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