A Multiperiod Binomial Model for Pricing Options in an Uncertain World

The aim of this paper is to price an option in a multiperiod binomial model, when there is uncertainty on the states of the world at each node of the tree . As a consequence, also the stock price at each state takes imprecise values. Possibility distributions are used to handle this type of problems. The pricing methodology is still based on a risk neutral valuation approach, but, as a consequence of the uncertainty on the two jumps of the stock, we obtain weighted intervals for risk -neutral probabilities. The distinctive feature of our model is that it tracks back the arising of these probability intervals to the imprecision of the value of the stock price i n the up and down states. This paper provides a generalization of the standard binomial option pricing model. We obtain an expected value interval for the option price within which it is possible to find a crisp representative value and an index of the uncertainty present in the model.