Option Theory with Stochastic Analysis An Introduction to Mathematical Finance
In contrast to many books addressed to an audience with greater mathematical experience, it can appeal to many practitioners, e.g. in industry, looking for an introduction to this theory without too much detail. It dispenses with introductory chapters summarising the theory of stochastic analysis an...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2004, 2004
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| Edition: | 1st ed. 2004 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Introduction
- 1.1 An Introduction to Options in 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 Itô Integral
- 3.2 The Itô 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))
- 4.4 The Girsanov Theorem and Equivalent Martingale Measures
- 4.5 Pricing and Hedging of General Contingent Claims
- 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
- 5 Numerical Pricing and Hedging of Contingent Claims
- 5.1 Pricing and Hedging with Monte Carlo Methods
- 5.2 Pricing and Hedging with the Finite Difference Method
- A Solutions to Selected Exercises
- References