Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps
Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps
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Lévy 跳跃随机波动率模型下隐含波动率偏度的短期渐近
DOI：
10.1007/s00780-016-0313-3
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发表时间：
2016
影响因子：
1.7
通讯作者：
Sveinn Ólafsson
中科院分区：
文献类型：
--
作者：
José E. Figueroa;Sveinn Ólafsson
隐含波动率偏差在具有跳跃的金融模型的短期渐近性的文献中得到的关注相对较少，尽管它在模型选择和校准中很重要。在一类具有独立稳定跳跃的随机波动率模型下，我们通过提供货币隐含波动率偏斜的高阶渐近展开式来纠正这一点。在最小可能条件下，我们还考虑了纯跳跃稳定的L模型的情形，所得到的展开式是定义良好的。与最近对“接近现金”的期权价格和隐含波动率的结果不同，本文的结果有助于理解隐含波动率在到期时如何受到连续成分的重要特征的影响，例如杠杆和Vol-of-Vol参数。作为中间结果，我们得到了在货币数字看涨期权价格的高阶展开，这进一步允许我们推断在货币期权的增量类似的结果。模拟结果表明，我们的渐近展开对于到期日在一个月以下的期权具有很好的拟合能力，支持了它们在实际应用中的相关性，而对最近S指数期权数据的隐含波动率偏度的分析表明，它与我们模型的无限变化跳跃分量是一致的。
The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing high order asymptotic expansions for the at-the-money implied volatility skew, under a rich class of stochastic volatility models with independent stable-like jumps of infinite variation. The case of a pure-jump stable-like Lévy model is also considered under the minimal possible conditions for the resulting expansion to be well defined. Unlike recent results for “near-the-money” option prices and implied volatility, the results herein aid in understanding how the implied volatility smile near expiry is affected by important features of the continuous component, such as the leverage and vol-of-vol parameters. As intermediary results, we obtain high order expansions for at-the-money digital call option prices, which furthermore allow us to infer analogous results for the delta of at-the-money options. Simulation results indicate that our asymptotic expansions give good fits for options with maturities up to one month, underpinning their relevance in practical applications, and an analysis of the implied volatility skew in recent S&P 500 options data shows it to be consistent with the infinite variation jump component of our models.