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Price a sequence of zero rates

Suppose you have the price a sequence of zero rates
Maturity (Yrs) Zero rates (Continuous compounding)
0.5 5.20%
1 5.30%
1.5 5.30%
2 5.45%

(a) If convert Zero rates to compound 12 times per annual, what is their value?

(b) What is the zero rate for year 2.5 if a bond has coupon rate=9%, price = $108.15, maturity =2.5? (Semiannually ex-coupon, continuous compounding)

(c) Calculate and fill in the table below. (Semiannually pay coupon, continuous compounding, Face value=100)
(first column of numbers given is Year; second column of numbers given is
Annual Coupon %; find Discount Factor, Forward Rate, Bond Price, YTM, Par Yield for each given Year and Annual Coupon %)

Year Discount Forward Annual Bond YTM* Par
Factor Rate Coupon(%) Price($) Yield
---------------------------------------------------------------
0.5 0%
1 5%
1.5 7%
2 8%
YTM* := Yield to Maturity (or bond yield)

(d) If there is an opportunity that you could lend (or borrow) money to (from) somebody at year 1 for one year charging 5.30% what would you do?

Solution Preview

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Suppose you have the price a sequence of zero rates
Maturity (Yrs) Zero Rate (Continuous compounding)
0.50 5.20%
1.00 5.30%
1.50 5.30%
2.00 5.45%

(a) If convert Zero rates to compound 12 times per annual, what is their value?
Maturity (Yrs) Zero Rate (Coumpound 12 times per year)
0.50 5.2113%
1.00 5.3117%
1.50 5.3117%
2.00 5.4624%

(b) What is the zero rate for year 2.5 if a bond has coupon rate=9%, price = $108.15, maturity =2.5? (Semiannually ...

Solution Summary

The solution discusses the price of a sequence of zero rates.

$2.19