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Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities

Author

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  • Fredrik Åkesson

    (Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, 15213, and Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden)

  • John P. Lehoczky

    (Department of Statistics, Carnegie Mellon University, Pittsburgh, Pennsylvania, 15213)

Abstract

Monte Carlo simulation is playing an increasingly important role in the pricing and hedging of complex, path dependent financial instruments. Low discrepancy simulation methods offer the potential to provide faster rates of convergence than those of standard Monte Carlo methods; however, in high dimensional problems special methods are required to ensure that the faster convergence rates hold. Indeed, Ninomiya and Tezuka (1996) have shown highdimensional examples, in which low discrepancy methods perform worse than Monte Carlo methods. The principal component construction introduced by Acworth et al. (1998) provides one solution to this problem. However, the computational effort required to generate each path grows quadratically with the dimension of the problem. This article presents two new methods that offer accuracy equivalent, in terms of explained variability, to the principal components construction with computational requirements that are linearly related to the problem dimension. One method is to take into account knowledge about the payoff function, which makes it more flexible than the Brownian Bridge construction. Numerical results are presented that show the benefits of such adjustments. The different methods are compared for the case of pricing mortgage backed securities using the Hull-White term structure model.

Suggested Citation

  • Fredrik Åkesson & John P. Lehoczky, 2000. "Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities," Management Science, INFORMS, vol. 46(9), pages 1171-1187, September.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:9:p:1171-1187
    DOI: 10.1287/mnsc.46.9.1171.12239
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    References listed on IDEAS

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    Cited by:

    1. Paoyu Huang & Chih-Te Yang & Yuhsin Chen & Yensen Ni, 2023. "A New Look on the Profitability of Fixed and Indexed Mortgage Products," Mathematics, MDPI, vol. 11(17), pages 1-16, August.
    2. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, July.
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    6. Nabil Kahalé, 2020. "Randomized Dimension Reduction for Monte Carlo Simulations," Management Science, INFORMS, vol. 66(3), pages 1421-1439, March.
    7. Eichler Andreas & Leobacher Gunther & Zellinger Heidrun, 2011. "Calibration of financial models using quasi-Monte Carlo," Monte Carlo Methods and Applications, De Gruyter, vol. 17(2), pages 99-131, January.
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    10. Xiaoqun Wang, 2009. "Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 488-504, August.

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