Option Pricing and Estimation of Financial Models with R / Edition 1by Stefano M. Iacus
Pub. Date: 05/24/2011
Presents inference and simulation of stochastic process in the field of model calibration for financial times series modeled with continuous time processes and numerical option pricing. Introduces the basis of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them and covers option pricing with… See more details below
Presents inference and simulation of stochastic process in the field of model calibration for financial times series modeled with continuous time processes and numerical option pricing. Introduces the basis of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them and covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models based on switching models or models with jumps are featured along with new models (Levy and telegraph process modeling) and topics such as; volatilty, covariation, p-variation and regime switching analysis, attention is focused on the calibration of these topics 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.
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Table of Contents
1. A Synthetic View.
1.1 The World of Derivatives.
1.2 Bibliographic Notes.
2. Probability, Random Variables and Statistics.
2.2 Bayes' Rule.
2.3 Random Variables.
2.5 Conditional Expectation.
2.7 Solution to Exercises.
2.8 Bibliographic Notes.
3. Stochastic Processes.
3.1 Definition and First Properties.
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 Bibliographic Notes.
4. Numerical Methods.
4.1 Monte Carlo Method.
4.2 Numerical Differentiation.
4.3 Root Finding.
4.4 Numerical Optimization.
4.5 Simulation of Stochastic Processes.
4.6 Solution to Exercises.
4.7 Bibliographic Notes.
5. Estimation of Stochastic Models for Finance.
5.1 Geometric Brownian Motion.
5.2 Quasi-Maximum Likelihood Estimation.
5.3 Short-Term Interest Rates Models.
5.4 Exponential Lévy Model.
5.5 Telegraph and Geometric Telegraph Process.
5.6 Solution to Exercises.
5.7 Bibliographic Notes.
6. European Option Pricing.
6.1 Contingent Claims.
6.2 Solution of the Black & Scholes Equation.
6.3 The 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 Bibliographic Notes.
7. American Options.
7.1 Finite Difference Methods.
7.2 Explicit Finite-Difference Method.
7.3 Implicit Finite-Difference Method.
7.4 The Quadratic Approximation.
7.5 Geske & Johnson and Other Approximations.
7.6 Monte Carlo Methods.
7.7 Bibliographic Notes.
8. Pricing Outside the Standard Black & Scholes Model.
8.1 The Lévy Market Model.
8.2 Pricing Under the Jump Telegraph Process.
8.3 Markov Switching Diffusions.
8.4 The Benchmark approach.
8.5 Bibliographic Notes.
9.1 Monitoring of the Volatility.
9.2 Asynchronous Covariation Estimation.
9.3 LASSO Model Selection.
9.4 Clustering of Financial Time Series.
9.5 Bibliographic Notes.
A. 'How to' Guide to R.
A.1 Something to Know Soon About R.
A.3 S4 Objects.
A.6 Parallel Computing in R.
A.7 Bibliographic Notes.
B. R in Finance.
B.1 Overview of Existing R Frameworks.
B.2 Summary of Main Time Series Objects in R.
B.3 Dates and Time Handling.
B.4 Binding of Time Series.
B.5 Loading Data From Financial Data Servers.
B.6 Bibliographic Notes.
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