Stochastic Analysis for Finance with Simulations
This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena,...
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| Format: | eBook |
| Language: | English |
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Cham
Springer International Publishing
2016, 2016
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| Edition: | 1st ed. 2016 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preface
- Acknowledgements
- List of Figures
- List of Tables
- List of Simulations
- Fundamental Concepts
- Financial Derivatives
- The Lebesgue Integral
- Basic Probability Theory
- Conditional Expectation
- Stochastic Processes
- Brownian Motion
- Girsanov's Theorem
- The Reflection Principle of Brownian Motion
- The Ito Integral
- The Ito Formula
- Stochastic Differential Equations
- The Feynmann-Kac Theorem
- The Binomial Tree Method for Option Pricing
- The Black-Scholes-Merton Differential Equation
- The Martingale Method
- Pricing of Vanilla Options
- Pricing of Exotic Options
- American Options
- The Capital Asset Pricing Model
- Dynamic Programming
- Bond Pricing
- Interest Rate Models
- Numeraires
- Numerical Estimation of Volatility
- Time Series
- Random Numbers
- The Monte Carlo Method for Option Pricing
- Numerical Solution of the Black-Scholes-Merton Equation
- Numerical Solution of Stochastic Differential Equations. Appendices
- Solutions for Selected Problems
- Glossary
- References
- Index.