An introduction to statistical computing : a simulation-based approach - Voss, Jochen (Chichester, West Sussex, UK : John Wiley & Sons, Inc., 2013)
"This is a book about exploring random systems using computer simulation and thus, this book combines two different topic areas which have always fascinated me: the mathematical theory of probability and the art of programming computers"--
6 Continuous-time models6.1 Time discretisation; 6.2 Brownian motion; 6.2.1 Properties; 6.2.2 Direct simulation; 6.2.3 Interpolation and Brownian bridges; 6.3 Geometric Brownian motion; 6.4 Stochastic differential equations; 6.4.1 Introduction; 6.4.2 Stochastic analysis; 6.4.3 Discretisation schemes; 6.4.4 Discretisation error; 6.5 Monte Carlo estimates; 6.5.1 Basic Monte Carlo; 6.5.2 Variance reduction methods; 6.5.3 Multilevel Monte Carlo estimates; 6.6 Application to option pricing; 6.7 Summary and further reading; Exercises; Appendix A Probability reminders; A.1 Events and probability.
Includes bibliographical references and index.
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Keywords: Mathematical statistics -- Data processing; MATHEMATICS -- Probability & Statistics -- General; Mathematical statistics -- Data processing; Electronic books