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Estimating Security Price Derivatives Using Simulation

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Author Info

  • Mark Broadie

    (The Graduate School of Business, Columbia University, New York, New York 10027)

  • Paul Glasserman

    (The Graduate School of Business, Columbia University, New York, New York 10027)

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    Abstract

    Simulation has proved to be a valuable tool for estimating security prices for which simple closed form solutions do not exist. In this paper we present two direct methods, a pathwise method and a likelihood ratio method, for estimating derivatives of security prices using simulation. With the direct methods, the information from a single simulation can be used to estimate multiple derivatives along with a security's price. The main advantage of the direct methods over resimulation is increased computational speed. Another advantage is that the direct methods give unbiased estimates of derivatives, whereas the estimates obtained by resimulation are biased. Computational results are given for both direct methods, and comparisons are made to the standard method of resimulation to estimate derivatives. The methods are illustrated for a path independent model (European options), a path dependent model (Asian options), and a model with multiple state variables (options with stochastic volatility).

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    File URL: http://dx.doi.org/10.1287/mnsc.42.2.269
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 42 (1996)
    Issue (Month): 2 (February)
    Pages: 269-285

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    Handle: RePEc:inm:ormnsc:v:42:y:1996:i:2:p:269-285

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    Related research

    Keywords: simulation; derivative estimation; security pricing; option pricing;

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    Cited by:
    1. Detemple, Jerome & Rindisbacher, Marcel, 2007. "Monte Carlo methods for derivatives of options with discontinuous payoffs," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3393-3417, April.
    2. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    3. Jan Baldeaux & Dale Roberts, 2012. "Quasi-Monte Carlo methods for the Heston model," Papers 1202.3217, arXiv.org, revised May 2012.
    4. Dan Galai & Alon Raviv & Zvi Wiener, 2003. "Liquidation Triggers and the Valuation of Equity and Debt," Finance 0305002, EconWPA.
    5. T. R. Cass & P. K. Friz, 2006. "The Bismut-Elworthy-Li formula for jump-diffusions and applications to Monte Carlo pricing in finance," Papers math/0604311, arXiv.org, revised May 2007.
    6. Tebaldi, Claudio, 2005. "Hedging using simulation: a least squares approach," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1287-1312, August.
    7. Tian-Shyr Dai & Yuh-Dauh Lyuu, 2002. "Efficient, exact algorithms for asian options with multiresolution lattices," Review of Derivatives Research, Springer, vol. 5(2), pages 181-203, May.
    8. Arturo Kohatsu & Montero Miquel, 2003. "Malliavin calculus in finance," Economics Working Papers 672, Department of Economics and Business, Universitat Pompeu Fabra.
    9. Lim, Andrew E.B. & Wong, Bernard, 2010. "A benchmarking approach to optimal asset allocation for insurers and pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 317-327, April.
    10. Mark J. Cathcart & Steven Morrison & Alexander J. McNeil, 2011. "Calculating Variable Annuity Liability 'Greeks' Using Monte Carlo Simulation," Papers 1110.4516, arXiv.org.
    11. Ballestra, Luca Vincenzo & Pacelli, Graziella & Zirilli, Francesco, 2007. "A numerical method to price exotic path-dependent options on an underlying described by the Heston stochastic volatility model," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3420-3437, November.
    12. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
    13. Adrien Nguyen Huu & Nadia Oudjane, 2014. "Hedging Expected Losses on Derivatives in Electricity Futures Markets," Papers 1401.8271, arXiv.org.
    14. Eric Benhamou, 2002. "A Generalisation of Malliavin Weighted Scheme for Fast Computation of the Greeks," Finance 0212003, EconWPA.
    15. Arturo Kohatsu-Higa & Miquel Montero, 2001. "An application of Malliavin Calculus to Finance," Papers cond-mat/0111563, arXiv.org.
    16. Fard, Farzad Alavi & Siu, Tak Kuen, 2013. "Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 712-721.
    17. Siddiqi, Mazhar A., 2009. "Investigating the effectiveness of convertible bonds in reducing agency costs: A Monte-Carlo approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(4), pages 1360-1370, November.
    18. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    19. Raoul Pietersz & Antoon Pelsser & Marcel van Regenmortel, 2005. "Fast drift approximated pricing in the BGM model," Finance 0502005, EconWPA.
    20. Christian P. Fries & Joerg Kampen, 2005. "Proxy simulation schemes using likelihood ratio weighted Monte Carlo for generic robust Monte-Carlo sensitivities and high accuracy drift approximation (with applications to the LIBOR Market Model)," Finance 0504010, EconWPA.
    21. Jiun Hong Chan and Mark Joshi, 2012. "Optimal Limit Methods for Computing Sensitivities of," Department of Economics - Working Papers Series 1142, The University of Melbourne.

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