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High Dimensional Radial Barrier Options

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Author Info
N.P. Firth
J.N. Dewynne
Abstract

Pricing high dimensional American options is a difficult problem in mathematical finance. Many simulation methods have been proposed, but Monte Carlo is numerically intensive, and therefore slow. We derive an analytic expression for a new type of multi-asset barrier option using Laplace transform methods. The solution is assumed to be radially symmetric in the normalized non dimensional variables, hence the name `Radial Barrier Options'. In the single-asset case our results reduce to published results for American binary barrier options.

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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2004mf02.

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Date of creation: 2004
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Handle: RePEc:sbs:wpsefe:2004mf02

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  1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 14(1), pages 113-47.
  2. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 11(3), pages 627-46.
  5. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May. [Downloadable!] (restricted)
  6. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412. [Downloadable!] (restricted)
  7. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December. [Downloadable!] (restricted)
  8. Barraquand, J?r?me & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(03), pages 383-405, September. [Downloadable!]
  9. Boyle, Phelim P. & Tse, Y. K., 1990. "An Algorithm for Computing Values of Options on the Maximum or Minimum of Several Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(02), pages 215-227, June. [Downloadable!]
  10. Johnson, Herb, 1987. "Options on the Maximum or the Minimum of Several Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 277-283, September. [Downloadable!]
  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. [Downloadable!] (restricted)
  12. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June. [Downloadable!] (restricted)
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