Simulation of the CEV process and the local martingale property

We consider the constant elasticity of variance (CEV) process, reviewing the relationships between its transition density and that of the non-central chi-squared distribution. When the CEV parameter exceeds one, the forward price process is a strictly local martingale, and the price of a plain vanilla European call option reflects this fact. We develop techniques for Monte Carlo simulation of the CEV process, for all parameter regimes, and compare the results against the analytic expressions for plain vanilla European option prices. Using these techniques, we also verify the local martingale property.