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

$110

$100

$48

X =

$110

$50

$40

$110

$40

$36

  1. Is there a risk-free asset in the market?
  2. Suppose that asset prices are $100, $70, and $40. Is there an arbitrage opportunity in the market?
  3. 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?
  4. What are the risk-neutral probabilities?
  5. 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.