The aim of this paper is to price an American option in a multiperiod binomial model,when there is uncertainty on the volatility of the underlying asset.American option valuation is usually performed, under the risk-neutralvaluation paradigm, by using numerical procedures such as the binomialoption pricing model of Cox, Ross, Rubinstein (1979). A key input of themultiperiod binomial model is the volatility of the underlying asset,that is an unobservable parameter.As it is hard to give a precise estimate forthe volatility, in this paper we use a possibility distribution in order to modelthe uncertainty on the volatility. Possibility distributions are one of the mostpopular mathematical tools for modelling uncertainty. The standard risk-neutralvaluation paradigm requires the derivation of the risk-neutral probabilities, thatin a one period binomial model boils down to the solution of a linear system ofequations. As a consequence of the uncertainty in the volatility, we obtain apossibility distribution on the risk-neutral probabilities. Under these measures,we perform the risk-neutral valuation of the American option.

American Option Pricing with Imprecise Risk-Neutral Probabilities / Muzzioli, Silvia; H., Reynaerts. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - STAMPA. - 49:1(2008), pp. 140-147. [10.1016/j.ijar.2007.06.011]

### American Option Pricing with Imprecise Risk-Neutral Probabilities

#### Abstract

The aim of this paper is to price an American option in a multiperiod binomial model,when there is uncertainty on the volatility of the underlying asset.American option valuation is usually performed, under the risk-neutralvaluation paradigm, by using numerical procedures such as the binomialoption pricing model of Cox, Ross, Rubinstein (1979). A key input of themultiperiod binomial model is the volatility of the underlying asset,that is an unobservable parameter.As it is hard to give a precise estimate forthe volatility, in this paper we use a possibility distribution in order to modelthe uncertainty on the volatility. Possibility distributions are one of the mostpopular mathematical tools for modelling uncertainty. The standard risk-neutralvaluation paradigm requires the derivation of the risk-neutral probabilities, thatin a one period binomial model boils down to the solution of a linear system ofequations. As a consequence of the uncertainty in the volatility, we obtain apossibility distribution on the risk-neutral probabilities. Under these measures,we perform the risk-neutral valuation of the American option.
##### Scheda breve Scheda completa Scheda completa (DC) 49
1
140
147
American Option Pricing with Imprecise Risk-Neutral Probabilities / Muzzioli, Silvia; H., Reynaerts. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - STAMPA. - 49:1(2008), pp. 140-147. [10.1016/j.ijar.2007.06.011]
Muzzioli, Silvia; H., Reynaerts
File in questo prodotto:
File
IJAR 2008.pdf

non disponibili

Descrizione: versione pubblicata
Tipologia: Versione dell'editore (versione pubblicata)
Dimensione 215.61 kB
##### Pubblicazioni consigliate

Caricamento pubblicazioni consigliate I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11380/455985`
##### Citazioni
• ND
• 35
• 28