Abstract:
Most existing multivariate models in finance are based on diffusion models. These models
typically lead to the need of solving systems of Riccati differential equations. In this paper, we
introduce an efficient method for solving systems of stiff Riccati differential equations. In this technique,
a combination of Laplace transform and homotopy perturbation methods is considered as
an algorithm to the exact solution of the nonlinear Riccati equations. The resulting technique is
applied to solving stiff diffusion model problems that include interest rates models as well as two
and three-factor stochastic volatility models. We show that the present approach is relatively easy,
efficient and highly accurate.
