Asymptotic formulae for implied volatility in the Heston model

  • Forde M
  • Jacquier A
  • Mijatović A
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Abstract

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.

Author-supplied keywords

  • Asymptotics
  • Closed-form formula
  • HESTON model
  • Implied volatility
  • Saddlepoint expansions

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Authors

  • Martin Forde

  • Antoine Jacquier

  • Aleksandar Mijatović

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