Consider a market with d=1 and X=X1 satisfying dXt=XtdWt,X0=1, where W is a Brownian motion process. Assume that F is the natural filtration of X and F=FT. Prove rigorously that there is only one ELMM for X. (10% or total points) Find the price of the contingent claim H=X2T. (20% or total points) Find the price of 1H. (20% or total points) 4. What happens if an EMM exists (regarding arbitrage)? (10% or total points) 5. Are there arbitrage opportunities in fair games? (10% or total points) 6. If we can perfectly hedge, what is the greatest number of EMMs there can be? (10% or total points) 7. If the market is complete, what is the greatest number of EMMs there can be? (10% or total points) 8. What do we call the volatility that comes from a risk-neutral pricing of a derivative contract? (10% or total points)