Put-Call Parity Basically Says That Combination of a Put, a Call

question 3

Essay

Put-call parity basically says that combination of a put, a call, and a risk-free bond 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 call plus the bond is equal to the prices of the put plus the stock. Currently, the price of a stock is $100 while the price of a call option at $100 is $10; the price of the put option is $4.59, and the rate of interest is 8 percent, so that the investor may purchase a $100 discounted note for $92.59.
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a. Do these prices indicate that the financial markets are in equilibrium? Show all calculations.
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b. An arbitrage opportunity exists, but if the position is set up incorrectly, losses will be sustained. Verify that a loss will be sustained if the arbitrage is set up incorrectly. Calculate the results based on stock prices of $80, $100, and $120 as of the expiration date of the options.

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