Computational Financial Mathematics using MATHEMATICA® Optimal Trading in Stocks and Options
Given the explosion of interest in mathematical methods for solving problems in finance and trading, a great deal of research and development is taking place in universities, large brokerage firms, and in the supporting trading software industry. Mathematical advances have been made both analyticall...
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Format: | eBook |
Language: | English |
Published: |
Boston, MA
Birkhäuser
2003, 2003
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Edition: | 1st ed. 2003 |
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Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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