Find the discount factors -linear interpolation, Mathematics

Find the discount factors -Linear interpolation:

All rates should be calculated to 3 decimal places in % (e.g. 1.234%), the discount factors to 5 decimal places (e.g. 0.98765), and the bond prices to 3 decimal places (e.g. 99.999).

You are given the following yields-to-maturity for semi-annually coupon paying Treasury Bonds on 31st December 2007 and 31st December 2008:

Term                0.5yr    1yr       2yr       3yr       5yr       7yr       10yr

31 Dec 2007    3.49% 3.34% 3.05% 3.07% 3.45% 3.70%  4.04%

31 Dec 2008    0.27% 0.37% 0.76% 1.00% 1.55% 1.87%  2.25%

(1) Using linear interpolation to estimate any other required rates, find the discount factors D(t) for t = 0.5, 1.0, 1.5, ..., 10.0 for both dates.

(2) From your answers to (1), calculate the price of a constant-maturity 3-year semi-annual coupon bond1 with an annual coupon rate of 3% and the face value 100, for both 31 December 2007 and 31 December 2008. Hence analyse the price change.

(3) Again from your answers to (1), find the 6-month forward rates f(t,t+½) for t = 0.5, 1.0, 1.5, ... , 9.5 for both dates.2 (See Appendix for the explanation for forward rates.)

You are also given the following historical data on the spot 6-month rate:

Date           31/12/07        30/06/08          31/12/08        30/06/09           31/12/09

6m Rate        3.49%            2.17%             0.27%             0.35%               0.20%

   30/06/10        31/12/10         30/06/11         30/12/11          29/06/12     31/12/12

      0.22%            0.19%            0.10%              0.06%              0.16%         0.11%

(4) Using a graph, comment on how well the market predicted the future moves of the spot 6-month rate on both dates.

(5) In general, are forward rates a good predictor of future interest rates? Briefly discuss.

Posted Date: 2/14/2013 4:49:31 AM | Location : United States

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