The valuation of equity warrants under the fractional Vasicek process of the short-term interest rate

Motivated by the empirical evidence of long range dependence in short-term interest rates and considering the long maturities of equity warrants, we propose the fractional Vasicek model to describe the dynamics of the short rate in the pricing environment of equity warrants. Using the partial differential equation approach, we present a valuation model for equity warrants under the assumption that the short rate follows the fractional Vasicek process. After identifying the pricing model for equity warrants, we provide the parameter estimation procedure for the proposed pricing model. Since obtaining the values of equity warrants from the proposed model needs to solve a nonlinear equation, we employ a hybrid intelligent algorithm to get around this optimization problem. Furthermore, to illustrate the practicality of our proposed model, we conduct an empirical study to ascertain the performance of our proposed model using the data from China’s warrant market and the China Foreign Exchange Trade System. The comparison of traditional models (such as the Black–Scholes model, the Noreen–Wolfson model, the Lauterbach–Schultz model, and the Ukhov model) with our proposed model is also presented. The empirical results show that the mean absolute percentage error of our pricing model is 10.30%. By contrast, the Black–Scholes model, the Noreen–Wolfson model, the Lauterbach–Schultz model, and the Ukhov model applied to the same warrant produce mean absolute errors of 35.26%, 37.67%, 33.40%, 32.81%, respectively. Thus the long memory property in stochastic interest rates cannot be ignored in determining the valuation of equity warrants.