3. Consider a stock which is currently selling at $4.5. The stock price will either go up to $5 + x with probability 0.5 or go down to $5 x 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-money call options that expire at the end of the period when x is set equal to $0.5, $1, $1.5, $2, and $2.5, respectively?

(b) Plot the one-period call option prices against the five possible values of x.

(c) What is the reason for the pattern that you find in part (b)?

(d) Redo parts (a) to (c) for at-the-money put options that expire at the end of the period.