Abstract
We present a multi-threaded parallel algorithm that computes the ask and bid prices of American options with the asset transaction costs being taken into consideration. The parallel algorithm is based on the recombining binomial tree model, and is designed for modern shared-memory multi-core processors. Although parallel pricing algorithms for American options have been well studied, the cases with transaction costs have not been addressed. The parallel algorithm was implemented via POSIX Threads, and was tested. The results demonstrated that the approach was efficient and light-weighted. Reasonable speedups were gained on problems of small sizes.
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References
Bisseling, R.H.: Parallel Scientific Computation: A Structured Approach using BSP and MPI. Oxford University Press, Oxford (2004)
Black, F., Scholes, M.: The Pricing of Options and Corporate Liabilities. The Journal of Political Economy 81(3), 637–659 (1973)
Gerbessiotis, A.V.: Architecture Independent Parallel Binomial Tree Option Price Valuations. Parallel Computing 30, 301–316 (2004)
Gerbessiotis, A.V.: Parallel Option Price Valuations with the Explicit Finite Difference Method. International Journal of Parallel Programming 38, 159–182 (2010)
Merton, R.: Theory of Rational Option Pricing. Bell Journal of Economics and Management Science 4, 141–183 (1973)
Peng, Y., Gong, B., Liu, H., Zhang, Y.: Parallel Computing for Option Pricing Based on the Backward Stochastic Differential Equation. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (eds.) HPCA 2009. LNCS, vol. 5938, pp. 325–330. Springer, Heidelberg (2010)
Perrakis, S., Lefoll, J.: Option Pricing and Replication with Transaction Costs and Dividends. Journal of Economic Dynamics & Control 24, 1527–1561 (2000)
Perrakis, S., Lefoll, J.: The American Put under Transactions Costs. Journal of Economic Dynamics & Control 28, 915–935 (2004)
Roux, A., Zastawniak, T.: American Options under Proportional Transaction Costs: Pricing, Hedging and Stopping Algorithms for Long and Short Positions. Acta Applicandae Mathematicae 28, 199–228 (2009)
Zubair, M., Mukkamala, R.: High Performance Implementation of Binomial Option Pricing. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds.) ICCSA 2008, Part I. LNCS, vol. 5072, pp. 852–866. Springer, Heidelberg (2008)
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Zhang, N., Roux, A., Zastawniak, T. (2011). Parallel Binomial Valuation of American Options with Proportional Transaction Costs. In: Temam, O., Yew, PC., Zang, B. (eds) Advanced Parallel Processing Technologies. APPT 2011. Lecture Notes in Computer Science, vol 6965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24151-2_7
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DOI: https://doi.org/10.1007/978-3-642-24151-2_7
Publisher Name: Springer, Berlin, Heidelberg
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