SHORT-TIME IMPLIED VOLATILITY IN EXPONENTIAL LÉVY MODELS

Erik Ekström () and Bing Lu ()
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Erik Ekström: Department of Mathematics, Uppsala University, Box 480, SE-75106 Uppsala, Sweden
Bing Lu: Department of Mathematics, Uppsala University, Box 480, SE-75106 Uppsala, Sweden

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 04, 1-14

Abstract: We show that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy 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 Lévy process as the time to maturity tends to zero. These results are proved by comparing the short-time asymptotics of the Black–Scholes price with explicit formulas for upper and lower bounds of option prices in exponential Lévy models.

Keywords: Implied volatility; exponential Lévy models; short-time asymptotic behavior (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0219024915500259

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