12. In each case identify the arbitrage and demonstrate how you would make money by creating a table showing your payoff.

a. Consider two European options on the same stock with the same time to expiration. The 90-strike call costs $10 and the 95-strike call costs $4.

b. Now suppose these options have 2 years to expiration and the continuously compounded interest rate is 10%. The 90-strike call costs $10 and the 95-

strike call costs $5.25. Showagain that there is an arbitrage opportunity. (Hint:

It is important in this case that the options are European.)

c. Suppose that a 90-strike European call sells for $15, a 100-strike call sells for $10, and a 105-strike call sells for $6. Showhowyou could use an asymmetric butterfly to profit from this arbitrage opportunity.