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...the 4th coupon payment period, given the following market data for $100 par Treasury bonds

Period | Years | Annual YTM (BEY)(%) | Price | Spot Rate (BEY) (%) |

1 | .5 | 3.0 | 3.0 | |

2 | 1.0 | 3.3 | 3.3 | |

3 | 1.5 | 3.5 | 100 | 3.5 |

4 | 2.0 | 4.1 | 100 | xxx |

- 2-year Treasury coupon = 4.1 / 2 = 2.05
- 1st period cash flow = 2.05 / (1+3/2/100) = 2.02
- 2st period cash flow = 2.05 / (1+3.3/2/100)^2 = 1.98
- 3st period cash flow = 2.05 / (1+3.5/2/100) ^3= 1.95
- 4st period cash flow = (100+2.05) / (1+R/2/100) ^4 = Price - 1st period cash flow - 2st - 3rd = 100 - 2.02 - 1.98 - 1.95 = 94.05. In Excel's rate function, enter FV = 102.055, PV =-94.05, Nper = 4, and one gets R =2%.
- annualize the spot rate, one should get 4%

*Bonus Points*

- The basic principle underlying the
*bootstrapping*method is that the value of a Treasury coupon security should be equal to the value of the package of zero-coupon Treasury securities that duplicates the coupon bond's cash flows. - Since the bond is at par the
*coupon*will be the annual YTM multiplied by par. - Since spot rates are normally quoted on
*an annual basis*, the calculation needs to adjusted to a semiannual rate.

*Category: C++ Quant > Debt > Valuation*

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