Financial Derivatives and Risk Management Homework

Q1. Suppose the following information is given on a European-style call option on a stock that pays no dividend:              

S₀ = 20

T = 1

K = 18

r = 10% (continuous compounding)

Please calculate the minimum value of the call option.

Q2. A finance student has been managing his family's investment portfolio for two years with good success. Although the student investor never invested in options before, he has decided to start doing so. Specifically, the student has decided to purchase simultaneously both call options and put options with the same strike price on the same stock. This strategy means that the call option will become profitable if the stock goes up and the put option will become profitable if the stock goes down. The student's parents think that their son is crazy and say this strategy is like placing two wagers on an athletic event-one on the home team and one on the away team. They tell their son that there is no possible way to get ahead because only one team will win.

1) What is the payoff graph (as done in class) for this joint strategy? Please use the following information to defend your strategy:

Dec call option (strike price = $50) premium: $5/share

Dec put option (strike price =$50) premium: $3/share

2) Suppose you are that student investor. With the help of the graph in part 1), please convince your parents when this strategy will work.