Chapter2012

Multilevel Monte Carlo methods for applications in finance

20 citations0/0 files storedInterdisciplinary mathematical sciences

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Stochastic processes and financial applications Markov Chains and Monte Carlo Methods Mathematical Approximation and Integration

Abstract

Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the key features in achieving a high rate of multilevel variance convergence, and suggests directions for future research.

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References

2003Monte Carlo Methods in Financial Engineering 1987Stochastic Simulation 2008Multilevel Monte Carlo Path Simulation 2011Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients 1997A Continuity Correction for Discrete Barrier Options 2007Improved Multilevel Monte Carlo Convergence using the Milstein Scheme 2014Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation 2010Multilevel Monte Carlo algorithms for Lévy-driven SDEs with Gaussian correction

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