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Heterogeneous Basket Options Pricing Using Analytical Approximations

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Author Info

  • Georges Dionne
  • Geneviève Gauthier
  • Nadia Ouertani
  • Nabil Tahani

Abstract

This paper proposes the use of analytical approximations to price an heterogeneous basket option combining commodity prices, foreign currencies and zero-coupon bonds. We examine the performance of three moment matching approximations: inverse gamma, Edgeworth expansion around the lognormal and Johnson family distributions. Since there is no closed-form formula for basket options, we carry out Monte Carlo simulations to generate the benchmark values. We perfom a simulation experiment on a whole set of options based on a random choice of parameters. Our results show that the lognormal and Johnson distributions give the most accurate results.

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File URL: http://www.cirpee.org/fileadmin/documents/Cahiers_2006/CIRPEE06-05.pdf
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Bibliographic Info

Paper provided by CIRPEE in its series Cahiers de recherche with number 0605.

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Date of creation: 2006
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Handle: RePEc:lvl:lacicr:0605

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Related research

Keywords: Basket Options; Options Pricing; Analytical Approximations; Monte Carlo Simulation;

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References

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  1. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
  2. Milevsky, Moshe Arye & Posner, Steven E., 1998. "Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 409-422, September.
  3. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  4. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
  5. Vanmaele, Michele & Deelstra, Griselda & Liinev, Jan, 2004. "Approximation of stop-loss premiums involving sums of lognormals by conditioning on two variables," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 343-367, October.
  6. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-50.
  7. Georges Dionne & Geneviève Gauthier & Nadia Ouertani, 2009. "Basket Options on Heterogeneous Underlying Assets," Cahiers de recherche 0918, CIRPEE.
  8. Griselda Deelstra & Jan Liinev & Michèle Vanmaele, 2004. "Pricing of arithmetic basket options by conditioning," ULB Institutional Repository 2013/7600, ULB -- Universite Libre de Bruxelles.
  9. Deelstra, G. & Liinev, J. & Vanmaele, M., 2004. "Pricing of arithmetic basket options by conditioning," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 55-77, February.
  10. Jèôme Barraquand, 1995. "Numerical Valuation of High Dimensional Multivariate European Securities," Management Science, INFORMS, vol. 41(12), pages 1882-1891, December.
  11. 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 637-54, May-June.
  12. Michèle Vanmaele & Griselda Deelstra & Jan Liinev, 2004. "Approximation of stop-loss premiums involving sums of lognormals by conditioning on two variables," ULB Institutional Repository 2013/7604, ULB -- Universite Libre de Bruxelles.
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Cited by:
  1. Ng, Andrew C.Y. & Li, Johnny Siu-Hang & Chan, Wai-Sum, 2013. "Pricing options on stocks denominated in different currencies: Theory and illustrations," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 339-354.

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