Back to Search
Start Over
Parallelizing Computation of Expected Values in Recombinant Binomial Trees
- Source :
- J. Stat. Comp. & Sim. 88 (2018) 657-674
- Publication Year :
- 2017
-
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.<br />Comment: 19 pages and 5 figures (png/jpeg files)
- Subjects :
- Statistics - Computation
Quantitative Finance - Computational Finance
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Stat. Comp. & Sim. 88 (2018) 657-674
- Publication Type :
- Report
- Accession number :
- edsarx.1701.03512
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1080/00949655.2017.1402898