Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Monte Carlo Pricing using Operator Methods and Measure Changes

Summary: Monte Carlo Pricing using Operator Methods and
Measure Changes
Claudio Albanese
, Hongyun Li
August 25, 2009, last revised September 7, 2009
A large class of generic stochastic processes which are not necessarily analyti-
cally solvable but are still numerically tractable can be described by giving transition
probability kernels over a contiguous set of time intervals. From the numerical view-
point, this procedure is highly effective on current microchip architectures as kernels
can be conveniently evaluated using GPU co-processors and then used for scenario
generation while storing them in CPU caches. This paper describes the pricing
methodology and a mathematical framework for Finance based on direct kernel ma-
nipulations, i.e. operator methods. We also discuss a number of techniques based
on measure changes to accomplish tasks such as variance reduction and sensitivity
calculations. Numerical experiments are included along with performance bench-
marks. Source code is distributed separately online under GPL license in a library
named OPLib.
1 Introduction 3


Source: Albanese, Claudio - Department of Mathematics, King's College London


Collections: Mathematics