Presents inference and simulation of stochastic process in thefield of model calibration for financial times series modelled bycontinuous time processes and numerical option pricing. Introducesthe bases of probability theory and goes on to explain how to modelfinancial times series with continuous models, how to calibratethem from discrete data and further covers option pricing with oneor more underlying assets based on these models.
Analysis and implementation of models goes beyond the standardBlack and Scholes framework and includes Markov switching models,Lévy models and other models with jumps (e.g. the telegraphprocess); Topics other than option pricing include: volatility andcovariation estimation, change point analysis, asymptotic expansionand classification of financial time series from a statisticalviewpoint.
The book features problems with solutions and examples. All theexamples and R code are available as an additional R package,therefore all the examples can be reproduced.
|Product dimensions:||6.20(w) x 9.30(h) x 1.20(d)|
About the Author
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.
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 ItôIntegral.
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 & ScholesModel.
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.