Deterministic and Stochastic Topics in Computational Finance

What distinguishes this book from other texts on mathematical finance is the use of both probabilistic and PDEs tools to price derivatives for both constant and stochastic volatility models, by which the reader has the advantage of computing explicitly a large number of prices for European, American and Asian derivatives.

The book presents continuous time models for financial markets, starting from classical models such as Black–Scholes and evolving towards the most popular models today such as Heston and VAR.

A key feature of the textbook is the large number of exercises, mostly solved, which are designed to help the reader to understand the material.

The book is based on the author's lectures on topics on computational finance for senior and graduate students, delivered in USA (Princeton University and EMU), Taiwan and Kuwait. The prerequisites are an introductory course in stochastic calculus, as well as the usual calculus sequence.

The book is addressed to undergraduate and graduate students in Masters of Finance programs as well as to those who wish to become more efficient in their practical applications.

Topics covered:

• Interest Rates and Bonds
• Forward Rates and Yield Curves
• Risk-neutral Valuation
• Martingale Measures
• Black–Scholes Analysis
• American Options
• Stochastic Volatility Models (Heston, AR, GARCH)
• Stochastic Return Models (VAR)

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Contents:

• Introduction:

• Determinism or Stochasticity?

  Calibration to the Market

• Interest Rates and Bonds:

• Modeling Stochastic Rates

  Bonds, Forward Rates and Yield Curves

• Risk-Neutral Valuation Pricing:

• Modeling Stock-Prices

  Risk-Neutral Valuation

  Martingale Measures

• PDE Approach:

• Black-Scholes Analysis

  Black-Scholes for Asian Derivatives

  American Options

• Stochastic Volatility and Return Models:

• Heston Model

  GARCH Model

  AR(1) Model

  Stochastic Return Models

  Hints and Solutions

• Appendices:

• Useful Transforms

  Probability Concepts

  Elements of Stochastic Calculus

  Series and Equations

• Bibliography

• Index

Readership: Undergraduates, graduate students and researchers in Mathematical Finance.
Key Features:

• The book contains a chapter on pricing options when the underlying asset has stochastic volatility. Models such as Heston, Garch and Arch are presented. Heston model is one of the most popular these days and the book provides a clear presentation involving only elementary mathematics
• The last chapter deals with pricing options in the case when the underlying asset has a stochastic rate of return. This is a topic of ongoing research and it is related with the topic of 2013 Nobel Price in Economics. There are very few sources that provide this type of developments. This chapter was developed by the author
• A large number of the proposed problems (about 150) are solved completely or partially in the Hints and Solutions chapter
• The book contains an Appendix section containing the most useful information the reader needs to have in order to fully understand the text, without consulting another text