Journal of Computational Finance

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A novel Fourier transform B-spline method for option pricing

Gareth G. Haslip and Vladimir K. Kaishev

  • An explicit, closed-form representation is derived that provides the option price in the form of a linear combination of low order divided differences of trigonometric functions.
  • The FTBS framework is easy to implement and utilises an optimal B-spline interpolation of two simple functions related to the asset model's characteristic function.
  • The FTBS method, by virtue of the properties of B-splines, provides significantly higher accuracy than alternative pricing methods for the same number of interpolation sites as quadrature points of the alternative methods.
  • The FTBS method provides stable calibration parameters extremely quickly under various asset models that include stochastic volatility and jumps, such as the popular models of Heston and Bates

ABSTRACT

In this paper, we present a new efficient and robust framework for European option pricing under continuous-time asset models from the family of exponential semimartingale processes. We introduce B-spline interpolation theory to derivative pricing in order to provide an accurate closed-form representation of the option price under an inverse Fourier transform.We compare our method with some state-of-the-art option pricing methods and demonstrate that it is extremely fast and accurate. This suggests a wide range of applications, including the use of more realistic asset models in highfrequency trading. Examples considered in the paper include option pricing under asset models, including stochastic volatility and jumps, computation of the Greeks and the inverse problem of cross-sectional calibration.

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