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 et al. (Quant Finance 17:873–888, 2017) 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.

Brignone, R., Sgarra, C. (2020). Asian options pricing in Hawkes-type jump-diffusion models. ANNALS OF FINANCE, 16(1), 101-119 [10.1007/s10436-019-00352-1].

Asian options pricing in Hawkes-type jump-diffusion models

BRIGNONE, RICCARDO;
2020

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 et al. (Quant Finance 17:873–888, 2017) 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.
Articolo in rivista - Articolo scientifico
Affine processes; Asian options; COS method; Hawkes processes; Jumps clustering; Option pricing;
Asian options; Option pricing; Jumps clustering; Hawkes processes; Affine Processes; COS Method
English
28-ago-2019
2020
16
1
101
119
none
Brignone, R., Sgarra, C. (2020). Asian options pricing in Hawkes-type jump-diffusion models. ANNALS OF FINANCE, 16(1), 101-119 [10.1007/s10436-019-00352-1].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/245223
Citazioni
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 8
Social impact