Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate

TL;DR

This paper extends the Merton model by incorporating subdiffusive fractional Brownian motion to price equity warrants and zero-coupon bonds when the short rate follows a subdiffusive fractional Black-Scholes model.

Contribution

It introduces a novel subdiffusive fractional Brownian motion framework for equity warrant pricing, deriving new formulas and PDEs for valuation.

Findings

Derived a new pricing formula for zero-coupon bonds.

Established a PDE for equity warrant valuation.

Provided explicit pricing formulas under the new model.

Abstract

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.