Computations of Greeks in a market with jumps via the Malliavin calculus
Computations of Greeks in a market with jumps via the Malliavin calculus
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通过 Malliavin 演算对希腊人在市场跳跃中的计算
DOI：
10.1007/s00780-003-0111-6
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发表时间：
2004
影响因子：
1.7
通讯作者：
Nicolas Privault
中科院分区：
文献类型：
--
作者：
Youssef El;Nicolas Privault
摘要：使用Poisson空间上的Malliavin演算，我们计算市场中的希腊人，该市场由具有Poisson跳跃时间和随机跳跃大小的不连续过程驱动，遵循[5]中在Wiener空间上发起的方法。欧式期权不满足我们的方法所需的正则性条件，但我们表明，亚洲选项可以被认为是由于随着时间的推移积分的平滑效果。对Delta和Gamma亚式期权进行了数值模拟，并证实了该方法优于经典的衍生物有限差分蒙特-卡罗近似。
Abstract.Using the Malliavin calculus on Poisson space we compute Greeks in a market driven by a discontinuous process with Poisson jump times and random jump sizes, following a method initiated on the Wiener space in [5]. European options do not satisfy the regularity conditions required in our approach, however we show that Asian options can be considered due to a smoothing effect of the integral over time. Numerical simulations are presented for the Delta and Gamma of Asian options, and confirm the efficiency of this approach over classical finite difference Monte-Carlo approximations of derivatives.