Monte Carlo Methods in Financial Engineering

Glasserman, Paul

doi:10.1007/978-0-387-21617-1

Cited by 2,289 publications

(2,249 citation statements)

References 250 publications

(646 reference statements)

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“…The main theorem in this paper proves that the computational complexity for this simple case can be reduced to O ( −2 (log ) 2 ) through the use of a multilevel method which reduces the variance, leaving unchanged the bias due to the Euler discretisation. The multilevel method is very easy to implement and can be combined, in principle, with other variance reduction methods such as stratified sampling [7] and quasi Monte Carlo methods [16,17,19] to obtain even greater savings.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Monte Carlo Path Simulation

Giles

2008

Operations Research

1,335

1,803

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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( ) is reduced from O( −3 ) to O( −2 (log ) 2 ). The analysis is supported by numerical results showing significant computational savings.

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Section: Introductionmentioning

confidence: 99%

Multilevel Monte Carlo Path Simulation

Giles

2008

Operations Research

1,335

1,803

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“…Our calibration procedure relies essentially upon the next formula which follows from (11), (12), (26), and taking the assumptions of Section 3.5 into account.…”

Section: Calibrationmentioning

confidence: 99%

A jump-diffusion Libor model and its robust calibration

Belomestny

Schoenmakers

2011

Quantitative Finance

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In this paper we propose a jump-diffusion Libor model with jumps in a high-dimensional space (R m ) and test a stable non-parametric calibration algorithm which takes into account a given local covariance structure. The algorithm returns smooth and simply structured Lévy densities, and penalizes the deviation from the Libor market model. In practice, the procedure is FFT based, thus fast, easy to implement, and yields good results, particularly in view of the severe ill-posedness of the underlying inverse problem.

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“…In condition (a) the inverse transformation requirement can be replaced by the assumption that all Y j -components are Gaussian: when Y ∼ N(µ, σ 2 ), thenỸ = 2µ −Y ∼ N(µ, σ 2 ), and clearly Y andỸ are negatively correlated. This alternative assumption is typically applied in financial engineering for option pricing (Glasserman, 2003).…”

Section: Antithetic and Common Random Numbersmentioning

confidence: 99%