Final answer:
To answer the student's question, we would use put-call parity to determine the strike price where European call and put options are equal. The relationship between the values of a call and a put is influenced by the interest rate, stock price, volatility, time to expiration, and whether the stock is paying dividends or not.
Step-by-step explanation:
The student's question pertains to determining strike prices for European style call and put options given certain market conditions. The interest rate mentioned is relevant as it affects the discounting of option payoffs. For a non-paying stock, such as TFS trading at S 0=25.00, we can apply put-call parity to find the strike price at which a European call and put would have equal prices. Put-call parity states that the price of a call option minus the price of a put option equals the current stock price minus the present value of the strike price. a) Assuming no arbitrage opportunities, zero dividends, and using the current interest rate, the formula simplifies, and we can see that the strike prices would be equal when the present value of the strike is equal to the current stock price. b) With regard to the question about whether there is some strike price at which the put is worth exactly half as much as the call, it's not as straightforward. The relationship between the call and put prices depends on various factors, including the stock's volatility, time to expiration, and the interest rate, which influences the present value of the strike price. Thus, a general answer without specific values cannot be accurately provided.