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Informationen zum Autor 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. Klappentext Option Pricing and Estimation of Financial Models with R Stefano M. Iacus , Department of Economics, Business and Statistics, University of Milan, Italy The aim of this book is twofold. The first goal is to summarize elementary and advanced topics on modern option pricing: from the basic models of the Black & Scholes theory to the more sophisticated approach based on Lévy processes and other jump processes. At the same time, the other goal of the book is to identify, estimate and justify, with the use of statistically sound techniques, the choice of particular financial models starting from real financial data. In the spirit of modern finance, this book considers only continuous time models like diffusion of Lévy processes. Therefore, the statistical techniques presented are those designed to work on real discrete time data obtained from these continuous time models. Key Features: Provides a comprehensive and in-depth guide to financial modeling. Looks at basic and advanced option pricing with R. Explores simulation of multidimensional stochastic differential equations with jumps. Provides a comprehensive survey on empirical finance in the R statistical environment. Addresses model selection and identification of financial models from empirical financial data. This book is an invaluable resource for post graduate students and researchers in economics, mathematics and statistics who want to approach mathematical finance from an applied point of view. Statisticians and data analysts working in a field related to finance will also benefit from this book. Zusammenfassung A practical text for calibrating financial models and numerical option pricing featuring R, Option Pricing and Estimation of Financial Models With R distills 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. Inhaltsverzeichnis Preface xiii 1 A synthetic view 1 1.1 The world of derivatives 2 1.1.1 Different kinds of contracts 2 1.1.2 Vanilla options 3 1.1.3 Why options? 6 1.1.4 A variety of options 7 1.1.5 How to model asset prices 8 1.1.6 One step beyond 9 1.2 Bibliographical notes 10 References 10 2 Probability, random variables and statistics 13 2.1 Probability 13 2.1.1 Conditional probability 15 2.2 Bayes' rule 16 2.3 Random variables 18 2.3.1 Characteristic function 23 2.3.2 Moment generating function 24 2.3.3 Examples of random variables 24 2.3.4 Sum of random variables 35 2.3.5 Infinitely divisible distributions 37 2.3.6 Stable laws 38 2.3.7 Fast Fourier Transform 42 2.3.8 Inequalities 46 2.4 Asymptotics 48 2.4.1 Types of convergences 48 2.4.2 Law of large numbers 50 2.4.3 Central limit theorem 52 2.5 Conditional expectation 54 2.6 Statistics 57 2.6.1 Properties of estimators 57 2.6.2 The likelihood function 61 2.6.3 Efficiency of estimators 63 2.6.4 Maximum likelihood estimation 64 2.6.5 Moment type estimators 65 2.6.6 Least squares method 65 2.6.7 Estimating functions 66 2.6.8 Confidence intervals 66 2.6.9 Numerical maximization of the likelihood 68 2.6.10 The ¿ -method 70 2.7 Solution to exercises 71 2.8 Bibliographical notes 77 References 77 3 Stochastic processes 79 3.1 Definition and first properties 79 3.1.1 Measurability and filt...
