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The small-time smile and term structure of implied volatility under the Heston model

Please always quote using this URN:urn:nbn:de:0296-matheon-8555
  • We characterise the asymptotic smile and term structure of implied volatility in the Heston model at small maturities and all strikes. Using saddlepoint methods we derive a small-maturity expansion formula for call option prices, which we then transform into a closed-form expansion (including the leading-order and correction terms) for implied volatility. This refined expansion reveals the relationship between the small-expiry smile and all Heston parameters (including the pair in the volatility drift coefficient), sharpening the leading-order result of~\cite{FJ09I} which found the relationship between the zero-expiry smile and the diffusion coefficients. We solve for in/out-of-the-money and at-the-money cases; in the latter case our proof involves subleading-order saddlepoint approximation along a suitable path of integration.

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Metadaten
Author:Antoine Jacquier
URN:urn:nbn:de:0296-matheon-8555
Referee:Peter Karl Friz
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/06/21
Release Date:2011/06/21
Tag:
Institute:Technische Universität Berlin
Preprint Number:797
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