Exact Simulation of Bessel Diffusions
Abstract
We consider the exact path sampling of the squared Bessel process and some other continuoustime Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change of measure. All these diffusions are broadly used in mathematical finance for modelling asset prices, market indices, and interest rates. We show how the probability distributions of a squared Bessel bridge and a squared Bessel process with or without absorption at zero are reduced to randomized gamma distributions. Moreover, for absorbing stochastic processes, we develop a new bridge sampling technique based on conditioning on the first hitting time at zero. Such an approach allows us to simplify simulation schemes. New methods are illustrated with pricing pathdependent options.
 Publication:

arXiv eprints
 Pub Date:
 October 2009
 arXiv:
 arXiv:0910.4177
 Bibcode:
 2009arXiv0910.4177M
 Keywords:

 Quantitative Finance  Computational Finance;
 Mathematics  Probability;
 Quantitative Finance  Pricing of Securities
 EPrint:
 22 page