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Foreign Exchange Options Under Stochastic Volatility And Stochastic Interest Rates

Author

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  • REHEZ AHLIP

    (School of Computing and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith South DC, NSW 1797, Australia)

Abstract

In this paper, we present a stochastic volatility model with stochastic interest rates in a Foreign Exchange (FX) setting. The instantaneous volatility follows a mean-reverting Ornstein–Uhlenbeck process and is correlated with the exchange rate. The domestic and foreign interest rates are modeled by mean-reverting Ornstein–Uhlenbeck processes. The main result is an analytic formula for the price of a European call on the exchange rate. It is derived using martingale methods in arbitrage pricing of contingent claims and Fourier inversion techniques.

Suggested Citation

  • Rehez Ahlip, 2008. "Foreign Exchange Options Under Stochastic Volatility And Stochastic Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 277-294.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:03:n:s0219024908004804
    DOI: 10.1142/S0219024908004804
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    Citations

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    Cited by:

    1. Recchioni, M.C. & Sun, Y., 2016. "An explicitly solvable Heston model with stochastic interest rate," European Journal of Operational Research, Elsevier, vol. 249(1), pages 359-377.
    2. Griselda Deelstra & Gr�gory Ray�e, 2013. "Local Volatility Pricing Models for Long-Dated FX Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(4), pages 380-402, September.
    3. Maria Cristina Recchioni & Yu Sun & Gabriele Tedeschi, 2017. "Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1257-1275, August.
    4. Ioannis Kyriakou & Nikos K. Nomikos & Nikos C. Papapostolou & Panos K. Pouliasis, 2016. "Affine†Structure Models and the Pricing of Energy Commodity Derivatives," European Financial Management, European Financial Management Association, vol. 22(5), pages 853-881, November.
    5. Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.
    6. 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.
    7. Roman Horsky & Tilman Sayer, 2015. "Joining The Heston And A Three-Factor Short Rate Model: A Closed-Form Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-17, December.
    8. Qianqian Zhou & Junyi Guo, 2020. "Optimal Control of Investment for an Insurer in Two Currency Markets," Papers 2006.02857, arXiv.org.
    9. van Haastrecht, Alexander & Lord, Roger & Pelsser, Antoon & Schrager, David, 2009. "Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 436-448, December.
    10. Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.

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