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.
Author: | Antoine Jacquier |
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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 |