Stefano M. Iacus

Option Pricing and Estimation of Financial Models with R (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 472
• Erscheinungstermin: 24. Februar 2011
• Englisch
• ISBN-13: 9781119990208
• Artikelnr.: 37354907

Autorenporträt

Stefano Maria Iacus, Professor (Professore Associato) of Probability and Mathematical Statistics at University of Milan, Department of Economics, Business and Statistics. Stefano is a member of the R development Core Team.

Inhaltsangabe

Preface. 1. A Synthetic View. 1.1 The World of Derivatives. 1.2
Bibliographic Notes. References. 2. Probability, Random Variables and
Statistics. 2.1 Probability. 2.2 Bayes' Rule. 2.3 Random Variables. 2.4
Asymptotics. 2.5 Conditional Expectation. 2.6 Statistics. 2.7 Solution to
Exercises. 2.8 Bibliographic Notes. References. 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 Bibliographic Notes. References. 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. References. 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. References. 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. References. 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. References. 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. References. 9. Miscellanea.
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. References. A. 'How to' Guide to R. A.1 Something to
Know Soon About R. A.2 Objects. A.3 S4 Objects. A.4 Functions. A.5
Vectorization. A.6 Parallel Computing in R. A.7 Bibliographic Notes.
References. 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. References. Index.