Question

20. For a European call option and a European put option on the same stock, with the same strike price and time to maturity, which of the following is true?

    A) Before expiration, only in-the-money options can have positive time premium.

    B) If you have a portfolio of protected put, you can replicate that portfolio by long a call and hold certain amount of risk-free bond.

    C) Since both the call and the put are risky assets, the risk-free interest rate cannot affect the premiums of call or put.

    D) The buyer of the call option receives the same premium as the writer of the put option.

    E) When the call option is in-the-money and the put option is out-of-the-money, the stock price must be lower than the strike price.

Answer 1

B) If you have a portfolio of protected put, you can replicate that portfolio by long a call and hold certain amount of risk-free bond.

This is the put-call parity theory. This equation always holds true. If not, there is an arbitrage opportunity. Here, the call and the put option have the same strike price and the same maturity.

A) Before expiration, only in-the-money options can have positive time premium - This is false. Irrespective of the moneyness of an option, an option has a positive time premium prior to expiration

C) Since both the call and the put are risky assets, the risk-free interest rate cannot affect the premiums of call or put - Risk-free rate affects the premiums of call and put as a high risk-free rate increases the probability of the call being exercised in the money and the put being exercised out of the money.

D) The buyer of the call option receives the same premium as the writer of the put option. - False. The call and the put might be priced differently according to the risk-free rate and the volatility of the stock.

E) When the call option is in-the-money and the put option is out-of-the-money, the stock price must be lower than the strike price.- False. The opposite is true as for a call to be in-the-money, the stock price must be higher than the strike price and vice-versa for the put option.