Affine Diffusions and Related Processes: Simulation, Theory and Applications
Description
This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error. It also presents some models, mostly in the field of finance, where these methods are relevant and provides some numerical experiments.
The book explains the mathematical background to understand affine diffusions and analyze the accuracy of the schemes.
Reviews / Votes
"The author provides an up-to-date treatment of simulations of affine diffusions and some related processes, from theory down to explicit algorithms. For readers familiar with stochastic analysis of diffusions, the book is self-contained. . the book will a useful for anyone interested in current perspectives of modelling the price of financial assets, in theory as well as practical application." (Heinrich Hering, zbMATH 1387.60002, 2018)
"It is written for students and researchers working in mathematical finance, but it should also be of interest to all those working with numerical methods in probability. I should add that the text is mathematically sound, carefully written and highly accessible for the novice . . Using this text for lectures and seminars is definitely an option. . it is a valuable source for students, scholars and practitioners interested in affine diffusion models." (René L. Schilling, Mathematical Reviews, March, 2016)
"This academic text is very well written and organized. . reader can find in this book an explanation of the mathematical background to understand affine diffusions and related processes and analyze the accuracy of the schemes. . This is a very interesting book adequate to support Master or PhD courses in Stochastic Processes, dealing very cleverly with the Affine Diffusions and Related Processes and the respective simulation. . it is accessible to larger audiences and very useful for finance professionals." (Manuel Alberto M. Ferreira, Acta Scientia et Intelectus, Vol. 1 (1), 2015)
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Content
1 Real valued affine diffusions.- 2 An introduction to simulation schemes for SDEs.- 3 Simulation of the CIR process.- 4 The Heston model and multidimensional affine diffusions.- 5 Wishart processes and affine diffusions on positive semidefinite matrices.- 6 Processes of Wright-Fisher type.- 7 Appendix A Some results on matrices.- 8 Appendix B Simulation of a gamma random variable.