FFT network for interest rate derivatives with Lévy processes

Mei Choi CHIU, Zhuolu XU, Hoi Ying WONG

Research output: Contribution to journalArticle

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. Copyright © 2017 The JJIAM Publishing Committee and Springer Japan KK.
Original languageEnglish
Pages (from-to)675-710
JournalJapan Journal of Industrial and Applied Mathematics
Volume34
Issue number3
Early online dateJul 2017
DOIs
Publication statusPublished - 2017

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Fast Fourier transform
Interest Rates
Fast Fourier transforms
Derivatives
Derivative
Term Structure of Interest Rates
Brownian movement
Finance
Random processes
Stochastic Modeling
Numerical Comparisons
Characteristic Function
Closed-form Solution
Japan
Valuation
Pricing
Brownian motion
Stochastic Processes
Calibration
Path

Citation

Chiu, M. C., Xu, Z., & Wong, H. Y. (2017). FFT network for interest rate derivatives with Lévy processes. Japan Journal of Industrial and Applied Mathematics, 34(3), 675-710.

Keywords

  • FFT newwork
  • Interest rate derivatives
  • Levy processes