Article2015

Multilevel Monte Carlo Approximation of Distribution Functions and Densities

Michael B. Giles · Tigran Nagapetyan · Klaus Ritter

70 citations0/0 files storedSIAM/ASA Journal on Uncertainty Quantification

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Stochastic processes and financial applications Probabilistic and Robust Engineering Design Mathematical Approximation and Integration

Abstract

We construct and analyze multilevel Monte Carlo methods for the approximation of distribution functions and densities of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide a general analysis under suitable assumptions on the weak and strong convergence. We apply the results to smooth path-independent and path-dependent functionals and to stopped exit times of stochastic differential equations (SDEs).

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References

2008Multilevel Monte Carlo Path Simulation 2004Stochastic Calculus for Finance II: Continuous-Time Models 1998Asymptotic error distributions for the Euler method for stochastic differential equations 1996The law of the Euler scheme for stochastic differential equations 2007Improved Multilevel Monte Carlo Convergence using the Milstein Scheme 1996The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density 2005Statistical Romberg extrapolation: A new variance reduction method and applications to option pricing 2010Dual pricing of multi-exercise options under volume constraints

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