The Small-Maturity Heston Forward Smile
The Small-Maturity Heston Forward Smile
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小成熟的赫斯顿向前微笑
DOI：
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发表时间：
2013
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
本文研究了赫斯顿模型中远期启动期权的渐近性和远期隐含波动率微笑在到期日趋近于零时的渐近性。证明了价外期权的正向微笑爆炸，并计算了一个封闭形式的高阶展开式，详细说明了爆炸的速度。此外，结果表明，方差过程的平方根行为诱导的奇异性，使得对于某些参数配置，不能获得高阶出的钱向前微笑渐近。在在货币的情况下，一个单独的模型独立的分析表明，小成熟度限制是很好地定义为任何伊藤扩散。的证据依赖于理论的尖锐的大偏差（和细化），顺便说一句，我们提供了一个例子，退化的大偏差行为。
In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the Heston model as the maturity approaches zero. We prove that the forward smile for out-of-the-money options explodes and compute a closed-form high-order expansion detailing the rate of the explosion. Furthermore the result shows that the square-root behaviour of the variance process induces a singularity such that for certain parameter configurations one cannot obtain high-order out-of-the-money forward smile asymptotics. In the at-the-money case a separate model-independent analysis shows that the small-maturity limit is well defined for any Ito diffusion. The proofs rely on the theory of sharp large deviations (and refinements) and incidentally we provide an example of degenerate large deviations behaviour.