Asymptotics of Implied Volatility to Arbitrary Order
29 Pages Posted: 26 Feb 2011
Date Written: February 24, 2011
Abstract
In a unified model-free framework that includes long-expiry, short-expiry, extreme-strike, and jointly-varying strike-expiry regimes, we find asymptotic implied volatility and implied variance formulas in terms of L, with rigorous error estimates of order 1/L to any given power, where L denotes the absolute log of an option price that approaches zero. Our results therefore sharpen, to arbitrarily-high order of accuracy, the model-free asymptotics of implied volatility in extreme regimes. We then apply these general formulas to particular examples: Levy and Heston.
Suggested Citation: Suggested Citation
Gao, Kun and Lee, Roger, Asymptotics of Implied Volatility to Arbitrary Order (February 24, 2011). Available at SSRN: https://ssrn.com/abstract=1768383 or http://dx.doi.org/10.2139/ssrn.1768383
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