@article{Jacquier:2012:10.1080/17442508.2012.720687,
author = {Jacquier, A and Keller-Ressel, M and Mijatovic, A},
doi = {10.1080/17442508.2012.720687},
journal = {Stochastics-An International Journal of Probability and Stochastic Processes},
title = {Large deviations and stochastic volatility with jumps: asymptotic  implied volatility for affine models},
url = {http://dx.doi.org/10.1080/17442508.2012.720687},
year = {2012}
}

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TY  - JOUR
AB  - Let $\sigma_t(x)$ denote the implied volatility at maturity $t$ for a strike$K=S_0 e^{xt}$, where $x\in\bbR$ and $S_0$ is the current value of theunderlying. We show that $\sigma_t(x)$ has a uniform (in $x$) limit as maturity$t$ tends to infinity, given by the formula$\sigma_\infty(x)=\sqrt{2}(h^(x)^{1/2}+(h^(x)-x)^{1/2})$, for $x$ in somecompact neighbourhood of zero in the class of affine stochastic volatilitymodels. The function $h^$ is the convex dual of the limiting cumulantgenerating function $h$ of the scaled log-spot process. We express $h$ in termsof the functional characteristics of the underlying model. The proof of thelimiting formula rests on the large deviation behaviour of the scaled log-spotprocess as time tends to infinity. We apply our results to obtain the limitingsmile for several classes of stochastic volatility models with jumps used inapplications (e.g. Heston with state-independent jumps, Bates withstate-dependent jumps and Barndorff-Nielsen-Shephard model).
AU  - Jacquier,A
AU  - Keller-Ressel,M
AU  - Mijatovic,A
DO  - 10.1080/17442508.2012.720687
PY  - 2012///
TI  - Large deviations and stochastic volatility with jumps: asymptotic  implied volatility for affine models
T2  - Stochastics-An International Journal of Probability and Stochastic Processes
UR  - http://dx.doi.org/10.1080/17442508.2012.720687
UR  - http://arxiv.org/abs/1108.3998v1
ER  - 

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