Exact Simulation of Bessel Diffusions

TL;DR

This paper introduces exact simulation methods for Bessel diffusions and related processes, enabling precise path sampling crucial for financial modeling and option pricing.

Contribution

It develops new exact simulation techniques for Bessel and related diffusions, including a bridge sampling method for absorbing processes, improving accuracy and efficiency.

Findings

Probability distributions are reduced to randomized gamma distributions.

New bridge sampling technique based on conditioning on first hitting time.

Methods are applied to pricing path-dependent options.

Abstract

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.