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Asian options pricing in Hawkes-type jump-diffusion models

Author

Listed:
  • Riccardo Brignone

    (Università di Milano Bicocca)

  • Carlo Sgarra

    (Politecnico di Milano)

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 $$ (\lambda (t), X(t) ) $$(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.

Suggested Citation

  • Riccardo Brignone & Carlo Sgarra, 2020. "Asian options pricing in Hawkes-type jump-diffusion models," Annals of Finance, Springer, vol. 16(1), pages 101-119, March.
    • Handle: RePEc:kap:annfin:v:16:y:2020:i:1:d:10.1007_s10436-019-00352-1
    DOI: 10.1007/s10436-019-00352-1
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    Cited by:

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    More about this item

    Keywords

    Asian options; Option pricing; Jumps clustering; Hawkes processes; Affine processes; COS method;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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