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 in 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.