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Parallel Binomial American Option Pricing with (and without) Transaction Costs

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  • Nan Zhang
  • Alet Roux
  • Tomasz Zastawniak
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    Abstract

    We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of 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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    File URL: http://arxiv.org/pdf/1110.2477
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1110.2477.

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    Date of creation: Oct 2011
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    Handle: RePEc:arx:papers:1110.2477

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    1. Stylianos PERRAKIS & Jean LEFOLL, 1999. "Option Pricing and Replication with Transaction Costs and Dividends," FAME Research Paper Series, International Center for Financial Asset Management and Engineering rp8, International Center for Financial Asset Management and Engineering.
    2. Boyle, Phelim P & Vorst, Ton, 1992. " Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, American Finance Association, vol. 47(1), pages 271-93, March.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    4. Schwartz, Eduardo S., 1977. "The valuation of warrants: Implementing a new approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 4(1), pages 79-93, January.
    5. Perrakis, Stylianos & Lefoll, Jean, 1997. "Derivative Asset Pricing with Transaction Costs: An Extension," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 10(4), pages 359-76, November.
    6. Perrakis, Stylianos & Lefoll, Jean, 2004. "The American put under transactions costs," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 28(5), pages 915-935, February.
    7. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 2(2), pages 63-86.
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