Please help me on working this problem with a step by step working. Thank you very much ! (Qeustion 3, (a) until (d)

3. Consider a stock which is currently selling at $4.5. The stock price will either go up to $5 + a: with probability 0.5 or go down to $5 m with probability 0.5 one period later. The one-period riskless rate of interest is 5%. (a) What are the market prices of at-the-rnoney call options that expire at the end of the period when :r is set equal to $0.5, $1, $1.5, $2, and $2.5, respectively? (b) Plot the oneperiod call option prices against the ve possible values of :3. (c) What is the reason for the pattern that you nd in part (b)? (d) Redo parts (a) to (c) for at-the-Inoney put options that expire at the end of the period