1. Assume that today, zero coupon bonds maturing in 6 months, 1 year and 1 and half a year are quoted at 99.1338, 97.8925, and 96.1531.

(a) Compute the todays continuously compounded rate of interests on zeros of varying maturities.

(b) Assume that the interest rate follows one-period binomial tree process such that the current

interest rate can go up to 3.39% or down to 0.95% in 6 months. What will happen to the price

of 1-year bond in each scenario?

(c) Consider an interest rate option, which matures in 6 months, with a payoff equal to 100*max(rk-r1, 0)

, where rk is the strike rate of 2%, and r1 denotes the interest rate in 6 months. Show a portfolio of zero coupon bonds that replicates the payoffs of the interest rate option.

(d) Consider a swap that pays in 6 months the amount (100/2)*(r1-c) , where c is the swap rate, and

is 2%. Compute the value of the swap when the interest rate changes, and construct a

replicating portfolio of bonds.

(e) Consider a bond option that matures in 6 months, where the underlying is a 6-month bond.

Assume that the strike price is $99.00. Compute the payoff of the bond option in 6 months and form a replicating portfolio of zeros.

2. Assume that the probability of the interest rate going up is 50%. Compute the dollar price of risk and compute the value of the interest rate securities in (1c), (1d) and (1e) above using the market price of risk.

3. Use the risk neutral probability to compute the value of the interest rate securities in (1c), (1d) and (1e) above.