2009/10/21 by Roman N. Makarov, Makarov, Roman N., Devin Glew +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #math.PR #q-fin.CP #q-fin.PR
paper · pdf · doi:10.48550/arxiv.0910.4177
22 page
arxiv created 2009/10/21 · arxiv updated 2009/12/01
We consider the exact path sampling of the squared Bessel process and some other continuous-time 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 path-dependent options.