Assume a finite state economy with three assets whose payoff matrix is given by

$110 $100 $48

X = $110 $50 $40

$110 $40 $36

a. Is there a risk - free asset in the market ?

b. Suppose that asset prices are $100, $70, and $40. Is there an arbitrage opportunity in the market ?

c. Suppose there is an asset that hedges the downside risk with $10 payoff in the third ( down ) state and nothing in other two states. What should the price of this asset be ?

d. Using the risk - neutral valuation approach, recalculate the asset that hedges the downside risk with a $10 payoff in the third (down ) state and nothing in other two states.