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Exact Monte Carlo simulation of killed diffusions

Published online by Cambridge University Press:  01 July 2016

Bruno Casella  and
Gareth O. Roberts
Bruno Casella*
Affiliation:
University of Warwick
Gareth O. Roberts*
Affiliation:
University of Warwick
*
∗ Current address: via novara, 31, Milan, 20147, Italy.
∗∗ Postal address: Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK. Email address: [email protected]
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Abstract

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We describe and implement a novel methodology for Monte Carlo simulation of one-dimensional killed diffusions. The proposed estimators represent an unbiased and efficient alternative to current Monte Carlo estimators based on discretization methods for the cases when the finite-dimensional distributions of the process are unknown. For barrier option pricing in finance, we design a suitable Monte Carlo algorithm both for the single barrier case and the double barrier case. Results from numerical investigations are in excellent agreement with the theoretical predictions.

Keywords

Monte Carlodiffusionsexact algorithm
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 1 , March 2008 , pp. 273 - 291
Copyright
Copyright © Applied Probability Trust 2008 

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