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An Analytical Approximation For European Option Prices Under Stochastic Interest Rates

Author

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  • HIDEHARU FUNAHASHI

    (Mizuho Securities Co. Ltd., Otemachi First Square 1-5-1, Otemachi, Chiyoda-ku, Tokyo 100-0004, Japan;
    Tokyo Metropolitan University, Tokyo Metropolitan University 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan)

Abstract

This paper extends the Wiener–Itô chaos expansion approach proposed by Funahashi & Kijima (2015) to an equity-interest-rate hybrid model for the pricing of European contingent claims with special emphasis on calibration to the option markets. Our model can capture the volatility skew and smile of option markets, as well as the stochastic nature of interest rates. Further, the proposed method is applicable to widely used option pricing models such as local volatility models (LVM), stochastic volatility models (SVM), and their combinations with the stochastic nature of interest rates; hence, it is suitable for practical purposes. Through numerical examples, we show that our approximation is quite accurate even for long-maturity and/or high-volatility cases.

Suggested Citation

  • Hideharu Funahashi, 2015. "An Analytical Approximation For European Option Prices Under Stochastic Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-43.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:04:n:s0219024915500260
    DOI: 10.1142/S0219024915500260
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    Cited by:

    1. Colin Turfus, 2018. "Quantifying Correlation Uncertainty Risk in Credit Derivatives Pricing," IJFS, MDPI, vol. 6(2), pages 1-20, April.

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