November 8th, 2007, 2:37 pm
Are you saying that in both cases the volatility would be constant during the life of the option, but in one case the volatility is known and in the other case, we are finding the expected price of the option given that the volatility is from a distribution centered at the known value?If so, I would pay more for the latter option. Suppose the price of an option is convex with respect to volatility. Then we can use Jensen's inequality.