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 mod
Option Pricing and Estimation of Financial Models with R; Contents; Preface; 1 A synthetic view; 1.1 The world of derivatives; 1.1.1 Different kinds of contracts; 1.1.2 Vanilla options; 1.1.3 Why options?; 1.1.4 A variety of options; 1.1.5 How to model asset prices; 1.1.6 One step beyond; 1.2 Bibliographical notes; References; 2 Probability, random variables and statistics; 2.1 Probability; 2.1.1 Conditional probability; 2.2 Bayes' rule; 2.3 Random variables; 2.3.1 Characteristic function; 2.3.2 Moment generating function; 2.3.3 Examples of random variables; 2.3.4 Sum of random variables 2.3.5 Infinitely divisible distributions2.3.6 Stable laws; 2.3.7 Fast Fourier Transform; 2.3.8 Inequalities; 2.4 Asymptotics; 2.4.1 Types of convergences; 2.4.2 Law of large numbers; 2.4.3 Central limit theorem; 2.5 Conditional expectation; 2.6 Statistics; 2.6.1 Properties of estimators; 2.6.2 The likelihood function; 2.6.3 Efficiency of estimators; 2.6.4 Maximum likelihood estimation; 2.6.5 Moment type estimators; 2.6.6 Least squares method; 2.6.7 Estimating functions; 2.6.8 Confidence intervals; 2.6.9 Numerical maximization of the likelihood; 2.6.10 The δ-method; 2.7 Solution to exercises 2.8 Bibliographical notesReferences; 3 Stochastic processes; 3.1 Definition and first properties; 3.1.1 Measurability and filtrations; 3.1.2 Simple and quadratic variation of a process; 3.1.3 Moments, covariance, and increments of stochastic processes; 3.2 Martingales; 3.2.1 Examples of martingales; 3.2.2 Inequalities for martingales; 3.3 Stopping times; 3.4 Markov property; 3.4.1 Discrete time Markov chains; 3.4.2 Continuous time Markov processes; 3.4.3 Continuous time Markov chains; 3.5 Mixing property; 3.6 Stable convergence; 3.7 Brownian motion; 3.7.1 Brownian motion and random walks 3.7.2 Brownian motion is a martingale3.7.3 Brownian motion and partial differential equations; 3.8 Counting and marked processes; 3.9 Poisson process; 3.10 Compound Poisson process; 3.11 Compensated Poisson processes; 3.12 Telegraph process; 3.12.1 Telegraph process and partial differential equations; 3.12.2 Moments of the telegraph process; 3.12.3 Telegraph process and Brownian motion; 3.13 Stochastic integrals; 3.13.1 Properties of the stochastic integral; 3.13.2 Itô formula; 3.14 More properties and inequalities for the Itô integral; 3.15 Stochastic differential equations 3.15.1 Existence and uniqueness of solutions3.16 Girsanov's theorem for diffusion processes; 3.17 Local martingales and semimartingales; 3.18 Lévy processes; 3.18.1 Lévy-Khintchine formula; 3.18.2 Lévy jumps and random measures; 3.18.3 Itô-Lévy decomposition of a Lévy process; 3.18.4 More on the Lévy measure; 3.18.5 The Itô formula for Lévy processes; 3.18.6 Lévy processes and martingales; 3.18.7 Stochastic differential equations with jumps; 3.18.8 Itô formula for Lévy driven stochastic differential equations; 3.19 Stochastic differential equations in Rn; 3.20 Markov switching diffusions 3.21 Solution to exercises
Description based upon print version of record. Includes bibliographical references and index.