Atomic Implied Volatilities
27 Pages Posted: 6 Oct 2008 Last revised: 30 Nov 2009
Date Written: September 1, 2008
In this note, we present a novel approach to derive asymptotics for Black implied volatilities under the same generic model as proposed in Antonov and Misirpashaev (2009). We perform a time substitution as used by Duru and Kleinert (1979) to calculate the path integral formulation of the H-atom. We demonstrate that the method provides asymptotic implied volatility formula comparable to the result of Hagan and Woodward (1999) for local volatility models and Hagan et al. (2001) for stochastic volatility models. We also discuss possible application to the pricing of basket options. The method is presented as an alternative to Markov projection as introduced by Piterbarg (2006) and is claimed to be applicable to a wide range of numerical problems arising in finance.
Keywords: SABR model, Duru-Kleinert transformation
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