Algebraic Problem (3 points - Address all questions, show your work)

5) XYZ Stock is binomially distributed. For each period, it will either go up 10%, or down 20%. The risk free rate is 5%. There are no dividends. Currently, (at period 1) the stock sells for $100/share. There is a call option with strike price $90 that expires at period 3.

a) What is the risk neutral probability that the stock price will go up?

b) Diagram the possibilities for the stock price over periods 1, 2 and 3.

c) For each possible price at periods 2 and 3, show what the option would be worth.

d) What is the option delta or hedge ratio at period 1?

e) What should the option be worth at period 1?