Section A (40%)

Time Ti 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Discount

Z(0,Ti) 0.9898 0.9729 0.9517 0.9268 0.8992 0.8737 0.8483 0.8220 0.7808 0.7520

The table above shows the discount factors with maturities from half a year to 5 years. (If x

follows the standard normal distribution, Prob( x < -2.326 ) = 1%, and the probability density

function of x is x =

1

2

2

2

)

1. Given the discount factors above, what is the yield of a 2-year STRIPS? (2%)

2. Given the discount factors above, what is the lowest possible value of the 5.5-year

continuously-compounding interest rate? (5%)

3. Given the discount factors above, what is the price of the default-free on-the-run four

year coupon bond with coupon rate equal to the constant semi-annual rate 3%? (3%)

4. Given the same coupon bond in Question A-3, what is its yield to maturity? (5%)

5. Given the same coupon bond in Question A-3, what is its duration? (3%)

6. Suppose that the monthly change in the interest rate dr follows a normal

distribution with mean 510

-6

and standard deviation 0.42%, what is the

99%Value-at-Risk of the coupon bond in Question A-3 with notional being 1

million? (2%)

7. Following Question A-6, what is the corresponding expected shortfall? (5%)

8. Given the same coupon bond in Question A-3, what is its convexity? (2%)

9. Suppose that you hold 1 million face value of the coupon bond in Question A-3, how

to hedge the interest rate risk of your position using 6-month zero-coupon bonds?

(3%)

10. Suppose Z(0,10)=0.4966, explain how to improve your answers in Question A-9 with

additional 10-year zero-coupon bonds. (5%)

11. Suppose Z(0,10)=0.4966, what is the curvature of the current yield curve? (3%)

12. If you worry about a potential change in the shape of the yield curve, what is the name

of the method to hedge such risks? (2%)