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Pricing of foreign exchange options under the Heston stochastic volatility model and CIR interest rates

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  • REHEZ AHLIP
  • MAREK RUTKOWSKI

Abstract

Foreign exchange options are studied in the Heston stochastic volatility model for the exchange rate combined with the Cox et al . dynamics for the domestic and foreign stochastic interest rates. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate. The main result furnishes a semi-analytical formula for the price of the foreign exchange European call option. The FX options pricing formula is derived using the probabilistic approach, which leads to explicit expressions for conditional characteristic functions. Stylized numerical examples show that the dynamics of interest rates are important for the valuation of foreign exchange options. We argue that the model examined in this paper is the only analytically tractable version of the foreign exchange market model that combines the Heston stochastic volatility model for the exchange rate with the CIR dynamics for interest rates.

Suggested Citation

  • Rehez Ahlip & Marek Rutkowski, 2013. "Pricing of foreign exchange options under the Heston stochastic volatility model and CIR interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 955-966, May.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:6:p:955-966
    DOI: 10.1080/14697688.2013.769688
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    Citations

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    Cited by:

    1. Andrei Cozma & Christoph Reisinger, 2015. "A mixed Monte Carlo and PDE variance reduction method for foreign exchange options under the Heston-CIR model," Papers 1509.01479, arXiv.org, revised Apr 2016.
    2. Andrei Cozma & Christoph Reisinger, 2015. "Exponential integrability properties of Euler discretization schemes for the Cox-Ingersoll-Ross process," Papers 1601.00919, arXiv.org.
    3. Jiling Cao & Teh Raihana Nazirah Roslan & Wenjun Zhang, 2018. "Pricing Variance Swaps in a Hybrid Model of Stochastic Volatility and Interest Rate with Regime-Switching," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1359-1379, December.
    4. Andrei Cozma & Matthieu Mariapragassam & Christoph Reisinger, 2015. "Convergence of an Euler scheme for a hybrid stochastic-local volatility model with stochastic rates in foreign exchange markets," Papers 1501.06084, arXiv.org, revised Oct 2016.
    5. Fazlollah Soleymani & Andrey Itkin, 2019. "Pricing foreign exchange options under stochastic volatility and interest rates using an RBF--FD method," Papers 1903.00937, arXiv.org.
    6. Jiaqi Zhu & Shenghong Li, 2020. "Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    7. 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).
    8. Ying Chang & Yiming Wang & Sumei Zhang, 2021. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    9. Qianqian Zhou & Junyi Guo, 2020. "Optimal Control of Investment for an Insurer in Two Currency Markets," Papers 2006.02857, arXiv.org.
    10. S. Simaitis & C. S. L. de Graaf & N. Hari & D. Kandhai, 2016. "Smile and default: the role of stochastic volatility and interest rates in counterparty credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1725-1740, November.

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