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Advancing the universality of quadrature methods to any underlying process for option pricing

Author

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  • Chen, Ding
  • Härkönen, Hannu J.
  • Newton, David P.

Abstract

Exceptional accuracy and speed for option pricing are available via quadrature (Andricopoulos, Widdicks, Duck, and Newton, 2003), extending into multiple dimensions with complex path-dependency and early exercise (Andricopoulos, Widdicks, Newton, and Duck, 2007). However, the exposition is incomplete, leaving many modelling processes outside the Black-Scholes-Merton framework unattainable. We show how to remove the remaining major block to universal application. Although this had appeared highly problematic, the solution turns out to be conceptually simple and implementation is straightforward (we provide code on the Journal of Financial Economics website at http://jfe.rochester.edu). Crucially, the method retains its speed and flexibility across complex combinations of option features but is now applicable across other underlying processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jfinec:v:114:y:2014:i:3:p:600-612
    DOI: 10.1016/j.jfineco.2014.07.014
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    References listed on IDEAS

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    1. Zhylyevskyy, Oleksandr, 2012. "Efficient Pricing of European-Style Options Under Heston's Stochastic Volatility Model," Staff General Research Papers Archive 34827, Iowa State University, Department of Economics.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    8. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    9. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    10. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    11. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    12. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    13. Oleksandr Zhylyevskyy, 2010. "A fast Fourier transform technique for pricing American options under stochastic volatility," Review of Derivatives Research, Springer, vol. 13(1), pages 1-24, April.
    14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    15. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    16. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    17. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    18. 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.
    19. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. Jean-Guy Simonato, 2016. "A Simplified Quadrature Approach for Computing Bermudan Option Prices," International Review of Finance, International Review of Finance Ltd., vol. 16(4), pages 647-658, December.
    2. Breton, Michèle & Marzouk, Oussama, 2018. "Evaluation of counterparty risk for derivatives with early-exercise features," Journal of Economic Dynamics and Control, Elsevier, vol. 88(C), pages 1-20.
    3. Cosma, Antonio & Galluccio, Stefano & Scaillet, Olivier, 2012. "Valuing American options using fast recursive projections," Working Papers unige:41856, University of Geneva, Geneva School of Economics and Management.
    4. Zhang, Meihui & Jia, Jinhong & Zheng, Xiangcheng, 2023. "Numerical approximation and fast implementation to a generalized distributed-order time-fractional option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    5. 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.
    6. Haozhe Su & M. V. Tretyakov & David P. Newton, 2021. "Deep learning of transition probability densities for stochastic asset models with applications in option pricing," Papers 2105.10467, arXiv.org, revised Jul 2023.
    7. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    8. Cho, Junhyun & Kim, Yejin & Lee, Sungchul, 2022. "An accurate and stable numerical method for option hedge parameters," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    9. Simon Scheidegger & Adrien Treccani, 2021. "Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations [Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion]," Journal of Financial Econometrics, Oxford University Press, vol. 19(2), pages 258-290.
    10. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    11. Jin-Yu Zhang & Wen-Bo Wu & Yong Li & Zhu-Sheng Lou, 2021. "Pricing Exotic Option Under Jump-Diffusion Models by the Quadrature Method," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 867-884, October.

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    More about this item

    Keywords

    Universal quadrature; QUAD; Option pricing; Numerical techniques; Transition density function;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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