SDE WEAK APPROXIMATION LIBRARY (SDE WA) (VERSION 1.0)

Abstract

In application of mathematical finance to practical problems, weak approximation of stochastic differential equations (SDEs) is one of the most important themes. In probabilistic approach to this problem, the Euler-Maruyama scheme which is a first-order weak approximation scheme has been used. Kusuoka recently proposed a weak approximation schceme for diffusion processes. Lyons andVictoir extensively developed the idea of this scheme to establish the cubature formula on the Weiner space. These results and the spread of quasi Monte Carlo method showed the efficiency of higher-order weak approximation which is often called Kusuoka approximation or KLV scheme. Ninomiya-Victoir and Ninomiya-Ninomiya successfully constructed algorithms of this scheme. These algorithms have been improved in a number of research. (Fujiwara, Ooshima-Teichman-Veluscek, etc.) The author constructed a universal numerical library written inCfor calculation of weak approximation of any fiven SDEs following the Kusuoka scheme. Two types of algorithms mentioned above (NV and NN) of the Kusuoka scheme are included in this library. The Euler-Maruyama scheme is also available in this library.The source code for this library can be obtained by downloading it from https://sites.google.com/site/marikoninomiya/