Asian Options Pricing in Hawkes-Type Jump-Diffusion Models
Annals of Finance (2020) 16:101–119 https://doi.org/10.1007/s10436-019-00352-1
17 Pages Posted: 11 Jun 2019 Last revised: 7 Dec 2020
Date Written: May 24, 2019
In this paper we propose a method for pricing Asian options in market models with the risky asset dynamics driven by a Hawkes process with exponential kernel. For these processes the couple (λ(t), X(t)) is affine, this property allows to extend the general methodology introduced by Hubalek, Keller-Ressel and Sgarra for Geometric Asian option pricing to jump-diffusion models with stochastic jump intensity. Although the system of ordinary differential equations providing the characteristic function of the related affine process cannot be solved in closed form, a COS-type algorithm allows to obtain the relevant quantities needed for options valuation. We describe, by means of graphical illustrations, the dependence of Asian options prices by the main parameters of the driving Hawkes process. Finally, by using Geometric Asian options values as control variates, we show that Arithmetic Asian options prices can be computed in a fast and efficient way by a standard Monte Carlo method.
Keywords: Asian options, Option pricing, Jumps clustering, Hawkes processes, Affine Processes, COS Method
JEL Classification: C63, G12, G13
Suggested Citation: Suggested Citation