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29-08-2018

Product code: Accounts-AW527

Fixed Income Securities – Exercise Problem Set

Topic D: Term Structure and Modeling of Interest Rates

Problem #1: Spot Rates (slide 21)

Today you obtain the market data on Treasuries up to year 2.  Assume a par value of \$100 for all Treasuries.  The coupon rate, yield to maturity and price of all the Treasuries are provided in the Table below:

 Period Years Coupon Rate Yield to Maturity Price Spot Rate 1 0.5 0.00% 3.00% \$98.52 2 1.0 0.00% 3.30% \$96.78 3 1.5 3.40% 3.51% \$99.85 4 2.0 4.00% 3.92% \$100.16

1. What is the spot rate for t=0.5 year?
2. What is the spot rate for t=1.0 year?
3. Compute the theoretical spot rate for t=1.5 year.
4. Compute the theoretical spot rate for t=2.0 year.

(e)  Use the spot curve you constructed to compute the arbitrage-free value of a Treasury coupon bond with 2 years to maturity and a coupon rate of 3

Problem #2: Par Rates; Implied Forward Rates (slide 31)

Using the Treasury spot rates shown in Exhibit 5-7, compute the followings:

1. The 3-year par rate, i.e., the coupon rate that would make

the price of a 3-year coupon bond equal to its par value.

1. the six-month forward rate two years from now.
2. the two-year forward rate eight years from now.

Problem #3: Interest Rate Volatility (slide 52)

Suppose that the following monthly interest rate volatility estimates are computed as:    absolute rate change = 8.56 basis points and percentage rate change = 5.27%.

(a) What is the annualized volatility for the absolute rate change?

(b) What is the annualized volatility for the percentage rate change?

Product code: Accounts-AW527

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