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FFT network for interest rate derivatives with Lévy processes

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Abstract

This paper extends the fast Fourier transform (FFT) network to interest derivative valuation under the Hull–White model driven by a Lévy process. The classical trinomial tree for the Hull–White model is a widely adopted approach in practice, but fails to accommodate the change in the driving stochastic process. Recent finance research supports the use of a Lévy process to replace Brownian motion in stochastic modeling. The FFT network overcomes the drawback of the trinomial approach but maintains its advantages in super-calibration to the term structure of interest rate and efficient computation to various kinds of interest rate derivatives under Lévy processes. The FFT network only requires knowledge of the characteristic function of the Lévy process driving the interest rate process, but not of the interest rate process itself. The numerical comparison between the closed-form solutions of interest rate caps and swaptions and those from FFT network confirms that the proposed network is accurate and efficient. We also demonstrate its use in pricing Bermudan swaptions and other American-style options. Finally, the FFT network is expanded to accommodate path-dependent variables, and is applied to interest rate target redemption notes and a range of accrual notes.

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Notes

  1. The effects of alternative initial term structures can be provided upon request.

  2. The basic contract is taken from Chu and Kwok [2] for comparison.

  3. Although not reported here, we verify that the TARN prices computed by the network agree with those reported in Chu and Kwok [2] under BM.

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Acknowledgements

We thank two anonymous referees and the Guest Editor of this special issue for their comments that improve the quality and readability of the paper. MC Chiu acknowledges the supports by Research Grants Council of Hong Kong with Project Numbers: ECS809913 and GRF18200114. HY Wong acknowledges a direct grant of the Chinese University of Hong Kong.

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Authors and Affiliations

  1. Department of Mathematics and Information Technology, Education University of Hong Kong, Tai Po, Hong Kong

    Mei Choi Chiu

  2. Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong

    Zhuolu Xu & Hoi Ying Wong

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  1. Mei Choi Chiu
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  2. Zhuolu Xu
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  3. Hoi Ying Wong
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Correspondence to Mei Choi Chiu.

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Chiu, M.C., Xu, Z. & Wong, H.Y. FFT network for interest rate derivatives with Lévy processes. Japan J. Indust. Appl. Math. 34, 675–710 (2017). https://doi.org/10.1007/s13160-017-0259-7

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  • DOI: https://doi.org/10.1007/s13160-017-0259-7

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