Computational Financial Mathematics using MATHEMATICA® Optimal Trading in Stocks and Options

Computational Financial Mathematics using MATHEMATICA® Optimal Trading in Stocks and Options / by Srdjan Stojanovic.

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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Bibliographic Details
Main Author: Stojanovic, Srdjan (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2003.
Edition:1st ed. 2003.
Series:Springer eBook Collection.
Subjects:
Finance.
Computer software.
Economics, Mathematical .
Application software.
Partial differential equations.
Probabilities.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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 Momentum Trading.

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