A New S.D.E. And Instantaneous Mean Reversion Rate Formula (Presented Via A Numerical Empirical Model Comparison)

A new short-rate model and a new explicit instantaneous mean reversion formula are introduced. The introduction is presented via a comparison of various short-rate one factor models, which are calibrated and analyzed numerically via a Monte Carlo simulation. Two variance reduction techniques, Stratified Sampling and the Sobol Algorithm, are compared. An empirical comparison is constructed using criteria of goodness-of-fit, in five exchange rates. The data is ex-ante ultimately measuring the predictability of the stochastic models and variance reduction.