British Call Option on Stocks under Stochastic Interest Rate

Abstract

The closed form expression for the price of the British put and call options have longbeen established where both interest rate and volatility are assumed to be constant. In reality,these assumptions do not fully reflect the variable nature of the financial markets. In this paper, wederived a closed form expression for the arbitrage-free price of the British call option by assumingstochastic interest rate which follows the Cox-Ingersoll-Ross model and constant volatility as where the first term is the arbitrage-free price of the European call option under stochastic interestrate and the second term is the early-exercise premmium. We have also shown that the pricefunction of the British call option satisfies the partial differential equation given by Moreover, we have shown that the contract drift satisfies μc < rt+ρσ1σ2√rtλ(0, t+u) for u ∈ [0, τ ] and t ∈ [0, T].