An efficient control variate method for pricing variance derivatives

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Ma, JunMei¹  Xu, Chenglong^1,2,3 

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Shanghai Normal Univ, Shanghai E Inst Sci Comp, Shanghai 200234, Peoples R China

[3] Shanghai Normal Univ, Shanghai Key Lab Sci Comp, Dept Math, Shanghai 200234, Peoples R China

关键词: Variance swap;    Stochastic volatility;    Monte Carlo method;    Control variate;   

DOI  :  10.1016/j.cam.2010.05.017

来源: Elsevier

【 摘 要 】

This paper studies the pricing of variance swap derivatives with stochastic volatility by the control variate method. A closed form solution is derived for the approximate model with deterministic volatility, which plays the key role in the paper, and an efficient control variate technique is therefore proposed when the volatility obeys the log-normal process. By the analysis of moments for the underlying processes, the optimal volatility function in the approximate model is constructed. The numerical results show the high efficiency of our method: the results coincide with the theoretical results. The idea in the paper is also applicable for the valuation of other types of variance swap, options with stochastic volatility and other financial derivatives with multi-factor models. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free