Book description
Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models.
Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint.
The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
Table of contents
- Cover
- Title Page
- Copyright
- Preface
- Chapter 1: A synthetic view
- Chapter 2: Probability, random variables and statistics
-
Chapter 3: Stochastic processes
- 3.1 Definition and First Properties
- 3.2 Martingales
- 3.3 Stopping Times
- 3.4 Markov Property
- 3.5 Mixing Property
- 3.6 Stable Convergence
- 3.7 Brownian Motion
- 3.8 Counting and Marked Processes
- 3.9 Poisson Process
- 3.10 Compound Poisson Process
- 3.11 Compensated Poisson Processes
- 3.12 Telegraph Process
- 3.13 Stochastic Integrals
- 3.14 More Properties and Inequalities for the Itô Integral
- 3.15 Stochastic Differential Equations
- 3.16 Girsanov's Theorem for Diffusion Processes
- 3.17 Local Martingales and Semimartingales
- 3.18 Lévy Processes
- 3.19 Stochastic Differential Equations in Rn
- 3.20 Markov Switching Diffusions
- 3.21 Solution to Exercises
- 3.22 Bibliographical Notes
- Chapter 4: Numerical methods
- Chapter 5: Estimation of stochastic models for finance
-
Chapter 6: European option pricing
- 6.1 Contingent Claims
- 6.2 Solution of the Black and Scholes Equation
- 6.3 The δ-hedging and the Greeks
- 6.4 Pricing Under the Equivalent Martingale Measure
- 6.5 More on Numerical Option Pricing
- 6.6 Implied Volatility and Volatility Smiles
- 6.7 Pricing of Basket Options
- 6.8 Solution to Exercises
- 6.9 Bibliographical Notes
- Chapter 7: American options
- Chapter 8: Pricing outside the standard Black and Scholes model
- Chapter 9: Miscellanea
- Appendix A: ‘How to’ guide to R
- Appendix B: R in finance
- Index
Product information
- Title: Option Pricing and Estimation of Financial Models with R
- Author(s):
- Release date: May 2011
- Publisher(s): Wiley
- ISBN: 9780470745847
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