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615
Multilevel Monte Carlo path simulation
 OPERATIONS RESEARCH
, 2008
"... 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 an Euler discretisation, the computational cost to achiev ..."
Abstract

Cited by 189 (23 self)
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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 an Euler discretisation, the computational cost to achieve an accuracy of O(É) is reduced from O(É â3) to O(É â2 (log É) 2). The analysis is supported by numerical results showing significant computational savings.
A stochastic mesh method for pricing highdimensional American options
 Journal of Computational Finance
, 1997
"... Highdimensional problems frequently arise in the pricing of derivative securities – for example, in pricing options on multiple underlying assets and in pricing term structure derivatives. American versions of these options, ie, where the owner has the right to exercise early, are particularly chal ..."
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Cited by 137 (8 self)
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Highdimensional problems frequently arise in the pricing of derivative securities – for example, in pricing options on multiple underlying assets and in pricing term structure derivatives. American versions of these options, ie, where the owner has the right to exercise early, are particularly challenging to price. We introduce a stochastic mesh method for pricing highdimensional American options when there is a finite, but possibly large, number of exercise dates. The algorithm provides point estimates and confidence intervals; we provide conditions under which these estimates converge to the correct values as the computational effort increases. Numerical results illustrate the performance of the method. 1
Exact Simulation of Stochastic Volatility and other
 Affine Jump Diffusion Processes, Working Paper
, 2004
"... The stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated. Discretization methods can be used for simulating security prices under these models. However, discretization introdamp;rft.genre=unknown&rft.aulast=Broadie&rft.aufirst=+Mark&rft.au=Broadie%2C+Mark&rft.au=Glasserman%2C+Paul">
Exact Simulation of Stochastic Volatility and other
 Affine Jump Diffusion Processes, Working Paper
, 2004
"... The stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated. Discretization methods can be used for simulating security prices under these models. However, discretization introd0