Lattice Option Pricing By Multidimensional Interpolation
This note proposes a method for pricing high-dimensional American options based on modern methods of multidimensional interpolation. The method allows using sparse grids and thus mitigates the curse of dimensionality. A framework of the pricing algorithm and the corresponding interpolation methods are discussed, and a theorem is demonstrated that suggests that the pricing method is less vulnerable to the curse of dimensionality. The method is illustrated by an application to rainbow options and compared to Least Squares Monte Carlo and other benchmarks.
|Date of creation:||07 Sep 2003|
|Date of revision:||29 Oct 2004|
|Note:||Type of Document - pdf; prepared on IBM PC ; pages: 17; figures: included|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
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- Frank Milne & Dilip Madan & Hersh Shefrin, 1990.
"The Multinomial Option Pricing Model and Its Brownian and Poisson Limits,"
1162, Queen's University, Department of Economics.
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- Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
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- Barraquand, Jérôme & 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.
- 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 113-47.
- Boyle, Phelim P & Evnine, Jeremy & Gibbs, Stephen, 1989. "Numerical Evaluation of Multivariate Contingent Claims," Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 241-50.
- 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.
- Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March.
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