The large-time smile and skew for exponential Levy models
Please always quote using this URN:urn:nbn:de:0296-matheon-8548
- We derive a full asymptotic expansion for call option prices and a third order approximation for implied volatility in the large-time, large log-moneyness regime for a general exponential Levy model, by extending the saddlepoint argument used in Forde,Jacquier & Mijatovic for the Heston model. As for the Heston model, there are two special log-moneyness values where the call option asymptotics are qualitatively different, and we use an Edgeworth expansion to deal with these cases. We also characterise the behaviour of the implied volatility skew at large-maturities; in particular we show that the derivative of the dimensionless implied variance with respect to log-moneyness exists and is less than or equal to 4 in the large-maturity limit, which is consistent with the bound on the right and left-side derivative given in Rogers&Tehranchi.
Author: | Antoine Jacquier |
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URN: | urn:nbn:de:0296-matheon-8548 |
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 |
MSC-Classification: | 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) |
Preprint Number: | 798 |