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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  


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  • What is the spot rate for t=0.5 year?
  • What is the spot rate for t=1.0 year?
  • Compute the theoretical spot rate for t=1.5 year.
  • 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:

    • 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.

    • the six-month forward rate two years from now.
    • 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?


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