Statistical Methods for Financial Engineering

While many financial engineering books are available, the statistical aspects behind the implementation of stochastic models used in the field are often overlooked or restricted to a few well-known cases. Statistical Methods for Financial Engineering guides current and future practitioners on implementing the most useful stochastic models used in financial engineering. After introducing properties of univariate and multivariate models for asset dynamics as well as estimation techniques, the book discusses limits of the Black-Scholes model, statistical tests to verify some of its assumptions, and the challenges of dynamic hedging in discrete time. It then covers the estimation of risk and performance measures, the foundations of spot interest rate modeling, Lévy processes and their financial applications, the properties and parameter estimation of GARCH models, and the importance of dependence models in hedge fund replication and other applications. It concludes with the topic of filtering and its financial applications. This self-contained book offers a basic presentation of stochastic models and addresses issues related to their implementation in the financial industry. Each chapter introduces powerful and practical statistical tools necessary to implement the models. The author not only shows how to estimate parameters efficiently, but he also demonstrates, whenever possible, how to test the validity of the proposed models. Throughout the text, examples using MATLAB® illustrate the application of the techniques to solve real-world financial problems. MATLAB and R programs are available on the author’s website.

Black-Scholes Model The Black-Scholes Model Dynamic Model for an AssetEstimation of Parameters Estimation Errors Black-Scholes FormulaGreeksEstimation of Greeks using the Broadie-Glasserman Methodologies Multivariate Black-Scholes Model Black-Scholes Model for Several AssetsEstimation of ParametersEstimation ErrorsEvaluation of Options on Several AssetsGreeks Discussion of the Black-Scholes ModelCritiques of the ModelSome Extensions of the Black-Scholes ModelDiscrete Time Hedging Optimal Quadratic Mean Hedging Measures of Risk and PerformanceMeasures of RiskEstimation of Measures of Risk by Monte Carlo MethodsMeasures of Risk and the Delta-Gamma ApproximationPerformance Measures Modeling Interest Rates Introduction Vasicek ModelCox-Ingersoll-Ross (CIR) ModelOther Models for the Spot Rates Lévy Models Complete Models Stochastic Processes with JumpsLévy ProcessesExamples of Lévy ProcessesChange of DistributionModel Implementation and Estimation of Parameters Stochastic Volatility Models GARCH ModelsEstimation of ParametersDuan Methodology of Option PricingStochastic Volatility Model of Hull-WhiteStochastic Volatility Model of Heston Copulas and Applications Weak Replication of Hedge Funds Default RiskModeling DependenceBivariate CopulasMeasures of DependenceMultivariate CopulasFamilies of CopulasEstimation of the Parameters of Copula ModelsTests of Independence Tests of Goodness-of-FitExample of Implementation of a Copula Model FilteringDescription of the Filtering Problem Kalman FilterIMM Filter General Filtering Problem Computation of the Conditional Densities Particle Filters Applications of Filtering Estimation of ARMA ModelsRegime-Switching Markov ModelsReplication of Hedge Funds Appendix A: Probability DistributionsAppendix B: Estimation of Parameters Index Suggested Reading, Exercises, Assignment Questions, Appendices, and References appear at the end of each chapter.

Bruno Remillard