Asymptotic formulae for implied volatility in the Heston model

Economy – Quantitative Finance – Pricing of Securities

Scientific paper

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Presentation in Section 2 has been improved. Theorem 3.1 has been slightly generalised. Figures 2 and 3 now include the at-the

Scientific paper

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.

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