1. You inherit a package of call options on a stock currently selling for $53 (all of the call options expire in exactly one year). In a year, the stock could sell for anywhere between $40 and $80. The package consists of 1 call with a exercise price at $50, 1 written call with an exercise price of $55, one written call with an exercise price of $60 and one call with an exercise price of $65. Just to be clear, you have two calls and two written calls.
a. What is the payoff structure for this portfolio of options? A graph would be an appropriate way to answer this part of the question.
b. What can be known about the sum of the prices of the $50 and $65 calls relative to the sum of the prices of the $55 and $60 call? That is, is C50+C65 greater than, equal to or less than C55+C60? How do you know?

2. You observe that a stock is currently selling for $100. Somehow you know that the two possible values for the stock at time T are $80 and $130. You also observe that (1+r)T = 1.1. You don't know the probabilities of the two states of the world occurring. Using the two-state approach, determine the value of a T period call option with an exercise price of $110.