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Multivariate Hawkes-Based Models In Limit Order Book: European And Spread Option Pricing

Author

Listed:
  • QI GUO

    (Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada)

  • ANATOLIY SWISHCHUK

    (Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada)

  • BRUNO RÉMIlLARD

    (Department of Decision Sciences, HEC Montréal, 3000 Chemin de la Cote-Sainte-Catherine, Montréal, QC H3T 2A7, Canada)

Abstract

In this paper, we consider the pricing problem of European options and spread options for the Hawkes-based model in the limit order book (LOB). We introduce a variant of Hawkes process and consider its limit theorems, namely the exponential multivariate general compound Hawkes process (EMGCHP). We also consider a special case of one-dimensional EMGCHP and its limit theorems. Option pricing with one-dimensional EMGCHP in LOB and numerical examples are presented. We also discuss implied volatility and implied order flow. It reveals the relationship between stock volatility and the order flow in the LOB system. In this way, the Hawkes-based model can provide more market forecast information than the classical Black–Scholes model. Margrabe’s spread options valuations with two one-dimensional and one two-dimensional Hawkes-based models for two assets are presented.

Suggested Citation

  • QI GUO & ANATOLIY SWISHCHUK & BRUNO RÉMIlLARD, 2024. "Multivariate Hawkes-Based Models In Limit Order Book: European And Spread Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 27(03n04), pages 1-20, May.
    • Handle: RePEc:wsi:ijtafx:v:27:y:2024:i:03n04:n:s0219024923500280
    DOI: 10.1142/S0219024923500280
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