Question:

a) A bank lends you $1750 at an initial nominal yearly interest rate of 7.5% compounded semi-annually. However, the interest rate will rise to 9.2% after the first year. You repay $580 both after the first year and halfway through the second year and wish to repay the rest after the third year.

i. What is the effective interest rate of the first year?

ii. Calculate the final payment.

b) Consider the n periods stock option model where the nominal interest rate is r per period. Let be the initial price of the stock, and for i = 1,2,4, n, let S(i) be its price at i time periods later. Suppose that S(i) is either u S(i-1) with probability p or d S(i-1) with probability 1-p, where u=1.25 and d=0.8.

i. Give appropriate bounds for the nominal interest rate, in order to get risk-neutral probabilities.
ii. If r = 8%, what are the risk-neutral probabilities p and 1-p when S=$120?
iii. Calculate the one period European call option with strike price $105.
iv. Calculate the one period European put option with strike price $120.
v. Calculate the two period European call option with strike price $125.