Reference no: EM133121963

Assume that:

-The spot rates for 6 months, 1 year, and 2 years are ??^(0.5) = 8% , ??^(1) = 9%, and ??^(2) = 10% respectively;

-The forward rate for 18 months is ??(1.5) = 8.4%

-The price of a zero-coupon bond maturing 2.5 years from now is $79.80

a) Find the 1-year forward rate ??(1).

b) Find the 18-month spot rate ??^(1.5)

c) Find the price of a 9% coupon bond maturing 2 years from now

d) Find the 2.5-year forward rate r(2.5)

e) Assume 2-year 5% coupon bond and 2-year 8% coupon bond are priced correctly while 2-year zero coupon bond is incorrectly priced at $98.30. You want to make an arbitrage by trading only these 3 bonds. Find an arbitrage strategy (i.e., state how many of each bond you want to buy or sell).

All interest rates are annual interest rates with semi-annual compounding. All coupon rates are annual rates paid semi-annually. All bonds have $100 face values. Keep at least 6 decimal digits in all your calculation and answers unless specified otherwise.