American option pricing with imprecise risk-neutral probabilities

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

Fuzzy linear systems of the form A(1)x plus b(1) = A(2)x plus b(2)

Linear systems of equations, with uncertainty on the parameters, play a major role in several applications in various areas such as economics, finance, engineering and physics. This paper investigates fuzzy linear systems of the form A(1) x + b(1) = A(2)x + b(2) with A(1), A(2) square matrices of fuzzy coefficients and b(1), b(2) fuzzy number vectors. The aim of this paper is twofold. First, we clarify the link between interval linear systems and fuzzy linear systems. Second, a generalization of the vector solution of Buckley and Qu [Solving systems of linear fuzzy equations, Fuzzy Sets and Systems 43 (1991) 33-43] to the fuzzy system A(1) x + b(1) = A(2)x + b(2) is provided. In particular, we give the conditions under which the system has a vector solution and we show that the linear systems Ax = b and A(1)x + b(1) = A(2)x + b(2), with A = A(1) - A(2) and b = b(2) - b(1), have the same vector solutions. Moreover, in order to find the vector solution, a simple algorithm is proposed

A sensitivity analysis for the pricing of call options in a binary tree model

The European call option prices have well-known formulae in the Cox-Ross-Rubinstein model [2], depending on the volatility of the underlying. Nevertheless it is hard to give a precise estimate of this volatility. S. Muzzioli and C. Toricelli [4] handle this problem by using possibility distributions. In the first part of our paper we correct a number of mistakes found in their work. In the second part we present an alternative solution to the problem by performing a sensitivity analysis for the pricing of the option. This method is very general in the sense that it can be applied if one describes the uncertainty in the volatility by confidence intervals as well as if one describes it by fuzzy numbers