Fast maximum likelihood estimation of parameters for square root and Bessel processes

Explicit formulae for maximum likelihood estimates of the parameters of square root processes and Bessel processes and first and second order approximate sufficient statistics are supplied. Applications of the estimation formulae to simulated interest rate and index time series are supplied, demonstrating the accuracy of the approximations and the extreme speed-up in estimation time. This significantly improved run time for parameter estimation has many applications where ex-ante forecasts are required frequently and immediately, such as in hedging interest rate, index and volatility derivatives based on such models, as well as modelling credit risk, mortality rates, population size and voting behaviour.