Parallelizing Computation of Expected Values in Recombinant Binomial Trees

Sai K. Popuri, Andrew M. Raim, Nagaraj K. Neerchal and Matthias K. Gobbert

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Abstract: Recombinant binomial trees are binary trees where each non-leaf node has two child nodes, but adjacent parents share a common child node. Such trees arise in finance when pricing an option. For example, valuation of a European option can be carried out by evaluating the expected value of asset payoffs with respect to random paths in the tree. In many variants of the option valuation problem, a closed form solution cannot be obtained and computational methods are needed. The cost to exactly compute expected values over random paths grows exponentially in the depth of the tree, rendering a serial computation of one branch at a time impractical. We propose a parallelization method that transforms the calculation of the expected value into an "embarrassingly parallel" problem by mapping the branches of the binomial tree to the processes in a multiprocessor computing environment. We also propose a parallel Monte Carlo method which takes advantage of the mapping to achieve a reduced variance over the basic Monte Carlo estimator. Performance results from R and Julia implementations of the parallelization method on a distributed computing cluster indicate that both the implementations are scalable, but Julia is significantly faster than a similarly written R code. A simulation study is carried out to verify the convergence and the variance reduction behavior in the proposed Monte Carlo method.

Date: 2017-01, Revised 2018-10
New Economics Papers: this item is included in nep-cmp
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Published in J. Stat. Comp. & Sim. 88 (2018) 657-674

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