1. Consider the following 3 European call options, all with expiration at time T=1: option A has strike $10; option B has strike $15; and option C has strike $20.

(a) Create a butterfly spread from options A, B, and C, and graph its payoff as a function of ST.

2. Consider the 3 calls from the previous problem expiring in T=1 year. Suppose that the premium of the 3 options are $7, $3, and $1 for A, B, and C, respectively, today (time 0). Suppose the price on the stock today is $14.

(a) Suppose the risk-free rate is constant at 0%. Graph the profit function for each of the previous strategies.

(b) Suppose the risk-free rate is constant at 5%. Graph the profit function for the butterfly strategy at time T taking into consideration the time value of the initial cost. By how much would the asset have to change over the year for your butterfly portfolio to be a loss?