Asymptotics of Forward Implied Volatility
Asymptotics of Forward Implied Volatility
复制标题
远期隐含波动率的渐近
DOI：
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发表时间：
2012
影响因子：
1
通讯作者：
P. Roome
中科院分区：
文献类型：
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作者：
A. Jacquier;P. Roome
本文证明了远期开始期权和远期隐含波动率SILE在一大类模型中的一般闭式展开公式，包括Heston随机波动率模型和时变指数Levy模型。这种扩展既适用于小规模到期债券，也适用于大额到期债券，并且仅基于基础过程的远期特征函数的性质。该方法基于尖锐的大偏差技术，允许我们恢复(特别是)许多针对现货隐含波动率微笑的结果。在传递过程中，我们(I)证明了远期开始日期必须被重新标度以获得非平凡的小到期日的渐近性，(Ii)证明远期开始日期可能影响正向微笑的大到期日行为，以及(Iii)提供一些具有有限二次变化的模型的例子，其中小到期日正向微笑不爆炸。
We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential Levy models. This expansion applies to both small and large maturities and is based solely on the properties of the forward characteristic function of the underlying process. The method is based on sharp large deviations techniques and allows us to recover (in particular) many results for the spot implied volatility smile. In passing we (i) show that the forward-start date has to be rescaled in order to obtain nontrivial small-maturity asymptotics, (ii) prove that the forward-start date may influence the large-maturity behavior of the forward smile, and (iii) provide some examples of models with finite quadratic variation where the small-maturity forward smile does not explode.