The Impact of Jump Distributions on the Implied Volatility of Variance

Elisa Nicolato; Camilla Pisani; David Sloth Pedersen

doi:10.1137/16M1059072

The Impact of Jump Distributions on the Implied Volatility of Variance

Elisa Nicolato, Camilla Pisani, David Sloth Pedersen

Department of Economics and Business Economics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

7 Citations (Scopus)

Abstract

We consider a tractable afine stochastic volatility model that generalizes the seminal Heston model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider both realized variance options and VIX options, and we examine the impact of the distribution of jumps on the associated implied volatility smile. We provide sufficient conditions for the asymptotic behavior of the implied volatility of variance for small and large strikes. In particular, by selecting alternative jump distributions, we show that one can obtain fundamentally different shapes of the implied volatility of variance smile|some clearly at odds with the upward-sloping volatility skew observed in variance markets.

Original language	English
Journal	SIAM Journal on Financial Mathematics
Volume	8
Issue	1
Pages (from-to)	28-53
Number of pages	26
ISSN	1945-497X
DOIs	https://doi.org/10.1137/16M1059072
Publication status	Published - 2017

Keywords

Affine Processes
Jump Distributions
Moment Formula
Realized Variance
Stochastic Volatility
Vix Options

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10.1137/16M1059072

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abstract = "We consider a tractable afine stochastic volatility model that generalizes the seminal Heston model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider both realized variance options and VIX options, and we examine the impact of the distribution of jumps on the associated implied volatility smile. We provide sufficient conditions for the asymptotic behavior of the implied volatility of variance for small and large strikes. In particular, by selecting alternative jump distributions, we show that one can obtain fundamentally different shapes of the implied volatility of variance smile|some clearly at odds with the upward-sloping volatility skew observed in variance markets.",

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N2 - We consider a tractable afine stochastic volatility model that generalizes the seminal Heston model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider both realized variance options and VIX options, and we examine the impact of the distribution of jumps on the associated implied volatility smile. We provide sufficient conditions for the asymptotic behavior of the implied volatility of variance for small and large strikes. In particular, by selecting alternative jump distributions, we show that one can obtain fundamentally different shapes of the implied volatility of variance smile|some clearly at odds with the upward-sloping volatility skew observed in variance markets.

AB - We consider a tractable afine stochastic volatility model that generalizes the seminal Heston model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider both realized variance options and VIX options, and we examine the impact of the distribution of jumps on the associated implied volatility smile. We provide sufficient conditions for the asymptotic behavior of the implied volatility of variance for small and large strikes. In particular, by selecting alternative jump distributions, we show that one can obtain fundamentally different shapes of the implied volatility of variance smile|some clearly at odds with the upward-sloping volatility skew observed in variance markets.

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KW - Jump Distributions

KW - Moment Formula

KW - Realized Variance

KW - Stochastic Volatility

KW - Vix Options

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The Impact of Jump Distributions on the Implied Volatility of Variance

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Keywords

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