Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4 percent. Assume one period world.

u = 1 + 10% = 1.1

d = 1 8% = 0.92

t = 1

r = 4%

S = 80

1. Call Price if Stock Goes Up = 80 * 1.1 80

= 8

2. Call Price if Stock Goes Down = 80 * 0.92 80

= 0

3. Hedge Ratio = (8 0 ) / [80 * (1.1 0.92)]

= 0.56

4. Theoretical Price = 0.67 * 8 + (1 0.67) * 0

= 5.15

Assume a two-period world.

Answer the following:

1. What is the value of the call if the stock goes up, then down?
2. What is the hedge ratio if the stock goes down one period?
3. What is the current value of the call?