scholarly journals A confidence interval for Monte Carlo methods with an application to simulation of obliquely reflecting Brownian motion

1988 ◽  
Vol 29 (2) ◽  
pp. 209-222 ◽  
Author(s):  
Antonella Calzolari ◽  
Cristina Costantini ◽  
Federico Marchetti
Keyword(s):  
Monte Carlo ◽  
Brownian Motion ◽  
Confidence Interval ◽  
Monte Carlo Methods ◽  
Reflecting Brownian Motion

scholarly journals Randomized quasi Monte Carlo methods for pricing of barrier options under fractional Brownian motion

2019 ◽  
Vol 1255 ◽  
pp. 012019
Author(s):  
Chatarina Enny Murwaningtyas ◽  
Sri Haryatmi Kartiko ◽  
Gunardi ◽  
Herry Pribawanto Suryawan
Keyword(s):  
Monte Carlo ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Monte Carlo Methods ◽  
Barrier Options ◽  
Quasi Monte Carlo

scholarly journals Error Bounds for Small Jumps of Lévy Processes

2013 ◽  
Vol 45 (1) ◽  
pp. 86-105
Author(s):  
E. H. A. Dia
Keyword(s):  
Monte Carlo ◽  
Brownian Motion ◽  
Error Bounds ◽  
Monte Carlo Methods ◽  
Lévy Process ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Lévy Measure ◽  
Exponential Lévy Models

The pricing of options in exponential Lévy models amounts to the computation of expectations of functionals of Lévy processes. In many situations, Monte Carlo methods are used. However, the simulation of a Lévy process with infinite Lévy measure generally requires either truncating or replacing the small jumps by a Brownian motion with the same variance. We will derive bounds for the errors generated by these two types of approximation.

SIMULATION OF MULTI-ASSET OPTION GREEKS UNDER A SPECIAL LÉVY MODEL BY MALLIAVIN CALCULUS

2016 ◽  
Vol 57 (3) ◽  
pp. 280-298 ◽  
Author(s):  
YONGZENG LAI ◽  
HAIXIANG YAO
Keyword(s):  
Monte Carlo ◽  
Brownian Motion ◽  
Malliavin Calculus ◽  
Monte Carlo Methods ◽  
Process Model ◽  
Motion Model ◽  
Quasi Monte Carlo ◽  
Brownian Motion Model ◽  
Payoff Functions ◽  
The Finite Difference Method

We discuss simulation of sensitivities or Greeks of multi-asset European style options under a special Lévy process model: that is, the subordinated Brownian motion model. The Malliavin calculus method combined with Monte Carlo and quasi-Monte Carlo methods is used in the simulations. Greeks are expressed in terms of the expectations of the option payoff functions multiplied by the weights involving Malliavin derivatives for multi-asset options. Numerical results show that the Malliavin calculus method is usually more efficient than the finite difference method for options with nonsmooth payoffs. The superiority of the former method over the latter is even more significant when both are combined with quasi-Monte Carlo methods.

scholarly journals Error Bounds for Small Jumps of Lévy Processes

2013 ◽  
Vol 45 (01) ◽  
pp. 86-105
Author(s):  
E. H. A. Dia
Keyword(s):  
Monte Carlo ◽  
Brownian Motion ◽  
Error Bounds ◽  
Monte Carlo Methods ◽  
Lévy Process ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Lévy Measure ◽  
Exponential Lévy Models

The pricing of options in exponential Lévy models amounts to the computation of expectations of functionals of Lévy processes. In many situations, Monte Carlo methods are used. However, the simulation of a Lévy process with infinite Lévy measure generally requires either truncating or replacing the small jumps by a Brownian motion with the same variance. We will derive bounds for the errors generated by these two types of approximation.

MODELING OF A TURBULENT ETHYLENE/AIR JET FLAME USING HYBRID FINITE VOLUME/MONTE CARLO METHODS

2009 ◽  
Vol 1 (1) ◽  
pp. 37-53 ◽  
Author(s):  
Ranjan S. Mehta ◽  
Anquan Wang ◽  
Michael F. Modest ◽  
Daniel C. Haworth
Keyword(s):  
Monte Carlo ◽  
Finite Volume ◽  
Monte Carlo Methods ◽  
Jet Flame ◽  
Air Jet
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