Application of Doss Transformation in Approximation of Stochastic Differential Equations

Abstract

The solution of the financial application, be it asset pricing, portfolio allocation or risk management, relies on the simulation of discretized versions of the stochastic differential equations(SDEs). The simplest way to confront SDEs in numerical situations is to discretize them and use monte carlo simulation. The Euler scheme is most often used for discretization of SDEs. This discretization involves an approximation error. In this topic at the first we recall an introduction to SDEs and Monte carlo simulation. Then, we study the asymptotic error distribution of Euler approximations of solutions of SDEs. We also study the error distribution associated with a Doss transformation of the state variables. Convergence results for Euler schemes with and without doss transformation and the comparison of them with Milshtein scheme are presented at the end.