A novel Fourier transform B-spline method for option pricing

Gareth G. Haslip and Vladimir K. Kaishev

Journal of Computational Finance

Abstract: 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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