# Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models

Economy – Quantitative Finance – Pricing of Securities

Scientific paper

[ 0.00 ] – not rated yet Voters 0   Comments 0

## Details Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models

30 pages, 1 figure

Scientific paper

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 the underlying. 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 some compact neighbourhood of zero in the class of affine stochastic volatility models. The function $h^*$ is the convex dual of the limiting cumulant generating function $h$ of the scaled log-spot process. We express $h$ in terms of the functional characteristics of the underlying model. The proof of the limiting formula rests on the large deviation behaviour of the scaled log-spot process as time tends to infinity. We apply our results to obtain the limiting smile for several classes of stochastic volatility models with jumps used in applications (e.g. Heston with state-independent jumps, Bates with state-dependent jumps and Barndorff-Nielsen-Shephard model).

No associations

LandOfFree

## Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

## Rating

Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models will most certainly appreciate the feedback.

Profile ID: LFWR-SCP-O-108714

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.