2015, Approx. 250 p. 17 illus., 16 illus. in color.
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Self contained and clear overview on affine diffusions
Presents the latest algorithms for simulating these processes and compares their efficiency
Explains and shows why and how these processes are used in Quantitative Finance
This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes. It also considers some related 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 also explains the mathematical background to affine diffusions and analysis of the accuracy of the schemes.
Content Level »Research
Keywords »Affine diffusions - Cox-Ingersoll-Ross process - Heston model - Simulation schemes - Wishart process
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.