Following the economic rationale of the British options, we present a new\nclass of binary options where the holder enjoys the early exercise feature of\nthe American binary options with his payoff is the â??best predictionâ? of the\nEuropean binary payoff under the hypothesis that the true drift equals a contract\ndrift. Based on the observed price movements, the option holder finds\nthat the true drift of the stock price is unfavourable then he can substitute it\nwith the contract drift. The key to the British binary option is the protection\nfeature and to minimize the losses. A closed form expression for the arbitrage-\nfree price is derived in terms of the rational exercise boundary and the\nrational exercise boundary itself can be characterized as the unique solution\nto a nonlinear integral equation. We also analyze the financial meaning of the\nBritish binary options using the results above.
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