Short-time implied volatility in exponential Lévy models
2015 (English)In: International Journal of Theoretical and Applied Finance, ISSN 0219-0249, Vol. 18, no 4, 1550025Article in journal (Other academic) Published
We show that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Levy models is the existence of jumps towards the strike price in the underlying process. When such jumps do not exist, the implied volatility converges to the volatility of the Gaussian component of the underlying Levy process as the time to maturity tends to zero.Those results are proved by comparing the short-time asymptotics of the Black-Scholes price to the explicit formulas for upper or lower bounds of option prices in exponential Levy models.
Place, publisher, year, edition, pages
2015. Vol. 18, no 4, 1550025
implied volatility; exponential Levy models; short-time asymptotic behavior.
Mathematics Other Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-209221DOI: 10.1142/S0219024915500259ISI: 000365773000004OAI: oai:DiVA.org:uu-209221DiVA: diva2:656385