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Pricing and Hedging Basket Options with Exact Moment Matching

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  • Tommaso Paletta
  • Arturo Leccadito
  • Radu Tunaru
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    Abstract

    Theoretical models applied to option pricing should take into account the empirical characteristics of the underlying financial time series. In this paper, we show how to price basket options when assets follow a shifted log-normal process with jumps capable of accommodating negative skewness. Our technique is based on the Hermite polynomial expansion that can match exactly the first m moments of the model implied-probability distribution. This method is shown to provide superior results for basket options not only with respect to pricing but also for hedging.

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    File URL: http://arxiv.org/pdf/1312.4443
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1312.4443.

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    Date of creation: Dec 2013
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    Handle: RePEc:arx:papers:1312.4443

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    1. Li, Minqiang & Deng, Shijie & Zhou, Jieyun, 2008. "Multi-asset Spread Option Pricing and Hedging," MPRA Paper 8259, University Library of Munich, Germany.
    2. Jèôme Barraquand, 1995. "Numerical Valuation of High Dimensional Multivariate European Securities," Management Science, INFORMS, INFORMS, vol. 41(12), pages 1882-1891, December.
    3. 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, Society for Financial Studies, vol. 14(1), pages 113-47.
    4. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, American Finance Association, vol. 33(1), pages 177-86, March.
    5. Bjerksund, Petter & Stensland, Gunnar, 2006. "Closed form spread option valuation," Discussion Papers, Department of Business and Management Science, Norwegian School of Economics 2006/20, Department of Business and Management Science, Norwegian School of Economics.
    6. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, Elsevier, vol. 11(5), pages 474-491, October.
    7. 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, Anderson Graduate School of Management, UCLA qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    8. Barraquand, Jérôme & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 30(03), pages 383-405, September.
    9. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 26(03), pages 377-389, September.
    10. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(1), pages 39-52.
    11. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    12. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 10(3), pages 347-369, November.
    13. P. Pellizzari, 1998. "Efficient Monte Carlo Pricing of Basket Options," Finance, EconWPA 9801001, EconWPA.
    14. Arturo Leccadito & Pietro Toscano & Radu S. Tunaru, 2012. "Hermite Binomial Trees: A Novel Technique For Derivatives Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1250058-1-1.
    15. Aanand Venkatramanan & Carol Alexander, 2011. "Closed Form Approximations for Spread Options," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(5), pages 447-472, January.
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