The British Binary Option

Abstract

Following the economic rationale of the British options, we present a new class of binary options where the holder enjoys the early exercise feature of the American binary options with his payoff is the “best prediction” of the European binary payoff under the hypothesis that the true drift equals a contract drift. Based on the observed price movements, the option holder finds that the true drift of the stock price is unfavourable then he can substitute it with the contract drift. The key to the British binary option is the protection feature and to minimize the losses. A closed form expression for the arbitrage-free price is derived in terms of the rational exercise boundary and the rational exercise boundary itself can be characterized as the unique solution to a nonlinear integral equation. We also analyze the financial meaning of the British binary options using the results above.