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Efficient computation of european option prices and their sensitivities with the complex fourier series method

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  • Chan, Tat Lung (Ron)

Abstract

Highly accurate approximation pricing formulae and option Greeks are obtained for European-type options using a complex Fourier series. We assume that risky assets are driven by exponential Lévy processes and affine stochastic volatility models. We provide a succinct error analysis to demonstrate that we can achieve an exponential convergence rate in the pricing method in many cases as long as we choose the correct truncated computational interval. As a novel pricing method, we also numerically demonstrate that the complex Fourier series performs either favourably or comparably with existing techniques in numerical experiments.

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  • Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    • Handle: RePEc:eee:ecofin:v:50:y:2019:i:c:s1062940818304200
    DOI: 10.1016/j.najef.2019.100984
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    Cited by:

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    3. Wenguang Yu & Yaodi Yong & Guofeng Guan & Yujuan Huang & Wen Su & Chaoran Cui, 2019. "Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    4. Yayun Wang, 2023. "Pricing a Specific Equity Index Annuity in a Regime-Switching Lévy Model with Jump," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1115-1135, March.
    5. Wang, Yayun & Zhang, Zhimin & Yu, Wenguang, 2021. "Pricing equity-linked death benefits by complex Fourier series expansion in a regime-switching jump diffusion model," Applied Mathematics and Computation, Elsevier, vol. 399(C).

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    More about this item

    Keywords

    Complex Fourier series; European options; Exotic options; Forward contracts; Futures; Lévy processes; Affine stochastic volatility;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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