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.

A Multiperiod Binomial Model for Pricing Options in an Uncertain World / Muzzioli, Silvia; Torricelli, Costanza. - STAMPA. - (2001), pp. 255-264. (Intervento presentato al convegno Second International Symposium on Imprecise Probabilities and Their Applications tenutosi a Itacha nel 26-29 June 2001).

### A Multiperiod Binomial Model for Pricing Options in an Uncertain World

#### Abstract

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.
##### Scheda breve Scheda completa Scheda completa (DC)
2001
Second International Symposium on Imprecise Probabilities and Their Applications
Itacha
26-29 June 2001
255
264
Muzzioli, Silvia; Torricelli, Costanza
A Multiperiod Binomial Model for Pricing Options in an Uncertain World / Muzzioli, Silvia; Torricelli, Costanza. - STAMPA. - (2001), pp. 255-264. (Intervento presentato al convegno Second International Symposium on Imprecise Probabilities and Their Applications tenutosi a Itacha nel 26-29 June 2001).
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/21159`
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