Option theory with stochastic analysis : an introduction to mathematical finance
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Bibliographic Information
Option theory with stochastic analysis : an introduction to mathematical finance
（Universitext）
Springer, c2004
- : pbk
- Other Title
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Matematisk finans
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Note
Originally published: Oslo : Universitetsforlaget AS, 2002
Includes bibliographical references (p. [157]-159) and index
Description and Table of Contents
Description
This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.
Table of Contents
1 Introduction.- 1.1 An Introduction to Options in Finance.- 1.1.1 Empirical Finance.- 1.1.2 Stochastic Finance.- 1.1.3 Computational Finance.- 1.2 Some Useful Material from Probability Theory.- 2 Statistical Analysis of Data from the Stock Market.- 2.1 The Black & Scholes Model.- 2.2 Logarithmic Returns from Stocks.- 2.3 Scaling Towards Normality.- 2.4 Heavy-Tailed and Skewed Logreturns.- 2.5 Logreturns and the Normal Inverse Gaussian Distribution.- 2.6 An Alternative to the Black & Scholes Model.- 2.7 Logreturns and Autocorrelation.- 2.8 Conclusions Regarding the Choice of Stock Price Model.- 3 An Introduction to Stochastic Analysis.- 3.1 The Ito Integral.- 3.2 The Ito Formula.- 3.3 Geometric Brownian Motion as the Solution of a Stochastic Differential Equation.- 3.4 Conditional Expectation and Martingales.- 4 Pricing and Hedging of Contingent Claims.- 4.1 Motivation from One-Period Markets.- 4.2 The Black & Scholes Market and Arbitrage.- 4.3 Pricing and Hedging of Contingent Claims X= f(S(T)).- 4.3.1 Derivation of the Black & Scholes Partial Differential Equation.- 4.3.2 Solution of the Black & Scholes Partial Differential Equation.- 4.3.3 The Black & Scholes Formula for Call Options.- 4.3.4 Hedging of Call Options.- 4.3.5 Hedging of General Options.- 4.3.6 Implied Volatility.- 4.4 The Girsanov Theorem and Equivalent Martingale Measures.- 4.5 Pricing and Hedging of General Contingent Claims.- 4.5.1 An Example: a Chooser Option.- 4.6 The Markov Property and Pricing of General Contingent Claims.- 4.7 Contingent Claims on Many Underlying Stocks.- 4.8 Completeness, Arbitrage and Equivalent Martingale Measures.- 4.9 Extensions to Incomplete Markets.- 4.9.1 Energy Markets and Incompleteness.- 5 Numerical Pricing and Hedging of Contingent Claims.- 5.1 Pricing and Hedging with Monte Carlo Methods.- 5.1.1 Pricing and Hedging of Contingent Claims with Payoff of the Form f(ST).- 5.1.2 The Accuracy' of Monte Carlo Methods.- 5.1.3 Pricing of Contingent Claims on Many Underlying Stocks.- 5.1.4 Pricing of Path-Dependent Claims.- 5.2 Pricing and Hedging with the Finite Difference Method.- A Solutions to Selected Exercises.- References.
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