A stock is currently trading at a price of 22. You observe the following prices for European put options on the stock (the strikes are in parentheses): $C ( 20 ) = 3.35$ and $C ( 22 ) = 1.95$ . Given this information, you can conclude that the minimum price of the 24-strike call consistent with no-arbitrage is
A) 0.00.
B) 0.55.
C) 1.40.
D) 2.00.

Question

Quizplus · Accepted Answer

To find the minimum price of the 24-strike call option consistent with no-arbitrage, we can use the put-call parity, which is a fundamental principle in options pricing that defines the relationship between the price of European call and put options with the same strike price and expiration date. The put-call parity formula is:$$C + Ke^{-rT} = P + S$$where:- $C$ is the price of the call option,- $K$ is the strike price,- $r$ is the risk-free interest rate,- $T$ is the time to maturity,- $P$ is the price of the put option, and- $S$ is the current stock price.However, we are not given the risk-free rate or the time to maturity, and we don't need them for a qualitative analysis based on arbitrage opportunities.Given the information, we can infer the minimum price of the 24-strike call by looking at the prices of the put options and the differences in their strike prices. The key here is to recognize that the difference in the strike prices between the options can be used to infer a no-arbitrage condition.The difference in strike prices between the $C(22)$ and the $C(24)$ call options is 2. If we were to construct a portfolio by buying the 22-strike put and selling the 24-strike call, the maximum loss would occur if the stock price is above 24, which would be 2 (the difference in strike prices). To prevent arbitrage, the cost of setting up this position (buying the put and selling the call) should be equal to the difference in their strike prices minus the difference in their premiums.Given the put prices, we don't have the exact prices for puts with strikes of 22 and 24, but we can infer that the price of the 24-strike call must be such that it does not allow for arbitrage. The price of the 22-strike put is given as 1.95, which is close but not directly applicable. However, the principle here is that the call's price must ensure no profit can be made from arbitrage given the prices of the puts and the current stock price.Without the exact formula application due to missing details (like the risk-free rate), we can't directly calculate the call price. However, the question seems to be asking for a conceptual understanding rather than a precise calculation. The correct answer would involve recognizing that the price of the call option must be set such that buying the put and selling the call does not lead to an arbitrage opportunity. Given the options provided and without the exact calculations possible from the given data, the minimum price of the 24-strike call option would be chosen to prevent arbitrage, which is conceptually closest to option B) 0.55, assuming it prevents arbitrage based on the relative pricing of options and the stock. This answer is more of a conceptual choice due to the lack of specific details for a precise calculation.

A Stock Is Currently Trading at a Price of 22 C(20)=3.35C ( 20 ) = 3.35C(20)=3.35

A Stock Is Currently Trading at a Price of 22 $C ( 20 ) = 3.35$