A short memory version of the Vasicek model and evaluating European options on zero-coupon bonds

This paper considers a fractional version of the Vasicek interest rate model where the noise part of the model is modeled as fractional Brownian motion with Hurst index H∈(0,12). We first show that the increments of the model have short-range dependence. Then, the efficiency of the proposed model versus the classical interest rate models is examined by employing the MLE calibration method and the Akaike Information Criterion (AIC). An analytic approximation formula for pricing zero-coupon bond when the dynamics of the interest rate governed by the model is derived. We also find a margin for the option price by using bid and ask formulas.