2) Suppose that the price of a non-dividend-paying stock is $37, its volatility is 30%, and the risk-free rate for all maturities is 7% per annum. Provide a table showing the relationship between profit and final stock price for a butterfly spread using European put options with strike prices of $30, $35, and $40 and a maturity of one year. Ignore the impact of time value of money. 3) The premium of a call option with a strike price of $50 is equal to $5.5 and the premium of a call option with a strike price of $55 is equal to 54. The premium of a put option with a strike price of $50 is equal to $3.5. The risk-free rate of interest is 9%. In the absence of arbitrage opportunities, what should be the premium of a put option with a strike price of $55? All these options have a time to maturity of 6 months. (You are not allowed to use the put-call parity to solve this problem) 2) Suppose that the price of a non-dividend-paying stock is $37, its volatility is 30%, and the risk-free rate for all maturities is 7% per annum. Provide a table showing the relationship between profit and final stock price for a butterfly spread using European put options with strike prices of $30, $35, and $40 and a maturity of one year. Ignore the impact of time value of money. 3) The premium of a call option with a strike price of $50 is equal to $5.5 and the premium of a call option with a strike price of $55 is equal to 54. The premium of a put option with a strike price of $50 is equal to $3.5. The risk-free rate of interest is 9%. In the absence of arbitrage opportunities, what should be the premium of a put option with a strike price of $55? All these options have a time to maturity of 6 months. (You are not allowed to use the put-call parity to solve this problem)