The Small-Time Smile and Term Structure of Implied Volatility under the Heston Model
The Small-Time Smile and Term Structure of Implied Volatility under the Heston Model
复制标题
DOI：
10.1137/110830241
复制
发表时间：
2012-01-01
影响因子：
1
通讯作者：
Lee, Roger
中科院分区：
文献类型：
--
作者：
Forde, Martin;Jacquier, Antoine;Lee, Roger
我们在 Heston 模型中描述了小期限隐含波动率的渐近微笑和期限结构。使用鞍点方法，我们推导出看涨期权价格的小期限展开式，然后将其转换为隐含波动率的封闭式展开式（包括主序和修正项）。这种精细的展开揭示了小到期微笑与所有 Heston 参数（包括波动率漂移系数中的参数对）之间的关系，从而锐化了 Forde 和 Jacquier [Int. J.理论。应用。 Finance, 12 (2009), pp. 861-876]，发现了零到期微笑与扩散系数之间的关系。
We characterize the asymptotic smile and term structure of implied volatility in the Heston model at small maturities. Using saddlepoint methods we derive a small-maturity expansion formula for call option prices, which we then transform into a closed-form expansion (including the leading-order and correction terms) for implied volatility. This refined expansion reveals the relationship between the small-expiry smile and all Heston parameters (including the pair in the volatility drift coefficient), sharpening the leading-order result of Forde and Jacquier [Int. J. Theor. Appl. Finance, 12 (2009), pp. 861-876], which found the relationship between the zero-expiry smile and the diffusion coefficients.