Introduction to Financial Option Valuation Mathematics, Stochastics and Computation

ISBN-10: 0521547571
ISBN-13: 9780521547574
Edition: 2004
List price: $64.99 Buy it from $39.98
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Description: This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its  More...

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Book details

List price: $64.99
Copyright year: 2004
Publisher: Cambridge University Press
Publication date: 4/15/2004
Binding: Paperback
Pages: 296
Size: 6.75" wide x 9.25" long x 0.75" tall
Weight: 1.100
Language: English

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained.

List of illustrations
Preface
Options
What are options?
Why do we study options?
How are options traded?
Typical option prices
Other financial derivatives
Notes and references
Program of Chapter 1 and walkthrough
Option valuation preliminaries
Motivation
Interest rates
Short selling
Arbitrage
Put-call parity
Upper and lower bounds on option values
Notes and references
Program of Chapter 2 and walkthrough
Random variables
Motivation
Random variables, probability and mean
Independence
Variance
Normal distribution
Central Limit Theorem
Notes and references
Program of Chapter 3 and walkthrough
Computer simulation
Motivation
Pseudo-random numbers
Statistical tests
Notes and references
Program of Chapter 4 and walkthrough
Asset price movement
Motivation
Efficient market hypothesis
Asset price data
Assumptions
Notes and references
Program of Chapter 5 and walkthrough
Asset price model: Part I
Motivation
Discrete asset model
Continuous asset model
Lognormal distribution
Features of the asset model
Notes and references
Program of Chapter 6 and walkthrough
Asset price model: Part II
Computing asset paths
Timescale invariance
Sum-of-square returns
Notes and references
Program of Chapter 7 and walkthrough
Black-Scholes PDE and formulas
Motivation
Sum-of-square increments for asset price
Hedging
Black-Scholes PDE
Black-Scholes formulas
Notes and references
Program of Chapter 8 and walkthrough
More on hedging
Motivation
Discrete hedging
Delta at expiry
Large-scale test
Long-Term Capital Management
Notes
Program of Chapter 9 and walkthrough
The Greeks
Motivation
The Greeks
Interpreting the Greeks
Black-Scholes PDE solution
Notes and references
Program of Chapter 10 and walkthrough
More on the Black-Scholes formulas
Motivation
Where is [mu]?
Time dependency
The big picture
Change of variables
Notes and references
Program of Chapter 11 and walkthrough
Risk neutrality
Motivation
Expected payoff
Risk neutrality
Notes and references
Program of Chapter 12 and walkthrough
Solving a nonlinear equation
Motivation
General problem
Bisection
Newton
Further practical issues
Notes and references
Program of Chapter 13 and walkthrough
Implied volatility
Motivation
Implied volatility
Option value as a function of volatility
Bisection and Newton
Implied volatility with real data
Notes and references
Program of Chapter 14 and walkthrough
Monte Carlo method
Motivation
Monte Carlo
Monte Carlo for option valuation
Monte Carlo for Greeks
Notes and references
Program of Chapter 15 and walkthrough
Binomial method
Motivation
Method
Deriving the parameters
Binomial method in practice
Notes and references
Program of Chapter 16 and walkthrough
Cash-or-nothing options
Motivation
Cash-or-nothing options
Black-Scholes for cash-or-nothing options
Delta behaviour
Risk neutrality for cash-or-nothing options
Notes and references
Program of Chapter 17 and walkthrough
American options
Motivation
American call and put
Black-Scholes for American options
Binomial method for an American put
Optimal exercise boundary
Monte Carlo for an American put
Notes and references
Program of Chapter 18 and walkthrough
Exotic options
Motivation
Barrier options
Lookback options
Asian options
Bermudan and shout options
Monte Carlo and binomial for exotics
Notes and references
Program of Chapter 19 and walkthrough
Historical volatility
Motivation
Monte Carlo-type estimates
Accuracy of the sample variance estimate
Maximum likelihood estimate
Other volatility estimates
Example with real data
Notes and references
Program of Chapter 20 and walkthrough
Monte Carlo Part II: variance reduction by antithetic variates
Motivation
The big picture
Dependence
Antithetic variates: uniform example
Analysis of the uniform case
Normal case
Multivariate case
Antithetic variates in option valuation
Notes and references
Program of Chapter 21 and walkthrough
Monte Carlo Part III: variance reduction by control variates
Motivation
Control variates
Control variates in option valuation
Notes and references
Program of Chapter 22 and walkthrough
Finite difference methods
Motivation
Finite difference operators
Heat equation
Discretization
FTCS and BTCS
Local accuracy
Von Neumann stability and convergence
Crank-Nicolson
Notes and references
Program of Chapter 23 and walkthrough
Finite difference methods for the Black-Scholes PDE
Motivation
FTCS, BTCS and Crank-Nicolson for Black-Scholes
Down-and-out call example
Binomial method as finite differences
Notes and references
Program of Chapter 24 and walkthrough
References
Index

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