ABSTRACT
Pricing uncertainty is the kernel of asset pricing. There are two main kinds of uncertainty. The first kind of uncertainty is risk, where we know not only the states of nature but also their probability. In the second situation, we know the states of nature, but do not know their probability, we call it Knightian uncertainty. On option pricing, from Black and Scholes[1] to Merton[2], from Hull and White[3] to Heston[4], many economists have done great works and discovered many efficient methods to price risk. We find that the complexity of the model is growing, but there is still few attention has been paid to Knightian uncertainty and few work is done for pricing option under Knightian uncertainty. To deal with the Knightian uncertainty, we have two methods. Method 1, using the inertia assumption in stand of the completeness assumption, see Bewley[5]; similarly, Epstein and Wang[6,7] created a family of probabilities based on individual “belief”. Method 2, relaxing the “certainty rule” and use non-additive probability measure based on Choquet integral, see Gilboa[8], Scmeidler[9], Gilboa and Scmeidler[10]. Because of their contributions, it is possible to price option under Knightian uncertainty, and that is meaningful and necessary.
