Final answer:
a) The value of the call option at T=0 using the two-period binomial model is $2.99. b) h at T+0 is -0.248. c) h at T=1 is -2.22.
Step-by-step explanation:
Two Period Binomial Model
a) To calculate the value of the call option at T=0 using the two-period binomial model, we need to calculate the option value at the end of each period and discount it back to T=0. Given that the stock can either go up 20% or down 20% over one year, we can construct a binomial tree to calculate the option values at each node. At the end of the first period, if the stock goes up, the option value would be max(0, stock price - exercise price) = max(0, $45 - $40) = $5. If the stock goes down, the option value would be 0. The option values at T=1 are then calculated following the same logic, and discounting back to T=0 gives us the option value at T=0, which is $2.99.
b) To calculate h at T+0, we divide the difference between the option values at T+1 and T-1 by the difference between the stock prices at T+1 and T-1. So, h = (Option Value(T+1) - Option Value(T-1)) / (Stock Price(T+1) - Stock Price(T-1)). Using the values from the binomial tree, h = (0 - $2.99) / (0.72 * $45 - 1.28 * $45) = -0.248.
c) To calculate h at T=1, we divide the difference between the option values at T+1 and T-1 by the difference between the stock prices at T+1 and T-1. Again, using the values from the binomial tree, h = (Option Value(T+1) - Option Value(T-1)) / (Stock Price(T+1) - Stock Price(T-1)). Using the values from the binomial tree, h = (0 - 20) / ($45 - $36) = -2.22.