具有局部波动率的跳跃-扩散模型下短期限亚洲期权的渐近性

Dan Pirjol, Lingjiong Zhu
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摘要

本文研究了具有局部波动分量的跳跃-扩散模型中亚洲期权的短期限渐近性,其中跳跃被建模为复合泊松过程,后来扩展到L\ \ evy跳跃,其中包括指数L\ \ evy模型作为特例。固定罢工和浮动罢工都是亚洲的选择。对于文献中比较流行的几种模型:默顿跳跃-扩散模型、双指数跳跃模型和方差伽玛模型,得到了亚洲期权价格一阶渐近的显式结果。我们提出了满足短期限渐近约束的亚洲期权价格的解析逼近,并用MonteCarlo模拟进行了检验。对于足够小的成熟度,其渐近结果与数值模拟结果很好地吻合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotics for Short Maturity Asian Options in a Jump-Diffusion model with Local Volatility
We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process which are later extended to L\'evy jumps, that includes the exponential L\'{e}vy model as a special case. Both fixed and floating strike Asian options are considered. Explicit results are obtained for the first-order asymptotics of the Asian options prices for a few popular models in the literature: the Merton jump-diffusion model, the double-exponential jump model, and the Variance Gamma model. We propose an analytical approximation for Asian option prices which satisfies the constraints from the short-maturity asymptotics, and test it against Monte Carlo simulations. The asymptotic results are in good agreement with numerical simulations for sufficiently small maturity.
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