The implied volatility slope has received relatively little attention in the literature on short-time asymptotics for financial models with jumps, despite its importance in model selection and calibration. In this paper, we fill this gap by providing high-order asymptotic expansions for the at-the-money implied volatility slope of a rich class of stochastic volatility models with independent stable-like jumps of infinite variation. The case of a pure-jump stable-like L\'evy model is also considered under the minimal possible conditions for the resulting expansion to be well defined. As an intermediary result, we also obtain high-order expansions for at-the-money digital call option prices . The results obtained herein are remarkably different from those obtained in recent papers close-to-the-money option prices in that they aid in understanding how the behavior of implied volatility near expiry is affected by important model parameters , such as the leverage and vol vol parameters, that were not present in the aforementioned earlier results . Our simulation results also indicate that for parameter values of relevance in finance, the asymptotic expansions give a good fit for maturities up to one month   .
The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing high-order asymptotic expansions for the at-the-money implied volatility skew, under a rich class of stochastic volatility models with independent stable-like jumps of infinite variation. The case of a pure-jump stable-like L\'evy model is also considered under the minimal possible conditions for the resulting expansion to be well defined. Unlike recent results for "near-the-money" option prices and implied volatility, the results herein aid in understanding how the implied volatility smile near expiry is affected by important features of the continuous component , such as the leverage and vol-of-vol parameters. As intermediary results we obtain high-order expansions for at-the-money digital call option prices, which furthermore allow us to infer analogous results for the delta of at-the-money options. Simulation results indicate that our asymptotic expansions give good fits for options with maturities up to one month , underpinning their relevance in practical applications, and an analysis of the implied volatility skew in recent S P500 options data shows it to be consistent with the infinite variation jump component of our models .
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slope
skew
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short-time
short-term
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In this paper, we fill this gap
We rectify this
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slope of
skew, under
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As an intermediary result, we also obtain high-order expansions for at-the-money digital call option prices . The results obtained herein are remarkably different from those obtained in recent papers close-to-the-money option prices in that they
Unlike recent results for "near-the-money" option prices and implied volatility, the results herein
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behavior of implied volatility
implied volatility smile
R
model parameters
features of the continuous component
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vol vol parameters, that were not present in the aforementioned earlier results . Our simulation results also indicate that for parameter values of relevance in finance, the
vol-of-vol parameters. As intermediary results we obtain high-order expansions for at-the-money digital call option prices, which furthermore allow us to infer analogous results for the delta of at-the-money options. Simulation results indicate that our
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a good fit for
good fits for options with
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, underpinning their relevance in practical applications, and an analysis of the implied volatility skew in recent S
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P500 options data shows it to be consistent with the infinite variation jump component of our models