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A revisited and stable Fourier transform method for affine jump diffusion models

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  • Minenna, Marcello
  • Verzella, Paolo

Abstract

In the last decade, fast Fourier transform methods (i.e. FFT) have become the standard tool for pricing and hedging with affine jump diffusion models (i.e. AJD), despite the FFT theoretical framework is still in development and it is known that the early solutions have serious problems in terms of stability and accuracy. This fact depends from the relevant computational gain that the FFT approach offers with respect to the standard Fourier transform methods that make use of a canonical inverse Levy formula. In this work we revisit a classic FT method and find that changing the quadrature algorithm and using alternative, less flawed, representation for the pricing formulas can improve the computational performance up to levels that are only three time slower than FFT can achieve. This allows to have at the same time a reasonable computational speed and the well known stability and accuracy of canonical FT methods.

Suggested Citation

  • Minenna, Marcello & Verzella, Paolo, 2008. "A revisited and stable Fourier transform method for affine jump diffusion models," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2064-2075, October.
    • Handle: RePEc:eee:jbfina:v:32:y:2008:i:10:p:2064-2075
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    References listed on IDEAS

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    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    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.
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    Cited by:

    1. Jang, Bong-Gyu & Yoon, Ji Hee, 2010. "Analytic valuation formulas for range notes and an affine term structure model with jump risks," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2132-2145, September.
    2. Seungho Yang & Jaewook Lee, 2014. "Do affine jump-diffusion models require global calibration? Empirical studies from option markets," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 111-123, January.
    3. Yang, Seungho & Oh, Gabjin, 2020. "A Bayesian estimation of exponential Lévy models for implied volatility smile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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