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? Group of answer choices:

a) the puts have higher implied volatility than the calls
b) there is insufficient information to determine
c) this is impossible due to put-call parity
d) you should short the calls and go long the puts
e) you should short the puts for a risk-less profit

Answer 1

Short selling the overpriced puts, as they are priced higher than the valuation from Black-Scholes and put-call parity indicates, allows for a risk-less profit.

Step-by-step explanation:

If you determine that put options should be priced at $1.00 using Black-Scholes and put-call parity, and they are currently priced at $2.00, the correct course of action would be short selling the puts. This is because the puts are overpriced according to your valuation and this presents an opportunity for a risk-less profit.

Put-call parity ensures that the pricing of calls and puts with the same strike price and expiration must be consistent with each other. Therefore, if the calls are fairly priced, the puts should also be correctly priced, assuming no arbitrage opportunities. Since this is not the case, the overpriced puts provide a clear signal for short selling.

Since the puts should be priced at $1.00 instead of $2.00, it indicates that the puts have higher implied volatility than the calls. Implied volatility measures the market's expectation of future volatility in the underlying stock.