• search hit 4 of 7
Back to Result List

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.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Antoine Jacquier
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
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.