British put option on stocks under stochastic interest rate

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The British option was first introduced by G. Peskir and F. Samee (2011). In a British option, the holder can enjoy the early exercise feature of American option whereupon his payoff is the ’best prediction’ of the European payoff given all the information up to the exercise date under the hypothesis that the true drift of the stock equals a specified contract drift. Consistent with the plain vanilla option, the authors considered the constant interest rate. In this paper, we will consider the pricing of the British put option in a stochastic interest rate environment, particularly the Vasicek model. We will derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary.