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Foreign Exchange Options on Heston-CIR Model Under Lévy Process Framework

Author

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  • Ascione, Giacomo
  • Mehrdoust, Farshid
  • Orlando, Giuseppe
  • Samimi, Oldouz

Abstract

In this paper, we consider the Heston-CIR model with Lévy process for pricing in the foreign exchange (FX) market by providing a new formula that better fits the distribution of prices. To do that, first, we study the existence and uniqueness of the solution to this model. Second, we examine the strong convergence of the Lévy process with stochastic domestic short interest rates, foreign short interest rates and stochastic volatility. Then, we apply Least Squares Monte Carlo (LSMC) method for pricing American options under our model with stochastic volatility and stochastic interest rate. Finally, by considering real-world market data, we illustrate numerical results for the four-factor Heston-CIR Lévy model.

Suggested Citation

  • Ascione, Giacomo & Mehrdoust, Farshid & Orlando, Giuseppe & Samimi, Oldouz, 2023. "Foreign Exchange Options on Heston-CIR Model Under Lévy Process Framework," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    • Handle: RePEc:eee:apmaco:v:446:y:2023:i:c:s0096300323000206
    DOI: 10.1016/j.amc.2023.127851
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    More about this item

    Keywords

    Heston-CIR model; Variance gamma process; Lévy processes; Foreign short interest rates;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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