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Your search keyword '"91G20, 60G51, 41A60, 44A15"' showing total 2 results
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2 results on '"91G20, 60G51, 41A60, 44A15"'

1. Small-maturity asymptotics for the at-the-money implied volatility slope in L\'evy models

Author

Gerhold, Stefan, Gülüm, I. Cetin, and Pinter, Arpad

Subjects
Quantitative Finance - Pricing of Securities, 91G20, 60G51, 41A60, 44A15
Abstract

We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behavior of the slope for infinite activity exponential L\'evy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity at-the-money digital call options, using Mellin transform asymptotics. Finally, we discuss when the at-the-money slope is consistent with the steepness of the smile wings, as given by Lee's moment formula.

Published
2013

2. Small-maturity asymptotics for the at-the-money implied volatility slope in L\'evy models

Author

Stefan Gerhold, I. Cetin G\\\'ul\\\'um, and Arpad Pinter

Subjects
91G20, 60G51, 41A60, 44A15, Quantitative Finance - Pricing of Securities
Abstract

We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behavior of the slope for infinite activity exponential L\'evy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity at-the-money digital call options, using Mellin transform asymptotics. Finally, we discuss when the at-the-money slope is consistent with the steepness of the smile wings, as given by Lee's moment formula.

Published
2013

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