 ] Implementation

[ S.13.5.6 ] See also

[ S.13.6 ] Cross-sectional LFM’s: generalized cross-sectional industry factors

[ S.14 ] Non-parametric LFM’s: pitfalls

[ S.14.1 ] Regression LFM’s: shifted-lognormal regression II

[ S.15 ] Machine learning foundations

[ S.15.1 ] s_continuum_discrete_model

[ S.15.1.1 ] Summary

[ S.15.1.2 ] Parameters

[ S.15.1.3 ] Outcomes and figures

[ S.15.1.4 ] Implementation

[ S.15.2 ] s_continuum_discrete_point_pred

[ S.15.2.1 ] Summary

[ S.15.2.2 ] Parameters

[ S.15.2.3 ] Outcomes and figures

[ S.15.2.4 ] Implementation

[ S.15.3 ] s_continuum_discrete_generative_pred

[ S.15.3.1 ] Summary

[ S.15.3.2 ] Parameters

[ S.15.3.3 ] Outcomes and figures

[ S.15.3.4 ] Implementation

[ S.15.4 ] s_logn_mean_regression

[ S.15.4.1 ] Summary

[ S.15.4.2 ] Parameters

[ S.15.4.3 ] Outcomes and figures

[ S.15.4.4 ] Implementation

[ S.15.4.5 ] See also

[ S.15.5 ] s_call_mean_regression

[ S.15.6 ] s_logn_mean_lin_regression

[ S.15.6.1 ] Summary

[ S.15.6.2 ] Parameters

[ S.15.6.3 ] Outcomes and figures

[ S.15.6.4 ] Implementation

[ S.15.6.5 ] See also

[ S.15.7 ] s_call_mean_lin_regression

[ S.15.8 ] s_sp_anova

[ S.15.9 ] s_logn_quant_regression

[ S.15.9.1 ] Summary

[ S.15.9.2 ] Parameters

[ S.15.9.3 ] Outcomes and figures

[ S.15.9.4 ] Implementation

[ S.15.9.5 ] See also

[ S.15.10 ] s_call_quant_regression

[ S.15.11 ] s_logn_quant_lin_regression

[ S.15.11.1 ] Summary

[ S.15.11.2 ] Parameters

[ S.15.11.3 ] Outcomes and figures

[ S.15.11.4 ] Implementation

[ S.15.11.5 ] See also

[ S.15.12 ] s_call_quant_lin_regression

[ S.15.13 ] s_supervised_point_prediction

[ S.15.13.1 ] Summary

[ S.15.13.2 ] Parameters

[ S.15.13.3 ] Outcomes and figures

[ S.15.13.4 ] Implementation

[ S.15.13.5 ] See also

[ S.15.14 ] s_continuum_discrete_kmeans

[ S.15.14.1 ] Summary

[ S.15.14.2 ] Parameters

[ S.15.14.3 ] Outcomes and figures

[ S.15.14.4 ] Implementation

[ S.15.15 ] s_bias_vs_variance_lognormal

[ S.16 ] Estimation and assessment

[ S.16.1 ] Predictive distribution assessment

[ S.17 ] Bias-variance enhancements

[ S.17.1 ] s_decision_tree_normal

[ S.17.1 ] s_encoding

[ S.17.2 ] s_ann_normal

[ S.17.3 ] s_perceptron_normal

[ S.17.4 ] s_svm_normal

[ S.17.5 ] s_bias_vs_variance_normal

[ S.17.6 ] s_gradient_boosting

[ S.19 ] Dynamic models

[ S.19.1 ] s_dyn_principal_component_var

[ S.19.1.1 ] Summary

[ S.19.1.2 ] Parameters

[ S.19.1.3 ] Outcomes and figures

[ S.19.1.4 ] Implementation

[ S.19.1.5 ] See also

[ S.19.2 ] s_kalman_filter_yield_curve

[ 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_hidden_markov_model_stocks

[ 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.20 ] Application: principal component analysis of the swap curve

[ S.20.1 ] Eigenvectors for Toeplitz structure

[ S.20.2 ] s_pca_empirical

[ S.20.2.1 ] Summary

[ S.20.2.2 ] Data

[ S.20.2.3 ] Parameters

[ S.20.2.4 ] Outcomes and figures

[ S.20.2.5 ] Implementation

[ S.20.2.6 ] See also

[ S.20.3 ] s_pca_continuum_limit

[ S.20.3.1 ] Summary

[ S.20.3.2 ] Parameters

[ S.20.3.3 ] Outcomes and figures

[ S.20.3.4 ] Implementation

[ S.20.3.5 ] See also

[ S.21 ] Application: market prediction regression

[ S.21.1 ] Equivalent formulations of maximum likelihood with flexible probabilities estimates (numerical proof)

[ S.21.2 ] s_market_prediction_regression

[ S.21.3 ] s_lasso_vs_ridge

[ S.21.3.1 ] Summary

[ S.21.3.2 ] Data

[ S.21.3.3 ] Parameters

[ S.21.3.4 ] Outcomes and figures

[ S.21.3.5 ] Implementation

[ S.21.3.6 ] See also

[ S.21.4 ] Regression LFM’s: randomized least square estimates

[ S.21.5 ] s_reg_lfm_bayes_prior_niw

[ S.21.5.1 ] Summary

[ S.21.5.2 ] Parameters

[ S.21.5.3 ] Outcomes and figures

[ S.21.5.4 ] Implementation

[ S.21.6 ] s_reg_lfm_bayes_posterior_niw

[ S.21.6.1 ] Summary

[ S.21.6.2 ] Parameters

[ S.21.6.3 ] Outcomes and figures

[ S.21.6.4 ] Implementation

[ S.21.6.5 ] See also

[ S.21.7 ] s_factors_selection

[ S.21.7.1 ] Summary

[ S.21.7.2 ] Parameters

[ S.21.7.3 ] Outcomes and figures

[ S.21.7.4 ] Implementation

[ S.21.7.5 ] See also

[ S.22 ] Application: credit default

[ S.23 ] Application: clustering

S.III. Valuation

[ S.24 ] Executive summary

[ S.25 ] Background definitions

[ S.26 ] Linear pricing theory: core

[ S.26.1 ] s_current_values

[ S.26.1.1 ] Summary

[ S.26.1.2 ] Data

[ S.26.1.3 ] Parameters

[ S.26.1.4 ] Outcomes and figures

[ S.26.1.5 ] Implementation

[ S.26.1.6 ] See also

[ S.26.2 ] Stochastic discount factor comparison

[ S.26.3 ] s_fund_theorem

[ S.26.3.1 ] Summary

[ S.26.3.2 ] Data

[ S.26.3.3 ] Parameters

[ S.26.3.4 ] Outcomes and figures

[ S.26.3.5 ] Implementation

[ S.26.3.6 ] See also

[ S.26.4 ] s_plot_sdf_mre

[ S.26.5 ] Fundamental theorem of asset pricing with risk-neutral measure: empirical verification

[ S.26.6 ] s_risk_neutral_density

[ S.26.6.1 ] Summary

[ S.26.6.2 ] Data

[ S.26.6.3 ] Parameters

[ S.26.6.4 ] Outcomes and figures

[ S.26.6.5 ] Implementation

[ S.26.7 ] s_capm_like_identity

[ S.26.7.1 ] Summary

[ S.26.7.2 ] Data

[ S.26.7.3 ] Parameters

[ S.26.7.4 ] Outcomes and figures

[ S.26.7.5 ] Implementation

[ S.26.7.6 ] See also

[ S.27 ] Linear pricing theory: further assumptions

[ S.27.1 ] s_simulate_call

[ S.27.1.1 ] Summary

[ S.27.1.2 ] Data

[ S.27.1.3 ] Parameters

[ S.27.1.4 ] Outcomes and figures

[ S.27.1.5 ] Implementation

[ S.27.2 ] s_simulate_payoff

[ S.27.3 ] Minimum variance factor-replicating portfolio

[ S.28 ] Non-linear pricing theory

[ S.29 ] Valuation implementation

[ S.29.1 ] Fitting implied volatility from the Black-Scholes-Merton valuation

[ S.29.2 ] Fitting yield curve from the Vasicek model

S.IV. Performance analysis

[ S.30 ] Executive summary

[ S.31 ] Performance definitions

[ S.31.1 ] Compounded return of a portfolio

[ S.32 ] Performance attribution

S.V. Quant toolbox

[ S.33 ] Summary

[ S.34 ] Distributions

[ S.34.1 ] Conditional expectation between normal random variables

[ S.34.2 ] Innovation: the normal case, implementation

[ S.34.3 ] Innovation: the lognormal case, implementation

[ S.34.4 ] Uniform distribution inside the unit circle

[ S.34.5 ] s_simulate_unif_in_ellipse

[ 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_ens_exp_decay

[ 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_display_dirac_delta

[ S.34.7.1 ] Summary

[ S.34.7.2 ] Input

[ S.34.7.3 ] Outcomes and figures

[ S.34.7.4 ] Implementation

[ S.34.7.5 ] See also

[ S.34.8 ] s_scen_prob_pdf

[ S.34.8.1 ] Summary

[ S.34.8.2 ] Parameters

[ S.34.8.3 ] Outcomes and figures

[ S.34.8.4 ] Implementation

[ S.34.8.5 ] See also

[ S.34.9 ] s_scen_prob_quantile

[ S.34.9.1 ] Summary

[ S.34.9.2 ] Input

[ S.34.9.3 ] Outcomes

[ S.34.9.4 ] Implementation

[ S.34.9.5 ] See also

[ S.34.10 ] s_generalized_expon_entropy

[ 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_normal_exponential_family

[ S.34.11.1 ] Summary

[ S.34.11.2 ] Parameters

[ S.34.11.3 ] Outcomes

[ S.34.11.4 ] Implementation

[ S.34.11.5 ] See also

[ S.34.12 ] s_saddle_point_vs_mcfp_quadn

[ S.34.12.1 ] 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_bivariate_wishart

[ S.34.13.1 ] Summary

[ S.34.13.2 ] Input

[ S.34.13.3 ] Outcomes and figures

[ S.34.13.4 ] Implementation

[ S.34.13.5 ] See also

[ S.35 ] Estimation techniques

[ S.35.1 ] Maximum likelihood estimation

[ S.36 ] Views processing

[ S.36.1 ] s_min_rel_ent_point_view

[ S.36.1.1 ] Summary

[ S.36.1.2 ] Parameters

[ S.36.1.3 ] Outcomes

[ S.36.1.4 ] Implementation

[ S.36.1.5 ] See also

[ S.36.2 ] s_min_rel_ent_distr_view

[ S.36.2.1 ] Summary

[ S.36.2.2 ] Parameters

[ S.36.2.3 ] Outcomes

[ S.36.2.4 ] Implementation

[ S.36.2.5 ] See also

[ S.36.3 ] s_min_rel_ent_partial_view

[ S.36.3.1 ] Summary

[ S.36.3.2 ] Parameters

[ S.36.3.3 ] Outcomes

[ S.36.3.4 ] Implementation

[ S.36.3.5 ] See also

[ S.36.4 ] s_entropy_view

[ S.36.4.1 ] Summary

[ S.36.4.2 ] Parameters

[ S.36.4.3 ] Outcomes and figures

[ S.36.4.4 ] Implementation

[ S.36.4.5 ] See also

[ S.36.5 ] s_views_linear_exp

[ S.36.5.1 ] Summary

[ S.36.5.2 ] Parameters

[ S.36.5.3 ] Outcomes

[ S.36.5.4 ] Implementation

[ S.36.5.5 ] See also

[ S.36.6 ] s_views_gen_expectations

[ S.36.6.1 ] Summary

[ S.36.6.2 ] Parameters

[ S.36.6.3 ] Outcomes

[ S.36.6.4 ] Implementation

[ S.36.6.5 ] See also

[ S.36.7 ] s_views_sorted_exp

[ S.36.7.1 ] Summary

[ S.36.7.2 ] Parameters

[ S.36.7.3 ] Outcomes

[ S.36.7.4 ] Implementation

[ S.36.7.5 ] See also

[ S.36.8 ] s_views_st_deviations

[ S.36.8.1 ] Summary

[ S.36.8.2 ] Parameters

[ S.36.8.3 ] Outcomes

[ S.36.8.4 ] Implementation

[ S.36.8.5 ] See also

[ S.36.9 ] s_views_correlations

[ S.36.9.1 ] Summary

[ S.36.9.2 ] Parameters

[ S.36.9.3 ] Outcomes

[ S.36.9.4 ] Implementation

[ S.36.9.5 ] See also

[ S.36.10 ] s_views_cond_prob

[ S.36.10.1 ] Summary

[ S.36.10.2 ] Parameters

[ S.36.10.3 ] Outcomes

[ S.36.10.4 ] Implementation

[ S.36.10.5 ] See also

[ S.36.11 ] s_views_cdf

[ S.36.11.1 ] Summary

[ S.36.11.2 ] Parameters

[ S.36.11.3 ] Outcomes

[ S.36.11.4 ] Implementation

[ S.36.11.5 ] See also

[ S.36.12 ] s_views_cond_exp

[ S.36.12.1 ] Summary

[ S.36.12.2 ] Parameters

[ S.36.12.3 ] Outcomes

[ S.36.12.4 ] Implementation

[ S.36.12.5 ] See also

[ S.36.13 ] Convexity test for relative entropy

[ S.36.14 ] Numerical verification of the gradient of entropy

[ S.36.15 ] Numerical verification of gradient of constraint function on signal

[ S.36.16 ] Numerical verification of the Hessian of entropy

[ S.36.17 ] Numerical and analytical Hessian of constraints on signal

[ S.36.18 ] Copula opinion pooling: uninformative views

[ S.37 ] Black-Litterman

[ S.37.1 ] s_bl_equilibrium_ret

[ S.37.1.1 ] Summary

[ S.37.1.2 ] Data

[ S.37.1.3 ] Parameters

[ S.37.1.4 ] Outcomes

[ S.37.1.5 ] Implementation

[ S.37.1.6 ] See also

[ S.37.2 ] s_info_processing_comparison

[ S.37.2.1 ] Summary

[ S.37.2.2 ] Data

[ S.37.2.3 ] Parameters

[ S.37.2.4 ] Outcomes and figures

[ S.37.2.5 ] Implementation

[ S.37.2.6 ] See also

[ S.38 ] Geometry of random variables

[ S.38.1 ] R-squared: numerical example

[ S.38.2 ] Euclidean vectors of joint normal variables

[ S.38.3 ] Euclidean vectors of joint lognormal variables

[ S.38.4 ] Orthogonality of principal directions

[ S.38.5 ] Euclidean vectors via linear transformation and Riccati root

[ S.39 ] Geometry of distributions

[ S.40 ] Decision theory with model uncertainty

[ S.41 ] Copulas

[ S.41.1 ] Display copula of a bivariate normal

[ S.41.2 ] Cdf-to-uniform mapping (normal distribution)

[ S.41.3 ] s_lognorm_to_uniform

[ S.41.3.1 ] Summary

[ S.41.3.2 ] Parameters

[ S.41.3.3 ] Outcomes and figures

[ S.41.3.4 ] Implementation

[ S.41.3.5 ] See also

[ S.41.4 ] Cdf-to-uniform mapping (gamma distribution)

[ S.41.5 ] Uniform-to-cdf mapping (normal distribution)

[ S.41.6 ] Uniform-to-cdf mapping (lognormal distribution)

[ S.41.7 ] Uniform-to-cdf mapping (gamma distribution)

[ S.41.8 ] Combination: from FP-copula/historical marginal to joint

[ S.41.9 ] s_copula_returns

[ S.41.9.1 ] Summary

[ S.41.9.2 ] Parameters

[ S.41.9.3 ] Outcomes and figures

[ S.41.9.4 ] Implementation

[ S.41.9.5 ] See also

[ S.41.10 ] s_cop_marg_combination

[ S.41.10.1 ] Script summary

[ S.41.10.2 ] Parameters

[ S.41.10.3 ] Outcomes and figures

[ S.41.10.4 ] Implementation

[ S.41.11 ] s_cop_marg_separation

[ S.41.11.1 ] Script summary

[ S.41.11.2 ] Parameters

[ S.41.11.3 ] Outcomes and figures

[ S.41.11.4 ] Implementation

[ S.41.11.5 ] See also

[ S.41.12 ] Combination: from t-copula/marginal to joint

[ S.41.13 ] Separation: from historical joint to copula/marginal

[ S.41.14 ] Display the pdf of a bivariate t-copula

[ S.42 ] Location and dispersion

[ S.42.1 ] s_logn_uncertainty_bands

[ S.42.1.1 ] Summary

[ S.42.1.2 ] Parameters

[ S.42.1.3 ] Outcomes and figures

[ S.42.1.4 ] Implementation

[ S.42.2 ] Different visualizations of the multivariate uncertainty band

[ S.42.3 ] Ellipsoid and uncertainty band of a bivariate normal

[ S.42.4 ] s_ellipsoid_multiv_loc_disp

[ S.42.4.1 ] Summary

[ S.42.4.2 ] Parameters

[ S.42.4.3 ] Outcomes and figures

[ S.42.4.4 ] Implementation

[ S.42.4.5 ] See also

[ S.42.5 ] Ellipsoid and uncertainty band of a bivariate lognormal

[ S.42.6 ] Ellipsoid and uncertainty band of normalized Wishart marginals

[ S.42.7 ] Affine transformation of a bivariate lognormal

[ S.42.8 ] Location-dispersion ellipsoid and features

[ S.42.9 ] Iso-contour of a lognormal bivariate distribution

[ S.42.10 ] s_chebyshev_ineq

[ S.42.10.1 ] Summary

[ S.42.10.2 ] Parameters

[ S.42.10.3 ] Outcomes and figures

[ S.42.10.4 ] Implementation

[ S.42.10.5 ] See also

[ S.42.11 ] Expectation-covariance as minimum volume ellipsoid

[ S.43 ] Correlation and generalizations

[ S.43.1 ] Schweizer-Wolff measure between normal variables

[ S.43.2 ] Normalization constant of Schweizer-Wolff measure

[ S.43.3 ] Normal copula and Frechet-Hoeffding bounds

[ S.43.4 ] Smooth approximation of call and put payoffs via regularization

[ S.43.5 ] Kendall’s tau between normal variables

[ S.43.6 ] Spearman’s rho between normal variables

[ S.43.7 ] Correlation between normal variables (numerical proof)

[ S.43.8 ] Correlation between lognormal variables (numerical proof)

[ S.43.9 ] Correlation between normalized Wishart marginals(numerical proof)

[ S.43.10 ] Correlation: normal stock prices, call option and put option

[ S.43.11 ] Uncorrelation versus independence

[ S.43.12 ] Uncorrelation versus independence via CLT

[ S.43.13 ] Fully dependent variables

[ 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 ] Stochastic processes cheat sheet

[ S.46 ] Continuous time processes

[ S.46.1 ] s_projection_brownian_motion

[ S.46.1.1 ] Summary

[ S.46.1.2 ] Data

[ S.46.1.3 ] Parameters

[ S.46.1.4 ] Outcomes and figures

[ S.46.1.5 ] Implementation

[ S.46.1.6 ] See also

[ S.46.2 ] s_projection_univ_rating

[ S.46.2.1 ] Summary

[ S.46.2.2 ] Data

[ S.46.2.3 ] Outcomes and figures

[ S.46.2.4 ] Implementation

[ S.46.2.5 ] See also

[ S.46.3 ] Projection of Poisson process

[ S.46.4 ] Simulate compound Poisson processes

[ S.46.5 ] Projection of a Compound Poisson Process

[ S.46.6 ] Projection of Cauchy distribution

[ S.46.7 ] Projection of the variance gamma distribution

[ S.46.8 ] Simulate the NIG and VG processes

[ S.46.9 ] Simulation of the variance gamma process by subordination

[ S.46.10 ] Projection of the Student t distribution

[ S.46.11 ] Projection of the uniform distribution

[ S.46.12 ] Projection of fractional Brownian motion

[ S.46.13 ] Projection of the Heston process

[ S.46.14 ] Simulation of the Heston process by Time Change

[ S.47 ] First order autoregression

[ S.47.1 ] Simulation of a Ornstein-Uhlenbeck process

[ S.47.2 ] MVOU change of coordinates

[ S.47.3 ] Projection of conditional mean and covariance of the MVOU process

[ S.48 ] Spectral analysis

[ S.48.1 ] Autocovariance of AR(1) processes: empirical derivation

[ S.48.2 ] s_spectral_representation

[ S.48.2.1 ] Summary

[ S.48.2.2 ] Parameters

[ S.48.2.3 ] Outcomes and figures

[ S.48.2.4 ] Implementation

[ S.48.2.5 ] Tips

[ S.48.2.6 ] See also

[ S.48.3 ] s_toeplitz_spectral

[ S.48.3.1 ] Summary

[ S.48.3.2 ] Parameters

[ S.48.3.3 ] Outcomes and figures

[ S.48.3.4 ] Implementation

[ S.48.3.5 ] See also

[ S.48.4 ] Bandpass filter applied to AR(1) processes

[ S.49 ] Signals

[ S.49.1 ] s_cointegration_detection

[ S.49.1.1 ] Summary

[ S.49.1.2 ] Data

[ S.49.1.3 ] Parameters

[ S.49.1.4 ] Outcomes and figures

[ S.49.1.5 ] Implementation

[ S.49.1.6 ] See also

[ S.49.2 ] s_cointegration_signal

[ S.49.2.1 ] Summary

[ S.49.2.2 ] Data

[ S.49.2.3 ] Parameters

[ S.49.2.4 ] Outcomes and figures

[ S.49.2.5 ] Implementation

[ S.49.2.6 ] See also

[ S.49.3 ] s_trade_autocorr_signal

[ S.49.3.1 ] Summary

[ S.49.3.2 ] Data

[ S.49.3.3 ] Parameters

[ S.49.3.4 ] Outcomes and figures

[ S.49.3.5 ] Implementation

[ S.49.3.6 ] See also

[ S.49.4 ] s_order_imbal_signal

[ S.49.4.1 ] Summary

[ S.49.4.2 ] Data

[ S.49.4.3 ] Parameters

[ S.49.4.4 ] Outcomes and figures

[ S.49.4.5 ] Implementation

[ S.49.4.6 ] See also

[ S.49.5 ] s_price_pred_signal

[ S.49.5.1 ] Summary

[ S.49.5.2 ] Data

[ S.49.5.3 ] Parameters

[ S.49.5.4 ] Outcomes and figures

[ S.49.5.5 ] Implementation

[ S.49.5.6 ] See also

[ S.49.6 ] s_volume_cluster_signal

[ S.49.6.1 ] Summary

[ S.49.6.2 ] Data

[ S.49.6.3 ] Parameters

[ S.49.6.4 ] Outcomes and figures

[ S.49.6.5 ] Implementation

[ S.49.6.6 ] See also

[ S.49.7 ] s_momentum_signals

[ S.49.7.1 ] Summary

[ S.49.7.2 ] Data

[ S.49.7.3 ] Parameters

[ S.49.7.4 ] Outcomes and figures

[ S.49.7.5 ] Implementation

[ S.49.7.6 ] See also

[ S.49.8 ] Signal filtering for systematic strategy (size)

[ S.50 ] Stochastic dominance

[ S.50.1 ] s_strong_dominance

[ S.50.1.1 ] Summary

[ S.50.1.2 ] Parameters

[ S.50.1.3 ] Outcomes and figures

[ S.50.1.4 ] Implementation

[ S.50.1.5 ] See also

[ S.50.2 ] s_weak_dominance

[ S.50.2.1 ] Summary

[ S.50.2.2 ] Parameters

[ S.50.2.3 ] Outcomes and figures

[ S.50.2.4 ] Implementation

[ S.50.2.5 ] See also

[ S.50.3 ] s_second_order_dominance

[ S.50.3.1 ] Summary

[ S.50.3.2 ] Parameters

[ S.50.3.3 ] Outcomes and figures

[ S.50.3.4 ] Implementation

[ S.51 ] Optimization primer

[ S.51.1 ] s_selection_toy

[ S.51.1.1 ] Summary

[ S.51.1.2 ] Parameters

[ S.51.1.3 ] Outcomes and figures

[ S.51.1.4 ] Implementation

[ S.51.1.5 ] See also

[ S.51.2 ] s_stock_selection

[ S.51.2.1 ] Summary

[ S.51.2.2 ] Data

[ S.51.2.3 ] Parameters

[ S.51.2.4 ] Outcomes and figures

[ S.51.2.5 ] Implementation

[ S.51.2.6 ] See also

[ S.52 ] Useful algorithms

[ S.52.1 ] Cholesky decomposition of the covariance (numerical proof)

[ S.52.2 ] Numerical proof

[ S.52.3 ] CPCA versus PCA

[ S.52.4 ] s_factor_analysis_algos

[ S.52.4.1 ] Summary

[ S.52.4.2 ] Parameters

[ S.52.4.3 ] Outcomes and figures

[ S.52.4.4 ] Implementation

[ S.52.4.5 ] See also

[ S.52.5 ] Transpose-square-root of a symmetric positive (semi)definite matrix

[ S.53 ] Matrix manipulations

[ S.53.1 ] s_spectral_theorem

[ S.53.1.1 ] Summary

[ S.53.1.2 ] Parameters

[ S.53.1.3 ] Outcomes and figures

[ S.53.1.4 ] Implementation

[ S.53.1.5 ] See also

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 ] cov_2_corr

[ 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 ] crisp_fp

[ F.1.3.1 ] Summary

[ F.1.3.2 ] Input

[ F.1.3.3 ] Output

[ F.1.3.4 ] Implementation

[ F.1.3.5 ] Example

[ F.1.3.6 ] Case studies

[ F.1.3.7 ] References

[ F.1.3.8 ] See also

[ F.1.4 ] effective_num_scenarios

[ F.1.4.1 ] Summary

[ F.1.4.2 ] Input

[ F.1.4.3 ] Output

[ 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 ] exp_decay_fp

[ 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.1.6 ] factor_analysis_mlf

[ F.1.6.1 ] Summary

[ F.1.6.2 ] Input

[ F.1.6.3 ] Output

[ F.1.6.4 ] Implementation

[ F.1.6.5 ] Example

[ F.1.6.6 ] Case studies

[ F.1.6.7 ] References

[ F.1.6.8 ] See also

[ F.1.7 ] factor_analysis_paf

[ 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.1.7.7 ] References

[ F.1.7.8 ] See also

[ F.1.8 ] fit_dcc_t

[ 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 ] See also

[ F.1.9 ] fit_factor_analysis

[ F.1.9.1 ] Summary

[ F.1.9.2 ] Input

[ F.1.9.3 ] Output

[ F.1.9.4 ] Implementation

[ F.1.9.5 ] Tips

[ F.1.9.6 ] Example

[ F.1.9.7 ] References

[ F.1.9.8 ] See also

[ F.1.10 ] fit_garch_fp

[ F.1.10.1 ] Summary

[ F.1.10.2 ] Input

[ F.1.10.3 ] Output

[ F.1.10.4 ] Implementation

[ F.1.10.5 ] Tips

[ F.1.10.6 ] Example

[ F.1.10.7 ] Case studies

[ F.1.10.8 ] See also

[ F.1.11 ] fit_lfm_lasso

[ F.1.11.1 ] Example

[ F.1.12 ] fit_lfm_lasso_path

[ F.1.12.1 ] Example

[ F.1.13 ] fit_lfm_mlfp

[ 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 ] Case studies

[ F.1.13.7 ] See also

[ F.1.14 ] fit_lfm_ols

[ F.1.14.1 ] Summary

[ F.1.14.2 ] Input

[ F.1.14.3 ] Output

[ F.1.14.4 ] Implementation

[ F.1.14.5 ] Example

[ F.1.14.6 ] Case studies

[ F.1.14.7 ] References

[ F.1.14.8 ] See also

[ F.1.15 ] fit_lfm_pcfp

[ F.1.15.1 ] Example

[ F.1.16 ] fit_lfm_ridge

[ F.1.16.1 ] Example

[ F.1.17 ] fit_lfm_ridge_path

[ F.1.17.1 ] Example

[ F.1.18 ] fit_lfm_roblasso

[ F.1.18.1 ] Example

[ F.1.19 ] fit_locdisp_mlfp

[ F.1.19.1 ] Summary

[ F.1.19.2 ] Input

[ F.1.19.3 ] Output

[ F.1.19.4 ] Implementation

[ F.1.19.5 ] Example

[ F.1.19.6 ] Case studies

[ F.1.19.7 ] See also

[ F.1.20 ] fit_locdisp_mlfp_difflength

[ F.1.20.1 ] Summary

[ F.1.20.2 ] Input

[ F.1.20.3 ] Output

[ F.1.20.4 ] Implementation

[ F.1.20.5 ] Tips

[ F.1.20.6 ] Example

[ F.1.20.7 ] Case studies

[ F.1.20.8 ] References

[ F.1.20.9 ] See also

[ F.1.21 ] fit_markov_chain

[ F.1.21.1 ] Example

[ F.1.22 ] fit_state_space

[ F.1.22.1 ] Summary

[ F.1.22.2 ] Input

[ F.1.22.3 ] Output

[ F.1.22.4 ] Implementation

[ F.1.22.5 ] Example

[ F.1.22.6 ] Case studies

[ F.1.22.7 ] References

[ F.1.22.8 ] See also

[ F.1.23 ] fit_t_dof

[ F.1.23.1 ] Example

[ F.1.24 ] fit_t_fp

[ F.1.24.1 ] Example

[ F.1.25 ] fit_var1

[ F.1.25.1 ] Summary

[ F.1.25.2 ] Input

[ F.1.25.3 ] Output

[ F.1.25.4 ] Implementation

[ F.1.25.5 ] Example

[ F.1.25.6 ] Case studies

[ F.1.25.7 ] See also

[ F.1.26 ] markov_network

[ F.1.26.1 ] Example

[ F.1.27 ] min_corr_toeplitz

[ F.1.27.1 ] Summary

[ F.1.27.2 ] Input

[ F.1.27.3 ] Output

[ F.1.27.4 ] Implementation

[ F.1.27.5 ] Example

[ F.1.27.6 ] Case studies

[ F.1.28 ] smooth_kernel_fp

[ F.1.28.1 ] Summary

[ F.1.28.2 ] Input

[ F.1.28.3 ] Output

[ F.1.28.4 ] Implementation

[ F.1.28.5 ] Example

[ F.1.28.6 ] Case studies

[ F.1.28.7 ] References

[ F.1.28.8 ] See also

[ F.1.29 ] spectrum_shrink

[ F.1.29.1 ] Example

[ F.1.30 ] var2mvou

[ F.1.30.1 ] Summary

[ F.1.30.2 ] Input

[ F.1.30.3 ] Output

[ F.1.30.4 ] Implementation

[ F.1.30.5 ] Tips

[ F.1.30.6 ] Example

[ F.1.30.7 ] Case studies

[ F.1.30.8 ] References

[ F.1.31 ] Generate FP profiles via multivariate Gaussian kernel: function implementation

[ F.1.32 ] Expectation Maximization algorithm with flexible probabilities for Missing Values. Routine

[ F.1.33 ] Homogeneous correlation cluster shrinkage

[ F.1.34 ] Iterated generalized method of moments with flexible probabilities for the Poisson distribution

[ F.1.35 ] Minimum volume ellipsoid enclosing data. Routine

[ F.1.36 ] Farthest Outlier Detection. Routine

[ F.1.37 ] High breakdown point with flexible probabilities. Routine

[ F.1.38 ] Outlier detection with flexible probabilities. Routine

[ F.1.39 ] SMTCovariance

[ F.1.40 ] FitFractionalIntegration

[ F.1.41 ] FitGenParetoMLFP

[ F.1.42 ] NormalMixtureFit

[ F.1.43 ] FitSkewtMLFP

[ F.1.44 ] FitVar_ATMSVI

[ F.1.45 ] GarchResiduals

[ F.1.46 ] MMFP

[ F.1.47 ] kMeansClustering

[ F.1.48 ] QuantileGenParetoMLFP

[ F.1.49 ] ObjectiveToeplitz

[ F.2 ] Portfolio

[ F.3 ] Pricing

[ F.3.1 ] bond_value

[ F.3.1.1 ] Summary

[ F.3.1.2 ] Input

[ F.3.1.3 ] Output

[ 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 ] Example

[ F.3.3 ] bsm_price

[ F.3.3.1 ] Example

[ F.3.4 ] cash_flow_reinv

[ 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.3.5 ] fit_nelson_siegel_bonds

[ F.3.5.1 ] Example

[ F.3.6 ] fit_nelson_siegel_yield

[ F.3.6.1 ] Example

[ F.3.7 ] implvol_delta2m_moneyness

[ F.3.7.1 ] Summary

[ F.3.7.2 ] Input

[ F.3.7.3 ] Output

[ F.3.7.4 ] Implementation

[ F.3.7.5 ] Example

[ F.3.7.6 ] Case studies

[ F.3.7.7 ] References

[ F.3.8 ] ytm_shadowrates

[ 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 ] nelson_siegel_yield

[ 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 ] shadowrates_ytm

[ 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 ] sdf_mre

[ F.3.11.1 ] Summary

[ F.3.11.2 ] Input

[ F.3.11.3 ] Output

[ F.3.11.4 ] Implementation

[ F.3.11.5 ] Tips

[ F.3.11.6 ] Example

[ F.3.11.7 ] Case studies

[ F.3.11.8 ] References

[ F.3.11.9 ] See also

[ F.3.12 ] zcb_value

[ F.3.12.1 ] Summary

[ F.3.12.2 ] Input

[ F.3.12.3 ] Output

[ F.3.12.4 ] Implementation

[ F.3.12.5 ] Example

[ F.3.12.6 ] Case studies

[ F.3.12.7 ] References

[ F.3.12.8 ] See also

[ F.3.13 ] Vasicek yield curve

[ F.3.14 ] Regularized put option payoff function

[ F.3.15 ] Regularized call option payoff function

[ 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 ] Example

[ F.4.2 ] cdf_sp

[ F.4.2.1 ] Summary

[ F.4.2.2 ] Input

[ F.4.2.3 ] Output

[ 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 ] Case studies

[ F.4.4.7 ] References

[ F.4.4.8 ] 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 ] ewma_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 ] Case studies

[ 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 ] kalman_filter

[ F.4.8.1 ] Example

[ F.4.8.2 ] References

[ F.4.9 ] kstest_ts

[ F.4.9.1 ] Example

[ F.4.10 ] marchenko_pastur

[ F.4.10.1 ] Example

[ F.4.11 ] meancov_sp

[ F.4.11.1 ] Summary

[ F.4.11.2 ] Input

[ F.4.11.3 ] Output

[ F.4.11.4 ] Implementation

[ F.4.11.5 ] Tips

[ F.4.11.6 ] Example

[ F.4.11.7 ] Case studies

[ F.4.11.8 ] References

[ F.4.12 ] meancov_inverse_wishart

[ F.4.12.1 ] Summary

[ F.4.12.2 ] Input

[ F.4.12.3 ] Output

[ F.4.12.4 ] Implementation

[ F.4.12.5 ] Example

[ F.4.12.6 ] Case studies

[ F.4.12.7 ] References

[ F.4.13 ] meancov_wishart

[ F.4.13.1 ] Summary

[ F.4.13.2 ] Input

[ F.4.13.3 ] Output

[ F.4.13.4 ] Implementation

[ F.4.13.5 ] Example

[ F.4.13.6 ] Case studies

[ F.4.13.7 ] References

[ F.4.14 ] moments_logn

[ F.4.15 ] moments_mvou

[ 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 ] multi_r2

[ F.4.16.1 ] Summary

[ F.4.16.2 ] Input

[ F.4.16.3 ] Output

[ F.4.16.4 ] Implementation

[ F.4.16.5 ] Example

[ F.4.16.6 ] See also

[ F.4.17 ] mvt_pdf

[ 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 ] mvt_logpdf

[ F.4.18.1 ] Example

[ F.4.19 ] normal_canonical

[ F.4.19.1 ] Summary

[ F.4.19.2 ] Input

[ F.4.19.3 ] Output

[ F.4.19.4 ] Implementation

[ F.4.19.5 ] Example

[ F.4.19.6 ] Case studies

[ F.4.19.7 ] References

[ F.4.20 ] objective_r2

[ 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 ] Case studies

[ F.4.20.7 ] See also

[ F.4.21 ] plot_all_tests

[ F.4.21.1 ] Example

[ F.4.22 ] plot_copula_test

[ F.4.22.1 ] Example

[ F.4.23 ] plot_kstest

[ F.4.23.1 ] Example

[ F.4.24 ] quantile_sp

[ F.4.24.1 ] Summary

[ F.4.24.2 ] Input

[ F.4.24.3 ] Output

[ F.4.24.4 ] Implementation

[ F.4.24.5 ] Example

[ F.4.24.6 ] References

[ F.4.25 ] pdf_sp

[ F.4.25.1 ] Summary

[ F.4.25.2 ] Input

[ F.4.25.3 ] Output

[ 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 ] Example

[ F.4.27 ] random_split

[ F.4.27.1 ] Example

[ 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 ] Example

[ F.4.30 ] scoring

[ F.4.30.1 ] Example

[ 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 ] Example

[ F.4.34 ] simulate_markov_chain

[ F.4.34.1 ] Example

[ F.4.35 ] simulate_mvou

[ F.4.35.1 ] Summary

[ F.4.35.2 ] Input

[ F.4.35.3 ] Output

[ F.4.35.4 ] Implementation

[ F.4.35.5 ] Tips

[ F.4.35.6 ] Example

[ F.4.35.7 ] Case studies

[ F.4.35.8 ] References

[ F.4.35.9 ] See also

[ F.4.36 ] simulate_normal

[ 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_dimred

[ F.4.37.1 ] Example

[ F.4.38 ] simulate_quadn

[ F.4.38.1 ] Summary

[ F.4.38.2 ] Input

[ F.4.38.3 ] Output

[ F.4.38.4 ] Implementation

[ F.4.38.5 ] Example

[ F.4.38.6 ] Case studies

[ F.4.38.7 ] References

[ F.4.38.8 ] See also

[ F.4.39 ] simulate_rw_hfp

[ F.4.39.1 ] Example

[ F.4.40 ] simulate_t

[ F.4.40.1 ] Summary

[ F.4.40.2 ] Input

[ F.4.40.3 ] Output

[ F.4.40.4 ] Implementation

[ F.4.40.5 ] Tips

[ F.4.40.6 ] Example

[ F.4.40.7 ] References

[ F.4.40.8 ] See also

[ F.4.41 ] simulate_unif_in_ellips

[ 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 ] Case studies

[ F.4.41.8 ] References

[ F.4.41.9 ] See also

[ F.4.42 ] simulate_var1

[ F.4.42.1 ] Summary

[ F.4.42.2 ] Input

[ F.4.42.3 ] Output

[ F.4.42.4 ] Implementation

[ F.4.42.5 ] Example

[ F.4.42.6 ] Case studies

[ F.4.42.7 ] References

[ F.4.42.8 ] See also

[ F.4.43 ] simulate_wishart

[ 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 ] smooth_quantile

[ F.4.44.1 ] Example

[ F.4.45 ] smoothing

[ F.4.45.1 ] Example

[ 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 ] Pdf of a multivariate normal copula, implementation

[ F.4.50 ] Pdf of a multivariate t-copula

[ 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.4.74 ] VGpdf

[ F.4.75 ] SmoothStep

[ F.4.76 ] SpinOutlier

[ F.4.77 ] ShiftedVGMoments

[ F.4.78 ] ParamChangeVG

[ 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 ] Example

[ 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.6.4.1 ] Example

[ F.6.5 ] cpca_cov

[ F.6.5.1 ] Summary

[ F.6.5.2 ] Input

[ F.6.5.3 ] Output

[ 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 ] forward_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.6.7 ] gram_schmidt

[ F.6.7.1 ] Summary

[ F.6.7.2 ] Input

[ F.6.7.3 ] Output

[ F.6.7.4 ] Implementation

[ F.6.7.5 ] Tips

[ F.6.7.6 ] Example

[ F.6.7.7 ] Case studies

[ F.6.7.8 ] References

[ F.6.8 ] histogram_sp

[ 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 ] Case studies

[ F.6.8.7 ] References

[ F.6.9 ] histogram2d_sp

[ F.6.9.1 ] Example

[ F.6.10 ] mahalanobis_dist

[ 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.6.10.7 ] References

[ F.6.11 ] naive_selection

[ 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.6.12 ] pca_cov

[ 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.6.12.7 ] See also

[ F.6.13 ] plot_dynamic_strats

[ F.6.13.1 ] Example

[ F.6.14 ] plot_ellipse

[ F.6.14.1 ] Summary

[ F.6.14.2 ] Input

[ F.6.14.3 ] Output

[ F.6.14.4 ] Implementation

[ F.6.14.5 ] Example

[ F.6.14.6 ] Case studies

[ F.6.14.7 ] References

[ F.6.14.8 ] See also

[ F.6.15 ] plot_ellipsoid

[ F.6.15.1 ] Example

[ F.6.16 ] quad_prog

[ F.6.16.1 ] Example

[ F.6.17 ] sector_select

[ F.6.17.1 ] Example

[ F.6.18 ] smart_solve

[ F.6.18.1 ] Example

[ F.6.19 ] solve_riccati

[ F.6.19.1 ] Summary

[ F.6.19.2 ] Input

[ F.6.19.3 ] Output

[ F.6.19.4 ] Implementation

[ F.6.19.5 ] Tips

[ F.6.19.6 ] Example

[ F.6.19.7 ] Case studies

[ F.6.19.8 ] References

[ F.6.20 ] test_ellipsoid

[ F.6.20.1 ] Summary

[ F.6.20.2 ] Input

[ F.6.20.3 ] Output

[ F.6.20.4 ] Implementation

[ F.6.20.5 ] Tips

[ F.6.20.6 ] Example

[ F.6.20.7 ] Case studies

[ F.6.20.8 ] References

[ F.6.20.9 ] See also

[ F.6.21 ] trade_quote_processing

[ F.6.21.1 ] Example

[ F.6.22 ] trade_quote_spreading

[ F.6.22.1 ] Example

[ F.6.23 ] transpose_square_root

[ F.6.23.1 ] Summary

[ F.6.23.2 ] Input

[ F.6.23.3 ] Output

[ F.6.23.4 ] Implementation

[ F.6.23.5 ] Example

[ F.6.23.6 ] Case studies

[ F.6.23.7 ] References

[ F.6.23.8 ] See also

[ F.6.24 ] Multivariate uncertainty band function

[ F.6.25 ] Log2Lin

[ F.6.26 ] MatchTime

[ F.6.27 ] binningHFseries

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