  In this paper we propose an extension of the Merton model. We apply the
subdiffusive mechanism to analyze equity warrant in a fractional Brownian
motion environment, when the short rate follows the subdiffusive fractional
Black-Scholes model. We obtain the pricing formula for zero-coupon bond in the
introduced model and derive the partial differential equation with appropriate
boundary conditions for the valuation of equity warrant. Finally, the pricing
formula for equity warrant is provided under subdiffusive fractional Brownian
motion model of the short rate.
