Consider a market withd=1 d=1andX=X 1 X=X1satisfying

dXt = XtdWt ,X0=1,

whereWis a Brownian motion process. Assume thatF is the natural filtration of X and F= FT.

1. Prove rigorously that there is only one ELMM forX
2. Find the price of the contingent claimH=X2T
3. Find the price of1/H

4.What happens if an EMM exists (regarding arbitrage)?

5.Are there arbitrage opportunities in fair games?

6.If we can perfectly hedge, what is the greatest number of EMMs there can be?

7.If the market is complete, what is the greatest number of EMMs there can be?

8.What do we call the volatility that comes from a risk-neutral pricing of a derivative contract?