Question

A Treasury Strips is sold for settlement on May 15, 2018.

        · Annual Coupon Rate 0%

        · Semi-annual compounding

        · Maturity Date: 15 October 2018

        · Annual Yield-to-Maturity: 6%

        · Face Value: $100

        · Day Count Convention: actual/actual

Calculate the full price of the zero-coupon bond

Hint: Note that in the case of a zero-coupon bond (with $100 par value), our bond pricing formula is simply

where T is the time to maturity in years and P(T) is the (full) pricee of the zero coupon bond.

Note that T is the exact number of years until maturity, including fractions of a year. For example, if a zero-coupon bond matures in 3 years and 15 days (counted using the actual/actual day count convention), then T is 3 + 15/365 = 3.04109589.

1) Calculate the number of days until maturity

2) Calculate the fraction of a year until maturity. Use 366 as the number of days (i.e. divide the number from the previous question by 366). Round your answer to six digits after the decimal.

3) Calculate the full price of the Treasury Strips. Round your answer to six digits after the decimal point (e.g. 98.123456)

Answer 1

Months	Number of days until Maturity
May	16
June	30
July	31
August	31
September	30
October	15
Total	153

Number of days until maturity = 153 days

The fraction of a year until maturity = Number of days until maturity / 366
= 153/366
The fraction of a year until maturity =  0.418033

Annual YTM = 6%
Daily YTM = ((1+0.06)^(1/366)) - 1
=  0.000159 %
Face Value = $100
Number of days until Maturity = 153 days
Coupon Payment = $0

Price of the Zero Coupon Bond = Principal Payment (Face Value) / [(1+ Daily Interest Rate) ^ (Number of Days Until Maturity)]
= 100/[(1+0.000159) ^ (153)]
Price of the Zero Coupon Bond =  97.593596

Hence, the price of the Zero Coupon Bond is $97.593596.