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Hedging and Pricing European-type, Early-Exercise and Discrete Barrier Options using Algorithm for the Convolution of Legendre Series

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  • Tat Lung Chan
  • Nicholas Hale

Abstract

This paper applies an algorithm for the convolution of compactly supported Legendre series (the CONLeg method) (cf. Hale and Townsend 2014a), to pricing/hedging European-type, early-exercise and discrete-monitored barrier options under a Levy process. The paper employs Chebfun (cf. Trefethen et al. 2014) in computational finance and provides a quadrature-free approach by applying the Chebyshev series in financial modelling. A significant advantage of using the CONLeg method is to formulate option pricing and option Greek curves rather than individual prices/values. Moreover, the CONLeg method can yield high accuracy in option pricing and hedging when the risk-free smooth probability density function (PDF) is smooth/non-smooth. Finally, we show that our method can accurately price/hedge options deep in/out of the money and with very long/short maturities. Compared with existing techniques, the CONLeg method performs either favourably or comparably in numerical experiments.

Suggested Citation

  • Tat Lung Chan & Nicholas Hale, 2018. "Hedging and Pricing European-type, Early-Exercise and Discrete Barrier Options using Algorithm for the Convolution of Legendre Series," Papers 1811.09257, arXiv.org, revised May 2019.
    • Handle: RePEc:arx:papers:1811.09257
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    References listed on IDEAS

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    1. Tat Lung (Ron) Chan, 2018. "Singular Fourier–Padé series expansion of European option prices," Quantitative Finance, Taylor & Francis Journals, vol. 18(7), pages 1149-1171, July.
    2. M. Broadie & Y. Yamamoto, 2005. "A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options," Operations Research, INFORMS, vol. 53(5), pages 764-779, October.
    3. Liu, Xialu & Xiao, Han & Chen, Rong, 2016. "Convolutional autoregressive models for functional time series," Journal of Econometrics, Elsevier, vol. 194(2), pages 263-282.
    4. Chen, Ding & Härkönen, Hannu J. & Newton, David P., 2014. "Advancing the universality of quadrature methods to any underlying process for option pricing," Journal of Financial Economics, Elsevier, vol. 114(3), pages 600-612.
    5. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    6. Andricopoulos, Ari D. & Widdicks, Martin & Duck, Peter W. & Newton, David P., 2003. "Universal option valuation using quadrature methods," Journal of Financial Economics, Elsevier, vol. 67(3), pages 447-471, March.
    7. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
    8. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    9. D. Andricopoulos, Ari & Widdicks, Martin & Newton, David P. & Duck, Peter W., 2007. "Extending quadrature methods to value multi-asset and complex path dependent options," Journal of Financial Economics, Elsevier, vol. 83(2), pages 471-499, February.
    10. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    11. Maximilian Gaß & Kathrin Glau & Mirco Mahlstedt & Maximilian Mair, 2018. "Chebyshev interpolation for parametric option pricing," Finance and Stochastics, Springer, vol. 22(3), pages 701-731, July.
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    Cited by:

    1. Tat Lung & Chan, 2019. "An SFP--FCC Method for Pricing and Hedging Early-exercise Options under L\'evy Processes," Papers 1909.07319, arXiv.org.

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