A Multiperiod Binomial Model for Pricing Options in a Vague World

The aim of this paper is to price an option in a multiperiod binomi-al model, when there is uncertainty on the states of the world at each node of the tree. The starting point is the one period model, where the two states of the world, namely state up, where the market is “bullish ” and state down, where the market is “bearish”, are vague. As a consequence, also the stock price at each state takes imprecise values. In a standard one period binomial model, we are required to give two crisp values, one for each state, for the stock price movement in the next time period. This problem boils down to the estimation of the volatility of the underlying asset, that is an unobservable parameter. Let u and d be the up and down crisp jump factors respectively, the standard methodology (Cox, Ross, Rubinstein, 1979) leads to set u = e s ÖD t d = e-s ÖD