Stochastic Runge-Kutta methods with the constant elasticity of variance (CEV) diffusion model for pricing option

Rajae Aboulaich (1, 2, 3) , Abdelilah Jraifi (2, 3) , Medarhri Ibtissam (2, 3)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 LERMA - Laboratoire d'Etudes et Recherche en Mathématiques Appliquées
3 LIRIMA - Laboratoire International de Recherche en Informatique et Mathématiques Appliquées

In order to solve numerically the constant elasticity of variance (CEV) model for pricing of European call option, we propose in this work the Stochastic Runge-Kutta method. We compare the obtained results using this approache, with those given by the Monte Carlo method in Broadie-Kaya [4]. Further, we demonstrate the faster convergence rate of the error obtained by the proposed method. Finally a comparative numerical study is done using different values of the coefficient of elasticity

Mots clés: CEV Model; Stochastic Volatility; Option pricing; Stochastic Runge-Kutta methods

Domaines: Mathématiques [math]

Rajae Aboulaich, Abdelilah Jraifi, Medarhri Ibtissam. Stochastic Runge-Kutta methods with the constant elasticity of variance (CEV) diffusion model for pricing option. Int. J. Math. Anal. , 2014, 8 (18), pp.849-856. ⟨10.12988/ijma.2014.4381⟩. ⟨hal-03135016⟩