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Multilevel Monte Carlo Path Simulation

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  • Michael B. Giles

    (Oxford University Mathematical Institute, and Oxford---Man Institute of Quantitative Finance, Oxford OX1 3LB, United Kingdom)

Abstract

We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O ((epsilon)) is reduced from O ((epsilon) -3 ) to O ((epsilon) -2 (log (epsilon)) 2 ). The analysis is supported by numerical results showing significant computational savings.

Suggested Citation

  • Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:3:p:607-617
    DOI: 10.1287/opre.1070.0496
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    References listed on IDEAS

    as
    1. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin & Tim Zajic, 1999. "Multilevel Splitting for Estimating Rare Event Probabilities," Operations Research, INFORMS, vol. 47(4), pages 585-600, August.
    4. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
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