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.

---

Definitions:

Percent of Sales Method

A financial forecasting technique that estimates certain balance sheet and income statement items as a fixed percentage of projected sales.

Uncollectible Expenses

Costs that a business incurs from credits extended to customers that are not expected to be paid back, often recognized as bad debt expense.

Credit Sales

Sales made by a business where the payment is deferred to a later date, typically recorded as accounts receivable until payment is received.

Debit Balance

An account balance that occurs when the total of debits in an account exceeds the total of credits, typical for asset and expense accounts.