On the pricing of options under limited information
Faculty of Applied Economics
Antwerp :UA, 2004
Research paper / UA, Faculteit TEW ; 2004:4
University of Antwerp
In spite of the power of the Black & Scholes option pricing method, there are situations in which the hypothesis of a lognormal model is too restrictive. One possibility to deal with this problem, consists of a weaker hypothesis, fixing only successive moments and eventually the mode of the price process of a risky asset, and not the complete distribution. The consequence of this generalization is the fact that the option price is no longer a unique value, but a range of several possible values. We show how to find upper and lower bounds, resulting in a rather narrow range. We give results in case two moments, three moments, or two moments and the mode of the underlying price process are fixed.