Journal
BIT NUMERICAL MATHEMATICS
Volume 56, Issue 4, Pages 1401-1423Publisher
SPRINGER
DOI: 10.1007/s10543-016-0616-y
Keywords
American option; Multi-asset option; Greeks; Radial basis function; Partition of unity; Operator splitting method; Penalty method
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The operator splitting method in combination with finite differences has been shown to be an efficient approach for pricing American options numerically. Here, the operator splitting formulation is extended to the radial basis function partition of unity method. An approach that has previously often been used together with radial basis function methods to deal with the free boundary arising in American option pricing is to solve a penalised version of the Black-Scholes equation. It is shown that the operator splitting technique outperforms the penalty approach when used with the radial basis function partition of unity method. Numerical experiments are performed for one, two and three underlying assets. The advantage of the operator splitting technique grows with the number of dimensions.
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