Question

You are researching a stock currently priced at $35 per share. Call options are currently priced at $3.00, and puts are priced at $2.00. You use Black-Scholes and put-call parity to determine that calls are fairly priced, but the puts should be priced at $1.00. What would be true given this information?

A. There is insufficient information to determine.
B. The puts have higher implied volatility than the calls.
C. This is impossible due to put-call parity.
D. You should short the puts for a risk-less profit.
E. You should short the calls and go long the puts.

Answer 1

Considering put-call parity and Black-Scholes, the puts are overpriced at $2.00 when they should be $1.00, implying that shorting the puts is the appropriate strategy for riskless profit, making option D the correct choice.

Step-by-step explanation:

If Black-Scholes and put-call parity suggest that the calls are fairly priced at $3.00, but the puts should be priced at $1.00 instead of $2.00, it indicates that the puts are overpriced in the market. Put-call parity is a financial concept that ensures that the pricing of puts and calls remains in equilibrium to prevent arbitrage opportunities; thus, answer C, stating the situation as impossible due to put-call parity, is incorrect.

Given that the puts are overpriced, the correct action to exploit this discrepancy for potential profit would be to short sell the puts. This involves selling the puts at their current high price and potentially buying them back later at the lower, fair value predicted by the model, thus locking in the difference as profit. Therefore, D is the correct choice: You should short the puts for a risk-less profit. This strategy assumes no transaction costs, taxes, and that markets are efficient except for the mispricing of the options.