A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus
A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus
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基于 Malliavin 演算的指数加性过程均值方差套期保值的数值有效封闭形式表示
DOI：
10.1080/1350486x.2018.1506259
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发表时间：
2018
影响因子：
--
通讯作者：
Imai Yuto
中科院分区：
文献类型：
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作者：
Arai Takuji;Imai Yuto
研究资产价格服从指数可加过程的均值-方差套期保值问题。跳跃型模型的均值-方差套期保值策略的一些表示已经被提出，但没有一个适合于开发任何给定时间直到到期的策略值的数值方法。在本文中，我们的目标是获得一个新的显式封闭形式的表示，这使我们能够开发一个有效的数值方法，使用快速傅立叶变换。请注意，我们的表示是用马利亚文导数来描述的。此外，我们说明了指数Lévy模型的数值结果。
We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models.