You are previewing Option Pricing and Estimation of Financial Models with R.
O'Reilly logo
Option Pricing and Estimation of Financial Models with R

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

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Chapter 1: A synthetic view
    1. 1.1 The World of Derivatives
    2. 1.2 Bibliographical Notes
  6. Chapter 2: Probability, random variables and statistics
    1. 2.1 Probability
    2. 2.2 Bayes' Rule
    3. 2.3 Random Variables
    4. 2.4 Asymptotics
    5. 2.5 Conditional Expectation
    6. 2.6 Statistics
    7. 2.7 Solution to Exercises
    8. 2.8 Bibliographical Notes
  7. Chapter 3: Stochastic processes
    1. 3.1 Definition and First Properties
    2. 3.2 Martingales
    3. 3.3 Stopping Times
    4. 3.4 Markov Property
    5. 3.5 Mixing Property
    6. 3.6 Stable Convergence
    7. 3.7 Brownian Motion
    8. 3.8 Counting and Marked Processes
    9. 3.9 Poisson Process
    10. 3.10 Compound Poisson Process
    11. 3.11 Compensated Poisson Processes
    12. 3.12 Telegraph Process
    13. 3.13 Stochastic Integrals
    14. 3.14 More Properties and Inequalities for the Itô Integral
    15. 3.15 Stochastic Differential Equations
    16. 3.16 Girsanov's Theorem for Diffusion Processes
    17. 3.17 Local Martingales and Semimartingales
    18. 3.18 Lévy Processes
    19. 3.19 Stochastic Differential Equations in Rn
    20. 3.20 Markov Switching Diffusions
    21. 3.21 Solution to Exercises
    22. 3.22 Bibliographical Notes
  8. Chapter 4: Numerical methods
    1. 4.1 Monte Carlo Method
    2. 4.2 Numerical Differentiation
    3. 4.3 Root Finding
    4. 4.4 Numerical Optimization
    5. 4.5 Simulation of Stochastic Processes
    6. 4.6 Solution to Exercises
    7. 4.7 Bibliographical Notes
  9. Chapter 5: Estimation of stochastic models for finance
    1. 5.1 Geometric Brownian Motion
    2. 5.2 Quasi-maximum Likelihood Estimation
    3. 5.3 Short-term Interest Rates Models
    4. 5.4 Exponential Lévy Model
    5. 5.5 Telegraph and Geometric Telegraph Process
    6. 5.6 Solution to Exercises
    7. 5.7 Bibliographical Notes
  10. Chapter 6: European option pricing
    1. 6.1 Contingent Claims
    2. 6.2 Solution of the Black and Scholes Equation
    3. 6.3 The δ-hedging and the Greeks
    4. 6.4 Pricing Under the Equivalent Martingale Measure
    5. 6.5 More on Numerical Option Pricing
    6. 6.6 Implied Volatility and Volatility Smiles
    7. 6.7 Pricing of Basket Options
    8. 6.8 Solution to Exercises
    9. 6.9 Bibliographical Notes
  11. Chapter 7: American options
    1. 7.1 Finite Difference Methods
    2. 7.2 Explicit Finite-difference Method
    3. 7.3 Implicit Finite-difference Method
    4. 7.4 The Quadratic Approximation
    5. 7.5 Geske and Johnson and Other Approximations
    6. 7.6 Monte Carlo Methods
    7. 7.7 Bibliographical Notes
  12. Chapter 8: Pricing outside the standard Black and Scholes model
    1. 8.1 The Lévy Market Model
    2. 8.2 Pricing Under the Jump Telegraph Process
    3. 8.3 Markov Switching Diffusions
    4. 8.4 The Benchmark Approach
    5. 8.5 Bibliographical Notes
  13. Chapter 9: Miscellanea
    1. 9.1 Monitoring of the Volatility
    2. 9.2 Asynchronous Covariation Estimation
    3. 9.3 LASSO Model Selection
    4. 9.4 Clustering of Financial Time Series
    5. 9.5 Bibliographical Notes
  14. Appendix A: ‘How to’ guide to R
    1. A.1 Something to Know First About R
    2. A.2 Objects
    3. A.3 S4 Objects
    4. A.4 Functions
    5. A.5 Vectorization
    6. A.6 Parallel Computing in R
    7. A.7 Bibliographical Notes
  15. Appendix B: R in finance
    1. B.1 Overview of Existing R frameworks
    2. B.2 Summary of Main Time Series Objects in R
    3. B.3 Dates and Time Handling
    4. B.4 Binding of Time Series
    5. B.5 Loading Data From Financial Data Servers
    6. B.6 Bibliographical Notes
  16. Index