Fast binomial procedures for pricing Parisian/ParAsian options

Fast binomial procedures for pricing Parisian/ParAsian options

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Article ID: iaor20172710
Volume: 14
Issue: 3
Start Page Number: 313
End Page Number: 331
Publication Date: Jul 2017
Journal: Computational Management Science
Authors: ,
Keywords: economics, investment, combinatorial optimization
Abstract:

The discrete procedures for pricing Parisian/ParAsian options depend, in general, on three dimensions: time, space, time spent over the barrier. Here we present some combinatorial and lattice procedures which reduce the computational complexity to second order. In the European case the reduction was already given by Lyuu and Wu (Decisions Econ Finance 33(1):49–61, 2010) and Li and Zhao (J Deriv 16(4):72–81, 2009), in this paper we present a more efficient procedure in the Parisian case and a different approach (again of order 2) in the ParAsian case. In the American case we present new procedures which decrease the complexity of the pricing problem for the Parisian/ParAsian knock‐in options. The reduction of complexity for Parisian/ParAsian knock‐out options is still an open problem.

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