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LATTICE OPTION PRICING BY MULTIDIMENSIONAL INTERPOLATION
Author(s) -
Kargin Vladislav
Publication year - 2005
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2005.00254.x
Subject(s) - curse of dimensionality , interpolation (computer graphics) , monte carlo methods for option pricing , monte carlo method , valuation of options , curse , sparse grid , mathematical optimization , computer science , multivariate interpolation , econometrics , mathematics , bilinear interpolation , machine learning , artificial intelligence , statistics , motion (physics) , sociology , anthropology , computer vision
This paper 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, which 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.