Implied Calibration and Moments Asymptotics in Stochastic Volatility Jump Diffusion Models

Abstract

In the context of arbitrage-free modelling of financial derivatives, we introduce a novel calibration technique for models in the affine-quadratic class for the purpose of over-the-counter option pricing and risk-management. In particular, we aim at calibrating a stochastic volatility jump diffusion model to the whole market implied volatility surface at any given time. We study the asymptotic behaviour of the moments of the underlying distribution and use this information to introduce and implement our calibration algorithm. We numerically show that the proposed approach is both statistically stable and accurate.

Keywords: Affine-quadratic models, Option pricing, Model calibration

JEL Classification: G12, G13