Static Hedging of Asian Options under Stochastic Volatility Models using Fast Fourier Transform

Static Hedging of Asian Options under Stochastic Volatility Models using Fast Fourier Transform
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使用快速傅里叶变换的随机波动模型下的亚洲期权静态对冲

DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
W. Schoutens
W. Schoutens
中科院分区：
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文献类型：
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作者：
H. Albrecher;W. Schoutens

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我们提出了一种简单的静态超级对冲策略，用于在各种随机波动率模型下根据欧洲期权投资组合计算算术亚洲期权的收益。此外，结果表明，所获得的对冲在某种意义上是最优的。该策略基于止损变换和共调性理论。数值实现基于快速傅立叶变换。我们说明了根据市场数据校准的几种模型的对冲性能，并将结果与​​其他（简单的）静态超级对冲策略进行了比较。 *格拉茨科技大学数学系，Steyrergasse 30, A-8010 Graz, Austria。电子邮件：albrecher@TUGraz.at †K.U.Leuven，U.C.S.，W. De Croylaan 54，B-3001 Leuven，比利时。电子邮件：Wim.Schoutens@wis.kuleuven.ac.be
We present a simple static super-hedging strategy for the payoff of an arithmetic Asian option in terms of a portfolio of European options under various stochastic volatility models. Moreover, it is shown that the obtained hedge is optimal in some sense. The strategy is based on stop-loss transforms and comonotonicity theory. The numerical implementation is based on the Fast Fourier transform. We illustrate the hedging performance for several models calibrated to market data and compare the results with other (trivial) static super-hedging strategies. ∗Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria. Email: albrecher@TUGraz.at †K.U.Leuven, U.C.S., W. De Croylaan 54, B-3001 Leuven, Belgium. Email: Wim.Schoutens@wis.kuleuven.ac.be