Homotopy perturbation transform method for pricing under pure diffusion models with affine coefficients

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Authors

Moutsinga, Claude Rodrigue Bambe
Pindza, Edson
Mare, Eben

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Publisher

Elsevier

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.

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Keywords

Diffusion model, Interest rate, Stochastic volatility, Stiffness, Laplace transform, Homotopy perturbation method

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Citation

Moutsinga, C.R.B., Pindza, E. & Mare, E. 2018, 'Homotopy perturbation transform method for pricing under pure diffusion models with affine coefficients', Journal of King Saud University–Science, vol. 30, no. 1, pp. 1-13.