Pricing formulas of binary options in uncertain financial markets

Binary options have a payoff that is either a fixed value or nothing at all. In this paper, the generalized pricing formulas of binary options, including European binary call options, European binary put options, American binary call options and American binary put options, are investigated in uncertain financial markets. By applying the Liu's stock model to describe the stock price, the explicit pricing formulas of binary options are derived successfully. Besides, the corresponding numerical examples for the above four kinds of binary options are discussed in this paper.