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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 ] s_bond_convergence

[ S.1.3.1 ] Summary

[ S.1.3.2 ] Data

[ S.1.3.3 ] Parameters

[ S.1.3.4 ] Outcomes and figures

[ S.1.3.5 ] Implementation

[ S.1.3.6 ] See also

[ S.1.4 ] Zero-coupon bond rolling price

[ S.1.5 ] s_logrollvalues_vs_yields

[ 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_yield_curve_evolution

[ 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 ] Log-yield representation

[ S.1.8 ] s_analyze_rates_jgb

[ 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 ] Shadow rates evolution

[ S.1.10 ] Nelson-Siegel parametrization of ...

[ S.1.11 ] Nelson-Siegel parametrization of ...

[ S.1.12 ] Call options value

[ S.1.13 ] Call options normalized value

[ S.1.14 ] Implied volatility surface

[ S.1.15 ] Delta parametrization of the impl...

[ S.1.16 ] Log-implied volatility

[ S.1.17 ] Inverse-call implied volatility

[ S.1.18 ] Market quotes in delta-moneyness ...

[ S.1.19 ] SVI parametrization of the implie...

[ S.1.20 ] s_fx_rates_vs_logrates

[ S.1.20.1 ] Summary

[ S.1.20.2 ] Data

[ S.1.20.3 ] Outcomes and figures

[ S.1.20.4 ] Implementation

[ S.1.21 ] Cumulative number of rating migra...

[ S.1.22 ] s_default_merton_model

[ S.1.22.1 ] Summary

[ S.1.22.2 ] Parameters

[ S.1.22.3 ] Outcomes and figures

[ S.1.22.4 ] Implementation

[ S.1.23 ] s_high_freq_stock_var

[ S.1.23.1 ] Summary

[ S.1.23.2 ] Data

[ S.1.23.3 ] Parameters

[ S.1.23.4 ] Outcomes and figures

[ S.1.23.5 ] Implementation

[ S.1.23.6 ] See also

[ S.1.24 ] High frequency flow variables

[ S.1.25 ] s_high_freq_tick_time

[ S.1.25.1 ] Summary

[ S.1.25.2 ] Data

[ S.1.25.3 ] Parameters

[ S.1.25.4 ] Outcomes and figures

[ S.1.25.5 ] Implementation

[ S.1.25.6 ] See also

[ S.1.26 ] Volume time activity evolution of...

[ S.1.27 ] Vasicek fit of the yield curve

[ S.1.28 ] Heston parametrization of the imp...

[ S.1.29 ] Rating thresholds and Merton mode...

[ S.1.30 ] s_checklist_scenariobased_step01

[ S.2 ] Quest for invariance

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

[ S.2.2 ] Kolmogorov-Smirnov test for invar...

[ S.2.3 ] Ellipsoid test for invariance on ...

[ S.2.4 ] Kolmogorov-Smirnov test for invar...

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

[ S.2.6 ] Kolmogorov-Smirnov test for invar...

[ 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 invar...

[ S.2.9 ] Ellipsoid test for invariance on ...

[ S.2.10 ] Kolmogorov-Smirnov test for invar...

[ S.2.11 ] Ellipsoid test for invariance on ...

[ S.2.12 ] Kolmogorov-Smirnov test for invar...

[ S.2.13 ] Ellipsoid test for invariance in ...

[ S.2.14 ] Kolmogorov-Smirnov test for invar...

[ S.2.15 ] Ellipsoid test for invariance on ...

[ S.2.16 ] Kolmogorov-Smirnov test for invar...

[ S.2.17 ] Ellipsoid test for invariance on ...

[ S.2.18 ] Kolmogorov-Smirnov test for invar...

[ S.2.19 ] Estimation of a quantile of a mix...

[ 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 sp...

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

[ S.2.24 ] Long Memory in high frequency tra...

[ S.2.25 ] Long Memory in high frequency tra...

[ S.2.26 ] Volatility clustering in the stoc...

[ S.2.27 ] Volatility Clustering in the stoc...

[ S.2.28 ] P&L realizations modeled by a GAR...

[ S.2.29 ] Ellipsoid test for invariance on ...

[ S.2.30 ] Stochastic volatility and leverag...

[ S.2.31 ] Implied leverage effect

[ S.2.32 ] s_fit_shadowrates_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 o...

[ S.2.35 ] Invariants for a call option

[ S.2.36 ] s_fit_garch_stocks

[ S.2.37 ] s_checklist_scenariobased_step02

[ S.3 ] Estimation

[ S.3.1 ] Standard deviation estimation wit...

[ S.3.2 ] State crisp probabilities

[ S.3.3 ] Time exponential decay probabilit...

[ S.3.4 ] Gaussian kernel and state conditi...

[ S.3.5 ] Approximation of the true distrib...

[ S.3.6 ] s_min_entropy_fp

[ S.3.6.1 ] Summary

[ S.3.6.2 ] Data

[ S.3.6.3 ] Parameters

[ S.3.6.4 ] Outcomes and figures

[ S.3.6.5 ] Implementation

[ S.3.6.6 ] See also

[ S.3.7 ] Glivenko-Cantelli theorem - Appli...

[ S.3.8 ] HFP ellipsoid dependence on flexi...

[ S.3.9 ] HFP quantile dependence on flexib...

[ S.3.10 ] Maximum of the effective number o...

[ S.3.11 ] Quantile estimation: maximum like...

[ S.3.12 ] Consistency of the maximum likeli...

[ S.3.13 ] MLFP estimators for elliptical va...

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

[ 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 flexi...

[ S.3.17 ] Quantile function tail approximat...

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

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

[ S.3.20 ] Sample mean and sample median bre...

[ S.3.21 ] Minimum volume ellipsoid enclosin...

[ S.3.22 ] Farthest outlier detection

[ S.3.23 ] High breakdown point with flexibl...

[ S.3.24 ] Robustness comparison between HFP...

[ S.3.25 ] Method of moments with flexible p...

[ S.3.26 ] Generalized method of moments wit...

[ S.3.27 ] P&L unconditional distribution

[ S.3.28 ] MLFP estimation of unconditional ...

[ S.3.29 ] MLFP estimation of unconditional ...

[ S.3.30 ] Non-synchronous data

[ S.3.31 ] Outlier detection with flexible p...

[ S.3.32 ] s_default_probabilities

[ S.3.33 ] Expectation-maximization with fle...

[ 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 p...

[ S.3.38 ] Hellinger distance and diversity ...

[ S.3.39 ] Ensemble FP: curse of dimensional...

[ S.3.40 ] Likelihood with flexible probabil...

[ S.3.41 ] Alternative FP specifications: bo...

[ S.3.42 ] Alternative FP specifications: Di...

[ S.3.43 ] Copula-marginal estimation for th...

[ S.3.44 ] Copula-marginal estimation for in...

[ S.3.45 ] Standardization of invariants’ ...

[ 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 homogen...

[ S.3.50 ] EWMA: numerical example

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

[ 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...

[ S.3.57 ] Random matrix theory: Marchenko-P...

[ S.3.58 ] Numerical integration of Marchenk...

[ S.3.59 ] Spectrum of the covariance matrix...

[ S.3.60 ] Spectrum of the covariance matrix...

[ 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 shri...

[ S.3.63 ] Shrinkage estimator of location: ...

[ S.3.64 ] Sample covariance and eigenvalue ...

[ S.3.65 ] Shrinkage estimator of dispersion...

[ S.3.66 ] Random matrix theory: Wigner semi...

[ S.3.67 ] Shrinkage estimators of location:...

[ 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: applica...

[ 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...

[ S.3.76 ] Estimation assessment of a moment...

[ S.3.77 ] Estimation assessment of the quan...

[ S.3.78 ] Estimation assessment of the quan...

[ 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...

[ S.3.82 ] Sample quantiles distribution

[ S.3.83 ] Distribution of conditioning vari...

[ S.3.84 ] s_checklist_scenariobased_steps03...

[ S.3.85 ] s_checklist_scenariobased_step03

[ S.4 ] Projection

[ S.4.1 ] Projection of historical with fle...

[ S.4.2 ] Projection of the reflected shift...

[ S.4.3 ] Sum of random variables via simul...

[ S.4.4 ] Empirical verification of the squ...

[ S.4.5 ] Projection of higher-order standa...

[ S.4.6 ] Projection of the GARCH process

[ S.4.7 ] s_projection_shadow_rates

[ 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 ...

[ 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...

[ S.4.11 ] Projection of a MVOU process with...

[ S.4.12 ] Multivariate GARCH: fit and proje...

[ S.4.13 ] Equity market: linear vs. compoun...

[ S.4.14 ] Projection of shadow rates via Mo...

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

[ S.4.16 ] Projection of risk drivers whose ...

[ 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 approac...

[ S.4.20 ] Historical projection: bootstrap

[ S.4.21 ] Projection via historical bootstr...

[ S.4.22 ] Hybrid Monte Carlo-historical pro...

[ S.4.23 ] Hybrid historical and Monte Carlo...

[ S.4.24 ] Copula-marginal projection for ri...

[ S.4.25 ] Risk propagation in the Heston pr...

[ S.4.26 ] s_checklist_scenariobased_steps03...

[ 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...

[ 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...

[ S.5.11 ] Call option value: parametric pro...

[ 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 approximat...

[ 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 nor...

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

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

[ 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...

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

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

[ 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 ...

[ 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: scen...

[ 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 stock...

[ 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_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-p...

[ 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 appl...

[ 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 tra...

[ 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 ...

[ 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 optimizat...

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

[ S.9a.2 ] Mean-variance robust efficient fr...

[ S.9a.3 ] s_checklist_scenariobased_step09

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

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

[ S.9b.1 ] Characteristic portfolio construc...

[ 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_re...

[ 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 strateg...

[ 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 mode...

[ 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 trajector...

[ S.10.3 ] Non-monotone trading trajectories...

[ 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_quan...

[ 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 multi...

[ S.10.7 ] Liquidation trajectory and tradin...

[ S.10.8 ] Liquidation trajectory and tradin...

[ 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_executive_summary_lfm

[ 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...

[ 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_regression_ols_fit

[ 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 formula...

[ 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: join...

[ 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 ...

[ S.12.12 ] Cross-sectional factor extraction...

[ S.12.13 ] Cross-sectional LFM’s optimal r...

[ S.12.14 ] Factor-replicating portfolio conv...

[ 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...

[ 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 gener...

[ S.12.21 ] Correlation of residuals in gener...

[ S.12.22 ] Hidden regression versus Principa...

[ S.12.23 ] Symmetric regression: numerical e...

[ 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...

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

[ S.13.4 ] Regression LFM’s: generalized r...

[ S.13.5 ] Principal-component LFM’s: trun...

[ S.13.6 ] Cross-sectional LFM’s: generali...

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

[ S.14.1 ] Regression LFM’s: shifted-logno...

[ 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_p...

[ 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_logn_quant_regression

[ S.15.5.1 ] Summary

[ S.15.5.2 ] Parameters

[ S.15.5.3 ] Outcomes and figures

[ S.15.5.4 ] Implementation

[ S.15.5.5 ] See also

[ 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_logn_quant_lin_regression

[ S.15.7.1 ] Summary

[ S.15.7.2 ] Parameters

[ S.15.7.3 ] Outcomes and figures

[ S.15.7.4 ] Implementation

[ S.15.7.5 ] See also

[ S.15.8 ] s_supervised_point_prediction

[ S.15.8.1 ] Summary

[ S.15.8.2 ] Parameters

[ S.15.8.3 ] Outcomes and figures

[ S.15.8.4 ] Implementation

[ S.15.8.5 ] See also

[ S.15.9 ] s_continuum_discrete_kmeans

[ S.15.9.1 ] Summary

[ S.15.9.2 ] Parameters

[ S.15.9.3 ] Outcomes and figures

[ S.15.9.4 ] Implementation

[ S.15.10 ] s_bias_vs_variance_lognormal

[ S.16 ] Estimation and assessment

[ S.16.1 ] Predictive distribution assessmen...

[ 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.18 ] Deep learning

[ 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 ...

[ S.20.1 ] Eigenvectors for Toeplitz structu...

[ 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 re...

[ 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 compar...

[ 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 pric...

[ 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 as...

[ 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-replicati...

[ S.28 ] Non-linear pricing theory

[ S.29 ] Valuation implementation

[ S.29.1 ] Fitting implied volatility from t...

[ S.29.2 ] Fitting yield curve from the Vasi...

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 ] Multivariate distributions

[ 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 entro...

[ S.36.14 ] Numerical verification of the gra...

[ S.36.15 ] Numerical verification of gradien...

[ S.36.16 ] Numerical verification of the Hes...

[ S.36.17 ] Numerical and analytical Hessian ...

[ S.36.18 ] Copula opinion pooling: uninforma...

[ 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...

[ S.38.3 ] Euclidean vectors of joint lognor...

[ S.38.4 ] Orthogonality of principal direct...

[ S.38.5 ] Euclidean vectors via linear tran...

[ S.39 ] Geometry of distributions

[ S.40 ] Decision theory with model uncert...

[ S.41 ] Copulas

[ S.41.1 ] Display copula of a bivariate nor...

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

[ 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 dis...

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

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

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

[ S.41.8 ] Separation: from FP-joint to copu...

[ S.41.9 ] Combination: from FP-copula/margi...

[ S.41.10 ] Combination: from FP-copula/histo...

[ S.41.11 ] s_copula_returns

[ S.41.11.1 ] 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 normal copula/m...

[ S.41.13 ] Combination: from t-copula/margin...

[ S.41.14 ] Separation: from historical joint...

[ S.41.15 ] Display the pdf of a bivariate t-...

[ 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 m...

[ S.42.3 ] Ellipsoid and uncertainty band of...

[ S.42.4 ] Ellipsoid and uncertainty band of...

[ S.42.5 ] Ellipsoid and uncertainty band of...

[ S.42.6 ] Affine transformation of a bivari...

[ S.42.7 ] Location-dispersion ellipsoid and...

[ S.42.8 ] Iso-contour of a lognormal bivari...

[ S.42.9 ] s_chebyshev_ineq

[ S.42.9.1 ] Summary

[ S.42.9.2 ] Parameters

[ S.42.9.3 ] Outcomes and figures

[ S.42.9.4 ] Implementation

[ S.42.9.5 ] See also

[ S.42.10 ] Expectation-covariance as minimum...

[ S.43 ] Correlation and generalizations

[ S.43.1 ] Schweizer-Wolff measure between n...

[ S.43.2 ] Normalization constant of Schweiz...

[ S.43.3 ] Normal copula and Frechet-Hoeffdi...

[ S.43.4 ] Smooth approximation of call and ...

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

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

[ S.43.7 ] Correlation between normal variab...

[ S.43.8 ] Correlation between lognormal var...

[ S.43.9 ] Correlation between normalized Wi...

[ S.43.10 ] Correlation: normal stock prices,...

[ S.43.11 ] Uncorrelation versus independence

[ S.43.12 ] Uncorrelation versus independence...

[ 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 invar...

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

[ S.44.4 ] Invariance tests on realized time...

[ 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 process...

[ S.46.5 ] Projection of a Compound Poisson ...

[ S.46.6 ] Projection of Cauchy distribution

[ S.46.7 ] Projection of the variance gamma ...

[ S.46.8 ] Simulate the NIG and VG processes

[ S.46.9 ] Simulation of the variance gamma ...

[ S.46.10 ] Projection of the Student t distr...

[ S.46.11 ] Projection of the uniform distrib...

[ S.46.12 ] Projection of fractional Brownian...

[ S.46.13 ] Projection of the Heston process

[ S.46.14 ] Simulation of the Heston process ...

[ S.47 ] First order autoregression

[ S.47.1 ] Simulation of a Ornstein-Uhlenbec...

[ S.47.2 ] MVOU change of coordinates

[ S.47.3 ] Projection of conditional mean an...

[ S.48 ] Spectral analysis

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

[ S.48.2 ] Spectral representation of AR(1) ...

[ S.48.3 ] Bandpass filter applied to AR(1) ...

[ 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 s...

[ S.50 ] Stochastic dominance

[ S.50.1 ] Strong dominance

[ S.50.2 ] Weak dominance

[ S.50.3 ] Second order dominance

[ S.51 ] Optimization primer

[ S.51.1 ] s_selection_toy

[ 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 cov...

[ S.52.2 ] Numerical proof

[ S.52.3 ] CPCA versus PCA

[ S.52.4 ] Implementation of factor analysis...

[ S.52.5 ] Transpose-square-root of a symmet...

[ S.52.6 ] Monte Carlo with flexible probabi...

[ S.53 ] Matrix manipulations

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 ] cov2corr

[ 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.1.3 ] 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_garch_fp

[ 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 ] Case studies

[ F.1.9.8 ] See also

[ F.1.10 ] fit_lfm_lasso

[ F.1.10.1 ] Example

[ F.1.11 ] fit_lfm_lasso_path

[ F.1.11.1 ] Example

[ F.1.12 ] fit_lfm_mlfp

[ F.1.12.1 ] Summary

[ F.1.12.2 ] Input

[ F.1.12.3 ] Output

[ F.1.12.4 ] Implementation

[ F.1.12.5 ] Example

[ F.1.12.6 ] Case studies

[ F.1.12.7 ] See also

[ F.1.13 ] fit_lfm_ols

[ 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_pcfp

[ F.1.14.1 ] Example

[ F.1.15 ] fit_lfm_ridge

[ F.1.15.1 ] Example

[ F.1.16 ] fit_lfm_ridge_path

[ F.1.16.1 ] Example

[ F.1.17 ] fit_lfm_roblasso

[ F.1.17.1 ] Example

[ F.1.18 ] fit_locdisp_mlfp

[ F.1.18.1 ] Summary

[ F.1.18.2 ] Input

[ F.1.18.3 ] Output

[ F.1.18.4 ] Implementation

[ F.1.18.5 ] Example

[ F.1.18.6 ] Case studies

[ F.1.18.7 ] See also

[ F.1.19 ] fit_locdisp_mlfp_difflength

[ F.1.19.1 ] Summary

[ F.1.19.2 ] Input

[ F.1.19.3 ] Output

[ F.1.19.4 ] Implementation

[ F.1.19.5 ] Tips

[ F.1.19.6 ] Example

[ F.1.19.7 ] Case studies

[ F.1.19.8 ] References

[ F.1.19.9 ] See also

[ F.1.20 ] fit_markov_chain

[ F.1.20.1 ] Example

[ F.1.21 ] fit_state_space

[ F.1.21.1 ] Example

[ F.1.22 ] fit_t_dof

[ F.1.22.1 ] Example

[ F.1.23 ] fit_t_fp

[ F.1.23.1 ] Example

[ F.1.24 ] fit_var1

[ 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 ] See also

[ F.1.25 ] markov_network

[ F.1.25.1 ] Example

[ F.1.26 ] min_corr_toeplitz

[ F.1.26.1 ] Summary

[ F.1.26.2 ] Input

[ F.1.26.3 ] Output

[ F.1.26.4 ] Implementation

[ F.1.26.5 ] Example

[ F.1.26.6 ] Case studies

[ F.1.27 ] spectrum_shrink

[ F.1.27.1 ] Example

[ F.1.28 ] var2mvou

[ 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.1.29 ] Generate FP profiles via multivar...

[ F.1.30 ] Expectation Maximization algorith...

[ F.1.31 ] Homogeneous correlation cluster s...

[ F.1.32 ] Iterated generalized method of mo...

[ F.1.33 ] Minimum volume ellipsoid enclosin...

[ F.1.34 ] Farthest Outlier Detection. Routi...

[ F.1.35 ] High breakdown point with flexibl...

[ F.1.36 ] Outlier detection with flexible p...

[ F.1.37 ] SMTCovariance

[ F.1.38 ] FitFractionalIntegration

[ F.1.39 ] FitGenParetoMLFP

[ F.1.40 ] NormalMixtureFit

[ F.1.41 ] FitSkewtMLFP

[ F.1.42 ] FitVar_ATMSVI

[ F.1.43 ] GarchResiduals

[ F.1.44 ] MMFP

[ F.1.45 ] kMeansClustering

[ F.1.46 ] QuantileGenParetoMLFP

[ F.1.47 ] ObjectiveToeplitz

[ F.2 ] Portfolio

[ F.3 ] Pricing

[ F.3.1 ] bond_value

[ F.3.1.1 ] Example

[ 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 ] Example

[ 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

[ F.3.7.1 ] Example

[ F.3.8 ] implvol_delta2m_moneyness

[ F.3.8.1 ] Example

[ F.3.9 ] inverse_call

[ 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 ] Example

[ F.3.11 ] perpetual_american_call

[ F.3.11.1 ] Example

[ F.3.12 ] rollvalue_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.3.13 ] rollvalue_ytm

[ F.3.13.1 ] Summary

[ F.3.13.2 ] Input

[ F.3.13.3 ] Output

[ F.3.13.4 ] Implementation

[ F.3.13.5 ] Example

[ F.3.13.6 ] Case studies

[ F.3.13.7 ] References

[ F.3.14 ] sdf_mre

[ F.3.14.1 ] Summary

[ F.3.14.2 ] Input

[ F.3.14.3 ] Output

[ F.3.14.4 ] Implementation

[ F.3.14.5 ] Tips

[ F.3.14.6 ] Example

[ F.3.14.7 ] Case studies

[ F.3.14.8 ] References

[ F.3.14.9 ] See also

[ F.3.15 ] zcb_value

[ F.3.15.1 ] Example

[ F.3.16 ] Vasicek yield curve

[ F.3.17 ] Regularized put option payoff fun...

[ F.3.18 ] Regularized call option payoff fu...

[ F.3.19 ] Stochastic discount factor and ke...

[ F.3.20 ] BachelierCallPrice

[ F.3.21 ] BondPriceNelSieg

[ F.3.22 ] blsimpv

[ F.3.23 ] FilterStochasticVolatility

[ F.3.24 ] FitCIR_FP

[ F.3.25 ] FitHeston

[ F.3.26 ] FitStochasticVolatilityModel

[ F.3.27 ] FitSigmaSVI

[ F.3.28 ] FitVasicek

[ F.3.29 ] HestonChFun

[ F.3.30 ] CallPriceHestonFFT

[ F.3.31 ] MapSVIparams

[ F.3.32 ] SigmaSVI

[ F.3.33 ] StochTime

[ F.3.34 ] RollPrices2Prices

[ F.3.35 ] 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.4.2.8 ] See also

[ F.4.3 ] cop_marg_comb

[ F.4.4 ] cop_marg_sep

[ F.4.4.1 ] Example

[ 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 ] kalman_filter

[ F.4.7.1 ] Example

[ F.4.8 ] kstest_ts

[ F.4.8.1 ] Example

[ F.4.9 ] marchenko_pastur

[ F.4.9.1 ] Example

[ F.4.10 ] meancov_sp

[ F.4.10.1 ] Summary

[ F.4.10.2 ] Input

[ F.4.10.3 ] Output

[ F.4.10.4 ] Implementation

[ F.4.10.5 ] Tips

[ F.4.10.6 ] Example

[ F.4.10.7 ] Case studies

[ F.4.10.8 ] References

[ F.4.11 ] moments_logn

[ F.4.12 ] moments_mvou

[ F.4.12.1 ] Example

[ F.4.13 ] multi_r2

[ F.4.13.1 ] Example

[ F.4.14 ] mvt_pdf

[ F.4.14.1 ] Example

[ F.4.15 ] mvt_logpdf

[ F.4.15.1 ] Example

[ F.4.16 ] objective_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 ] Case studies

[ F.4.16.7 ] See also

[ F.4.17 ] plot_all_tests

[ F.4.17.1 ] Example

[ F.4.18 ] plot_copula_test

[ F.4.18.1 ] Example

[ F.4.19 ] plot_kstest

[ F.4.19.1 ] Example

[ F.4.20 ] quantile_sp

[ F.4.20.1 ] Example

[ F.4.21 ] pdf_sp

[ 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 ] project_trans_matrix

[ F.4.22.1 ] Example

[ F.4.23 ] random_split

[ F.4.23.1 ] Example

[ F.4.24 ] saddle_point_quadn

[ F.4.24.1 ] Example

[ F.4.25 ] schweizer_wolff

[ F.4.25.1 ] Example

[ F.4.26 ] scoring

[ F.4.26.1 ] Example

[ F.4.27 ] simulate_garch

[ 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 ] See also

[ F.4.28 ] simulate_niw

[ F.4.28.1 ] Example

[ F.4.29 ] simulate_bm

[ F.4.29.1 ] Example

[ F.4.30 ] simulate_markov_chain

[ F.4.30.1 ] Example

[ F.4.31 ] simulate_mvou

[ F.4.31.1 ] Example

[ F.4.32 ] simulate_normal

[ F.4.32.1 ] Summary

[ F.4.32.2 ] Input

[ F.4.32.3 ] Output

[ F.4.32.4 ] Implementation

[ F.4.32.5 ] Tips

[ F.4.32.6 ] Example

[ F.4.32.7 ] Case studies

[ F.4.32.8 ] References

[ F.4.32.9 ] See also

[ F.4.33 ] simulate_normal_dimred

[ F.4.33.1 ] Example

[ F.4.34 ] simulate_quadn

[ F.4.34.1 ] Example

[ F.4.35 ] simulate_rw_hfp

[ F.4.35.1 ] Example

[ F.4.36 ] simulate_t

[ F.4.36.1 ] Example

[ F.4.37 ] simulate_unif_in_ellips

[ 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_var1

[ F.4.38.1 ] Example

[ F.4.39 ] smooth_quantile

[ F.4.39.1 ] Example

[ F.4.40 ] smoothing

[ F.4.40.1 ] Example

[ F.4.41 ] twist_prob_mom_match

[ F.4.41.1 ] Example

[ F.4.42 ] twist_scenarios_mom_match

[ 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 ] Flexible probabilities and scenar...

[ F.4.44 ] Pdf of a multivariate normal copu...

[ F.4.45 ] Pdf of a multivariate t-copula

[ F.4.46 ] Elliptical Copula Scenarios via d...

[ F.4.47 ] Normalized empirical histogram of...

[ F.4.48 ] Metropolis-Hastings algorithm: im...

[ F.4.49 ] Projection to horizon of central ...

[ F.4.50 ] Normal innovation function

[ F.4.51 ] Projection of the pdf via DFT: fu...

[ F.4.52 ] GHCalibration

[ F.4.53 ] Stats

[ F.4.54 ] Raw2Cumul

[ F.4.55 ] PnlVolatility_ewma

[ F.4.56 ] ffgn

[ F.4.57 ] Central2Raw

[ F.4.58 ] CentralAndStandardizedStatistics

[ F.4.59 ] Schout2ConTank

[ F.4.60 ] ProjectionStudentT

[ F.4.61 ] QuantileMixture

[ F.4.62 ] ScoringAssessmentFP

[ F.4.63 ] SharpeRatio

[ F.4.64 ] PathsCauchy

[ F.4.65 ] SimulateCompPoisson

[ F.4.66 ] JumpDiffusionKou

[ F.4.67 ] JumpDiffusionMerton

[ F.4.69 ] VGpdf

[ F.4.70 ] SmoothStep

[ F.4.71 ] SpinOutlier

[ F.4.72 ] ShiftedVGMoments

[ F.4.73 ] ParamChangeVG

[ F.6.1 ] adjusted_value

[ F.6.1.1 ] Example

[ 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 ] Example

[ F.6.9 ] histogram2d_sp

[ F.6.9.1 ] Example

[ F.6.10 ] mahalanobis_dist

[ 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 ] Example

[ 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 fun...

[ F.6.25 ] Log2Lin

[ F.6.26 ] MatchTime

[ F.6.27 ] binningHFseries

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