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An extension of Heston's SV model to Stochastic Interest Rates

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  • Javier de Frutos
  • Victor Gaton

Abstract

In 'A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options', Heston proposes a Stochastic Volatility (SV) model with constant interest rate and derives a semi-explicit valuation formula. Heston also describes, in general terms, how the model could be extended to incorporate Stochastic Interest Rates (SIR). This paper is devoted to the construction of an extension of Heston's SV model with a particular stochastic bond model which, just increasing in one the number of parameters, allows to incorporate SIR and to derive a semi-explicit formula for option pricing.

Suggested Citation

  • Javier de Frutos & Victor Gaton, 2018. "An extension of Heston's SV model to Stochastic Interest Rates," Papers 1809.09069, arXiv.org.
    • Handle: RePEc:arx:papers:1809.09069
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    References listed on IDEAS

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    1. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    5. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
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