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For example, you might pay $5,000 for a zero-coupon bond with a face value of $10,000 and receive the full price, $10,000, upon maturity in 20 or 30 years. Zero-coupon CDs work the same way.
The Z-spread of a bond is the number of basis points (bp, or 0.01%) that one needs to add to the Treasury yield curve (or technically to Treasury forward rates) so that the Net present value of the bond cash flows (using the adjusted yield curve) equals the market price of the bond (including accrued interest). The spread is calculated iteratively.
Zero coupon bonds have a duration equal to the bond's time to maturity, which makes them sensitive to any changes in the interest rates. Investment banks or dealers may separate coupons from the principal of coupon bonds, which is known as the residue, so that different investors may receive the principal and each of the coupon payments.
Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below:
A corporate bond has a coupon rate of 7.2% and pays 4 times a year, on 15 January, April, July, and October. It uses the 30/360 US day count convention.. A trade for 1,000 par value of the bond settles on January 25.
Therefore, (2) some multiple (or fraction) of zero-coupon bonds, each corresponding to the bond's coupon dates, can be specified so as to produce identical cash flows to the bond. Thus (3) the bond price today must be equal to the sum of each of its cash flows discounted at the discount rate implied by the value of the corresponding ZCB.
Government bonds are conventionally considered to be relatively risk-free to a domestic holder of a government bond, because there is by definition no risk of default – the bond is a form of government obligation which is being discharged through the payment of another form of government obligation (i.e. the domestic currency). [5]
A unit zero-coupon bond maturing at time is a security paying to its holder 1 unit of cash at a predetermined date in the future, known as the bond's maturity date. Let B ( t , T ) {\displaystyle B(t,T)} stand for the price at time t ∈ [ 0 , T ] {\displaystyle t\in [0,T]} of a bond maturing at time T {\displaystyle T} .