Asymptotics of implied volatility to arbitrary order

作者：Gao Kun; Lee Roger^*

来源：Finance and Stochastics, 2014, 18(2): 349-392.

DOI：10.1007/s00780-013-0223-6

• Implied volatility
• Asymptotics

In a unified model-free framework that includes long-expiry, short-expiry, extreme-strike, and jointly-varying strike-expiry regimes, we generate implied volatility and implied variance approximations, with rigorous error estimates asymptotically smaller than any given power of L, where L denotes the exogenously given absolute log of an option price that approaches zero. Our results, therefore, sharpen to arbitrarily high order of accuracy (and, moreover, extend to general extreme regimes) the model-free asymptotics of implied volatility. We then apply these general formulas to particular examples: Heston (using a previously known L expansion) and L,vy (using saddlepoint methods to derive L expansions).

• 出版日期2014-4