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

See all articles by Riccardo Brignone

Riccardo Brignone

University of Freiburg

Carlo Sgarra

Politecnico di Milano- Dipartimento di Matematica

Date Written: May 24, 2019

Abstract

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

Brignone, Riccardo and Sgarra, Carlo, Asian Options Pricing in Hawkes-Type Jump-Diffusion Models (May 24, 2019). Annals of Finance (2020) 16:101–119 https://doi.org/10.1007/s10436-019-00352-1, Available at SSRN: https://ssrn.com/abstract=3394410 or http://dx.doi.org/10.2139/ssrn.3394410

Riccardo Brignone

University of Freiburg ( email )

Platz der Alten Synagoge, KG II
Platz der Alten Synagoge, KG II
Freiburg, DE
Germany

Carlo Sgarra (Contact Author)

Politecnico di Milano- Dipartimento di Matematica ( email )

Piazza Leonardo da Vinci
Milan, Milano 20100
Italy

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