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SMALL-TIME ASYMPTOTICS IN GEOMETRIC ASIAN OPTIONS FOR A STOCHASTIC VOLATILITY JUMP-DIFFUSION MODEL

Research paper by HOSSEIN JAFARI, GHAZALEH RAHIMI

Indexed on: 01 Mar '19Published on: 22 Jan '19Published in: International Journal of Theoretical and Applied Finance



Abstract

International Journal of Theoretical and Applied Finance, Ahead of Print. The aim of this paper is to study the small time to maturity of the behavior of the geometric Asian option price and implied volatility under a general stochastic volatility model with Lévy process. The volatility process does not need to be a diffusion or a Markov process, but the future average volatility in the model is a nonadapted process. An anticipating Itô formula for Lévy process and the decomposition of the price (Hull–White formula) are obtained using the Malliavin calculus techniques. The decomposition formula is applied to find the small-time limit of the geometric Asian option price and the implied volatility for the model in at-the-money and out-of-the-money cases.