Asymptotic Formulae for Implied Volatility in the Heston Model
Proceedings of the Royal Society A
Posted: 16 Nov 2009 Last revised: 23 Mar 2012
Date Written: November 16, 2009
In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions.
Keywords: implied volatility, Heston model, closed-form formula, saddlepoint approximation, calibration
JEL Classification: G12, G13, C6
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