VIX and European options with jumps in the short-maturity regime

TL;DR

This paper derives closed-form short-maturity asymptotics for VIX and European options in models with jumps, providing accurate predictions validated through numerical examples.

Contribution

It introduces explicit asymptotic formulas for option prices with jumps in local-stochastic volatility models, covering both OTM and ATM cases.

Findings

Asymptotic formulas match numerical results closely

Applicable to Eraker, Kou-type, and folded normal models

Enhances understanding of short-maturity option pricing with jumps

Abstract

We present a study of the short-maturity asymptotics for VIX and European option prices in local-stochastic volatility models with compound Poisson jumps. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. The leading-order asymptotics are obtained in closed-form. We apply our results to three examples: the Eraker model, a Kou-type model, and a folded normal model. Numerical illustrations are provided for these three examples that show the accuracy of predictions based on the asymptotic results.