Abstract:
In this work, is an introduction and survey of numerical solution methods for stochastic differential equations. we are interested with the solve stochastic differential equations (SDEs) by numerical methods. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial systems. These methods are based on the truncated Ito- Taylor expansion. In our study we deal with a nonlinear SDE. We include a review of fundamental con-cepts, a description of elementary numerical methods and the concepts of convergence and order for stochastic differential equation solvers. Also we describe applications of SDE solvers to Monte-Carlo sampling for financial pricing of derivatives. By using Monte Carlo simulation and exact solution for each method we approximate to numerical solution and obtained from Itos formula. approximation solutions are compared with exact solution to show the effectiveness of the numerical methods.
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