Numerical method for option pricing under jump-diffusion process

Abstract

Abstract: Numerical method for partial integro-differential equation (PIDE) resulting from option value under jump-diffusion process was studied. A non-homogeneous linear system was obtained by discretizing the spatial derivatives utilizing the fourth-order difference and extending boundary using fourth-order Lagrange interpolating polynomial. Based on $\mathrm{Pad\acute{e}}$\ approximations and partial fraction version of the matrix exponential, a high-order smoothing Crank-Nicolson scheme was constructed. Numerical calculation discussed the influence of jump intensity on vanilla option value and barrier option value, showed that the algorithm was efficient. Compared with classic Crank-Nicolson scheme, the numerical scheme avoided the spurious oscillation near the strike price and barrier value. The algorithm also can be used in the general linear boundary value problem which has non-smooth boundary.

Key words: option, jump-diffusion process, numerical method, $\mathrm{Pad\acute{e}}$ approximation, smoothing Crank-Nicolson scheme

CLC Number:

LI Wei, ZHOU Sheng-wu. Numerical method for option pricing under jump-diffusion process[J]. Journal of East China Normal University(Natural Sc, 2012, 2012(4): 27-35.

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