A general control variate method for option pricing under L茅vy processes

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• 作者：Kemal Dinç ; er Dingeç ; ; ^{kemal.dingec@boun.edu.tr} ; Wolfgang Hö ; rmann ^{hormannw@boun.edu.tr}
• 关键词：Finance ; Option pricing ; L&eacute ; vy processes ; Monte Carlo simulation ; Control variate ; Numerical inversion
• 刊名：European Journal of Operational Research
• 出版年：2012
• 期刊代码：58_03772217
• 类别：et
• 出版时间：1 September, 2012
• 卷：221
• 期：2
• 页码：368-377
• 文件大小：269 K

摘要

We present a general control variate method for simulating path dependent options under L茅vy processes. It is based on fast numerical inversion of the cumulative distribution functions and exploits the strong correlation of the payoff of the original option and the payoff of a similar option under geometric Brownian motion. The method is applicable for all types of L茅vy processes for which the probability density function of the increments is available in closed form. Numerical experiments confirm that our method achieves considerable variance reduction for different options and L茅vy processes. We present the applications of our general approach for Asian, lookback and barrier options under variance gamma, normal inverse Gaussian, generalized hyperbolic and Meixner processes.