Approximate solutions for the British put option and its optimal exercise boundary

Abstract

British put options are financial derivatives with an early exercise feature whereby on payoff, the holder receives the best prediction of the European put payoff under the hypothesis that the true drift of the stock price is equal to a contract drift. In this paper we derive simple analytic approximations for the optimal exercise boundary and the option valuation, valid for short times to expiry - which is a common feature of most options traded in the market. Empirical results show that the approximations provide accurate results for expiries at least up to 2 months. doi:10.1017/S1446181115000450