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- Title
Pricing Options with Non-Standard Barrier Mechanisms.
- Authors
ANDERLUH, JASPER; MEESTER, LUDOLF
- Abstract
This article enhances the standard Monte Carlo simulation by adding the features of hitting time simulation and backward-in-time simulation conditional on this hitting time. This results in very efficient algorithms for path-dependent options that are of Asian type or involving some barrier-type feature. Efficiency is gained because i) fewer points need to be simulated and ii) a variety of control variates are made available, because exact (non-time-discretized) hitting times are simulated. Steps in developing the algorithm involve a Gir-sanov transform to rewrite the problem in terms of standard Brownian motion and an acceptance-rejection algorithm to sample from the conditional distribution. A simulation study is performed on a particularly intricate barrier-type option; its results show how the relative efficiency of the enhanced algorithm, ranging from 1 to 50 000, is influenced by the problem parameters.
- Subjects
DERIVATIVE securities; MATHEMATICAL models of security prices; MONTE Carlo method; RICHARDSON extrapolation; MATHEMATICAL sequences; MATHEMATICAL formulas
- Publication
Journal of Derivatives, 2013, Vol 21, Issue 2, p75
- ISSN
1074-1240
- Publication type
Article
- DOI
10.3905/jod.2013.21.2.075