Multilevel Monte Carlo Path Simulation
Top Cited Papers
- 1 June 2008
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Operations Research
- Vol. 56 (3), 607-617
- https://doi.org/10.1287/opre.1070.0496
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(ε) is reduced from O(ε-3) to O(ε-2(logε)2). The analysis is supported, by numerical results showing significant computational savings. © 2008 INFORMSThis publication has 16 references indexed in Scilit:
- Fast strong approximation Monte Carlo schemes for stochastic volatility modelsQuantitative Finance, 2006
- Statistical Romberg extrapolation: A new variance reduction method and applications to option pricingThe Annals of Applied Probability, 2005
- Multilevel Monte Carlo MethodsLecture Notes in Computer Science, 2001
- Multilevel Splitting for Estimating Rare Event ProbabilitiesOperations Research, 1999
- A Continuity Correction for Discrete Barrier OptionsMathematical Finance, 1997
- The law of the Euler scheme for stochastic differential equationsProbability Theory and Related Fields, 1996
- Efficient Monte Carlo Simulation of Security PricesThe Annals of Applied Probability, 1995
- Random Generation of Stochastic Area IntegralsSIAM Journal on Applied Mathematics, 1994
- A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency OptionsThe Review of Financial Studies, 1993
- Expansion of the global error for numerical schemes solving stochastic differential equationsStochastic Analysis and Applications, 1990