10. Answer the following questions:

a)Suppose a 10-yr 4.1% coupon bond has a price of 100.3% of face, and a 10-yr zero coupon bond has a price of 62.1% of face. What is the price (to nearest $0.01, with $100 face) of an inverse floater that pays a coupon rate of (11.1% - 1.1 \times LIBOR)?

Assume that all cash flows are "risk free", including LIBOR rates.

b) Suppose a 10-yr 7.4% coupon bond (paid seminannually) is callable in 4 years at 105% of face. If the yield to call is 4.6%, what is the price of the bond? (nearest $0.01, assume $100 face)

c) You are a bond dealer who is lending money via reverse repo, starting from Friday Oct 29, 2021 for a term of one business day (i.e. until Nov 1, 2021). The face value of the bond is $9M, the dirty price is 102.3% of face, the haircut is 5%, and the repo rate is 0.8%. How much will you receive on Nov 1, 2021? (nearest 0.01).

d) Suppose that the current spot rate curve (annually compounded) is s₁=0.4%, s₂=0.7%, s₃=1.3%.

Assume that one year from now, the spot rate curve will be s'₁=0.9%, s'₂=1%, s'₃=1.7%.

Consider a 3-year bond with annual coupon 2%. If you purchase that bond today and hold it for one year, what will be your total return (i.e. consider both price change and coupon)? (nearest 0.01%, and e.g. write 5.02 for 5.02%).

e)

Suppose that the spot rate curve (continuously compounded) is 4% for t less than or equal to 7 years, and the forward rate f_7,t is 5% (continuously compounded) for t > 7 years. Suppose you have an obligation to pay $1,000,000 per year in perpetuity starting 11 years from now. Suppose further that you may invest in a LIBOR floating rate bond (on issue date, with first coupon rate still unfixed) and also in a 50 year zero coupon bond.

After calculating the spot rate curve to t > 7 years, the price of the zero coupon bond, the durations of the zero coupon bond and the floating rate bond, the present value of the obligation, and the Fisher-Weil duration of the obligation, finally calculate the face values of the floating rate bond and the zero coupon bond necessary to immunize your obligation.

What face value must you purchase of the zero coupon bond? (nearest $1)

Hint: For the obligation,

The answer to these problems are a) 123.83 b) 114.29 c) 8,747,233.11 d) 1.85 e) 87,923,611.

I want the equations to get these answers.

Thank you!

Dew= FW InPW=0 di = Dew= FW InPW=0 di =