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Function-approximation-based perfect control variates for pricing American options

Published: 04 December 2005 Publication History

Abstract

Monte Carlo simulation techniques that use function approximations have been successfully applied to approximately price multi-dimensional American options. However, for many pricing problems the time required to get accurate estimates can still be prohibitive, and this motivates the development of variance reduction techniques. In this paper, we describe a zero-variance or 'perfect' control variate to price American options. We then discuss how function approximation may be used to approximate this perfect control variate. Empirically, we observe that on simple one dimensional examples, this approximately perfect control variate gives orders of magnitude of variance reduction compared to naive estimation.

References

[1]
Bertsekas, D. P. and J. N. Tsitsiklis. 1996. Neuro-Dynamic Programming. Belmont, Massachusetts: Athena Scientific.
[2]
Bolia, N., P. Glasserman, and S. Juneja. 2004. Function-Approximation-based Importance Sampling for Pricing American Options. In Proceedings of the 2004 Winter Simulation Conference, ed. R. G. Ingalls, M. D. Rossetti, J. S. Smith, and B. A. Peters, 604--611. Piscataway, New Jersey: Institute of Electrical and Electronics Engineers.
[3]
Bolia, N. and S. Juneja. 2005. Monte Carlo Methods for Pricing Financial Options. Sadhana, 30, 347--386.
[4]
Carrière, J. 1996. Valuation of Early-Exercise Price of Options Using Simulations and Non-Parametric Regression. Insurance: Mathematics and Economics 19, 19--30.
[5]
Duffie, D. 1996. Dynamic Asset Pricing Theory. Princeton, New Jersey: Princeton University Press.
[6]
Glasserman, P. 2004. Monte Carlo Methods in Financial Engineering. New York: Springer-Verlag.
[7]
Haugh, M. B. and L. Kogan. 2004. Pricing American Options: A Duality Approach. Operations Research 52(2), 258--270.
[8]
Henderson, S. and P. Glynn. 2001. Approximating Martingales for Variance Reduction in Markov Process Simulation. Mathematics of Operations Research 27, 253--271.
[9]
Kallianpur, G. and R. L. Karandikar. 1999. Introduction to Option Pricing Theory. Birkhauser Verlag.
[10]
Karatzas, I. and S. Shreve. 1991. Brownian Motion and Stochastic Calculus. New York: Springer Verlag.
[11]
Longstaff, F. A., and E. S. Schwartz. 2001. Valuing American Options by Simulation: A Simple Least-Squares Approach. Review of Financial Studies 14, 113--147.
[12]
Tsitsiklis, J., and B. Van Roy. 2001. Regression Methods for Pricing Complex American-Style Options. IEEE Transactions on Neural Networks 12, 694--703.
[13]
Williams, D. 1991. Probability with Martingales, U.K.: Cambridge University Press.

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  • (2006)American options from MARSProceedings of the 38th conference on Winter simulation10.5555/1218112.1218246(719-726)Online publication date: 3-Dec-2006
  1. Function-approximation-based perfect control variates for pricing American options

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    cover image ACM Conferences
    WSC '05: Proceedings of the 37th conference on Winter simulation
    December 2005
    2769 pages
    ISBN:0780395190

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    Published: 04 December 2005

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    WSC '05 Paper Acceptance Rate 209 of 316 submissions, 66%;
    Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

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    • (2006)American options from MARSProceedings of the 38th conference on Winter simulation10.5555/1218112.1218246(719-726)Online publication date: 3-Dec-2006

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