Problems 4-11 illustrate arbitrage. Problems 5-8 use put-call parity while 9-11 are based on Black-Scholes.

Put-call parity in effect states that long positions in a call and a risk-free bond plus a short position in a put must be the same value as the underlying stock. If not, at least one market is in disequilibrium. The resulting arbitrage alters the securities' prices until the value of the three securities equals the value of the stock. Currently, the price of a stock is $50, while the price of a call option at $50 is $3, the price of the put option is $1.50, and the rate of interest is 10 percent-so that the investor may purchase a $50 discounted note for $45.50.

Given these prices, an arbitrage opportunity exists. Verify this by setting up a riskless arbitrage. Show the possible profit if the price of the stock is $45, $50, or $55 at the expiration of the options.