In the last post, I provided a brief introduction to forward mode automatic differentiation with CppAD. In this post, I propose to use automatic differentiation for the computation of cumulants of option pricing models based on characteristic functions. This is useful, for example, when pricing European vanilla options using the Fang and Oosterlee (2008) COS method. Here, the first four cumulants are used to determine the integration range.
In quantitative finance, automatic differentiation is commonly used to efficiently compute price sensitivities. See Homescu (2011) for a general introduction and overview. I recently started to look into it with two different applications in mind: i) computation of moments from characteristic functions and ii) computation of implied densities from parametric volatility smiles. In this post, I provide a short introduction into computing general order derivatives with CppAD in forward mode.
I worked through most of this book when studying for MATH5985 “Term Structure Modelling” at UNSW. The attached document lists some potential typos/inconsistencies in the notation of the 2005 printing.
The book by Cont and Tankov (2004) is an excellent introduction to jump processes in finance. The attached document lists some potential typos/inconsistencies in the notation of the 2004 printing that are neither included in the errata published under http://www.cmap.polytechnique.fr/~rama/Jumps/ nor in an updated PDF version of some of the book chapters.