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

question 40

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.
a. Do these prices indicate that the financial markets are in equilibrium? Show me how you derived your answer.
b. An arbitrage opportunity should exist, but if you set up the position incorrectly, you will always sustain losses. Verify to me that if you do set up an incorrect arbitrage, you will always sustain a loss. Please use prices of the stock at $80, $100, and $120 as of the expiration date of the options.

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Definitions:

Variable Selling Expense

Costs that vary directly with the volume of sales, such as commissions and shipping charges.

Fixed Selling Expense

Costs associated with the selling process that do not vary with the level of sales, such as salaries of sales personnel and rent for sales space.

Variable Administrative Expense

Indirect costs that change in proportion with the level of a company’s production or sales activities.

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Expenses that do not change with the level of production or sales over a certain period, related to the administration of a business.