Suppose that the price of a non-dividend-paying stock is $60, its volatility is 40%, and the risk-free rate for all maturities is 2% per annum.

Suppose that the price of a non-dividend-paying stock is $60, its volatility is 40%, and the risk-free rate for all maturities is 2% per annum. You are interested in creating various optionsspreads using

calls and puts with different strike prices (but all of them have same time-to-maturity of six-= months).

Calculate the cost of setting up the following positions. In each case

also draw the payoff diagrams at the time of maturity (it may be easier to draw the diagrams with hand)

a. A bull spread using European call options with strike prices of $60 and $80

b. A bear spread using European put options with strike prices of $40 and $60

c. A butterfly spread using European call options with strike prices of $40,$60, and $80

d. A butterfly spread using European put options with strike prices of $40, $60, and $80.