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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:
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.
Volatility and interest rate risk: Without regular interest payments to cushion price fluctuations, zero-coupon bonds are more volatile than short-term bonds. In general, the current value of any ...
The zero-coupon bond will have the highest sensitivity, changing at a rate of 9.76% per 100bp change in yield. This means that if yields go up from 5% to 5.01% (a rise of 1bp) the price should fall by roughly 0.0976% or a change in price from $61.0271 per $100 notional to roughly $60.968.
An affine term structure model is a financial model that relates zero-coupon bond prices (i.e. the discount curve) to a spot rate model. It is particularly useful for deriving the yield curve – the process of determining spot rate model inputs from observable bond market data.
For example, if a zero-coupon bond with a $20,000 face value and a 20-year term pays 5.5% interest, the interest rate is knocked off the purchase price and the bond might sell for $7,000.
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.
The accrued interest is based on the day count convention, coupon rate, and number of days from the preceding coupon payment date. [2] The clean price more closely reflects changes in value due to issuer risk and changes in the structure of interest rates. Its graph is smoother than that of the dirty price.