Parallel Binomial American Option Pricing under Proportional Transaction Costs ()

Nan Zhang, Alet Roux, Tomasz Zastawniak

Department of Computer Science and Software Engineering, Xi’an Jiaotong-Liverpool University (XJTLU), Suzhou, China.

Department of Mathematics, University of York, York, UK.

**DOI: **10.4236/am.2012.331245
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Department of Computer Science and Software Engineering, Xi’an Jiaotong-Liverpool University (XJTLU), Suzhou, China.

Department of Mathematics, University of York, York, UK.

We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to trading in the underlying asset. The algorithm computes the prices on recombining binomial trees, and is designed for modern multi-core processors. Although parallel option pricing has been well studied, none of the existing approaches takes transaction costs into consideration. The algorithm that we propose partitions a binomial tree into blocks. In any round of computation a block is further partitioned into regions which are assigned to distinct processors. To minimise load imbalance the assignment of nodes to processors is dynamically adjusted before each new round starts. Synchronisation is required both within a round and between two successive rounds. The parallel speedup of the algorithm is proportional to the number of processors used. The parallel algorithm was implemented in C/C++ via POSIX Threads, and was tested on a machine with 8 processors. In the pricing of an American put option, the parallel speedup against an efficient sequential implementation was 5.26 using 8 processors and 1500 time steps, achieving a parallel efficiency of 65.75%.

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N. Zhang, A. Roux and T. Zastawniak, "Parallel Binomial American Option Pricing under Proportional Transaction Costs," *Applied Mathematics*, Vol. 3 No. 11A, 2012, pp. 1795-1810. doi: 10.4236/am.2012.331245.

Conflicts of Interest

The authors declare no conflicts of interest.

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