Computational Financial Mathematics using MATHEMATICA®
Springer-Verlag New York Inc.
978-1-4612-6586-3 (ISBN)
This book provides a comprehensive overview of existing and original material, about what mathematics when allied with Mathematica can do for finance. Sophisticated theories are presented systematically in a user-friendly style, and a powerful combination of mathematical rigor and Mathematica programming. Three kinds of solution methods are emphasized: symbolic, numerical, and Monte-- Carlo. Nowadays, only good personal computers are required to handle the symbolic and numerical methods that are developed in this book.
Key features: * No previous knowledge of Mathematica programming is required * The symbolic, numeric, data management and graphic capabilities of Mathematica are fully utilized * Monte--Carlo solutions of scalar and multivariable SDEs are developed and utilized heavily in discussing trading issues such as Black--Scholes hedging * Black--Scholes and Dupire PDEs are solved symbolically and numerically * Fast numerical solutions to free boundary problems with details of their Mathematica realizations are provided * Comprehensive study of optimal portfolio diversification, including an original theory of optimal portfolio hedging under non-Log-Normal asset price dynamics is presented
The book is designed for the academic community of instructors and students, and most importantly, will meet the everyday trading needs of quantitatively inclined professional and individual investors.
0 Introduction.- 0.1 Audience, Highlights, Agenda.- 0.2 Software Installation.- 0.3 Acknowledgments.- Chapter1 Cash Account Evolution.- 1.1 Symbolic Solutions of ODEs.- 1.2 Numerical Solutions of ODEs.- 2 Stock Price Evolution.- 2.1 What are Stocks?.- 2.2 Stock Price Modeling: Stochastic Differential Equations.- 2.3 Itô Calculus.- 2.4 Multivariate and Symbolic Itô Calculus.- 2.5 Relationship Between SDEs and PDEs.- 3 European Style Stock Options.- 3.1 What Are Stock Options?.- 3.2 Black-Scholes PDE and Hedging.- 3.3 Solving Black-Scholes PDE Symbolically.- 3.4 Generalized Black-Scholes Formulas: Time-Dependent Data.- 4 Stock Market Statistics.- 4.1 Remarks.- 4.2 Stock Market Data Import and Manipulation.- 4.3 Volatility Estimates: Scalar Case.- 4.4 Appreciation Rate Estimates: Scalar Case.- 4.5 Statistical Experiments: Bayesian and Non-Bayesian.- 4.6 Vector Basic Price Model Statistics.- 4.7 Dynamic Statistics: Filtering of Conditional Gaussian Processes.- 5 Implied Volatility for European Options.- 5.1 Remarks.- 5.2 Option Market Data.- 5.3 Black-Scholes Theory vs. Market Data: Implied Volatility.- 5.4 Numerical PDEs, Optimal Control, and Implied Volatility.- 6 American Style Stock Options.- 6.1 Remarks.- 6.2 American Options and Obstacle Problems.- 6.3 General Implied Volatility for American Options.- 7 Optimal Portfolio Rules.- 7.1 Remarks.- 7.2 Utility of Wealth.- 7.3 Merton’s Optimal Portfolio Rule Derived and Implemented.- 7.4 Portfolio Rules under Appreciation Rate Uncertainty.- 7.5 Portfolio Optimization under Equality Constraints.- 7.6 Portfolio Optimization under Inequality Constraints.- 8 Advanced Trading Strategies.- 8.1 Remarks.- 8.2 Reduced Monge—Ampere PDEs of Advanced Portfolio Hedging.- 8.3 Hypoelliptic Obstacle Problems in Optimal MomentumTrading.
| Zusatzinfo | XI, 481 p. |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Wirtschaft ► Allgemeines / Lexika | |
| Wirtschaft ► Betriebswirtschaft / Management ► Finanzierung | |
| Wirtschaft ► Volkswirtschaftslehre | |
| ISBN-10 | 1-4612-6586-X / 146126586X |
| ISBN-13 | 978-1-4612-6586-3 / 9781461265863 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
aus dem Bereich
