Complete Markets

In the discrete case, we saw that the notion of completeness plays an important role in option pricing if the underlying market is complete, and the price of both European and American call and put options are uniquely determined. The same is the case in continuous time, as we will see later. We begin by defining completeness of a market. Section 2 is a digression into stochastic calculus. Next we show that in the examples considered earlier, namely that of geometric Brownian motion and that of diffusions, the markets are complete. We will also show that the completeness of the underlying market is characterized by the uniqueness of the equivalent martingale measure.