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Then continuing by trial and error, a bond gain of 5.53 divided by a bond price of 99.47 produces a yield to maturity of 5.56%. Also, the bond gain and the bond price add up to 105. Finally, a one-year zero-coupon bond of $105 and with a yield to maturity of 5.56%, calculates at a price of 105 / 1.0556^1 or 99.47.
The yield to maturity (YTM) is the discount rate which returns the market price of a bond without embedded optionality; it is identical to (required return) in the above equation. YTM is thus the internal rate of return of an investment in the bond made at the observed price. Since YTM can be used to price a bond, bond prices are often quoted ...
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.
"Trees" are widely applied here. Other common pricing-methods are simulation and PDEs.. Option-adjusted spread (OAS) is the yield spread which has to be added to a benchmark yield curve to discount a security's payments to match its market price, using a dynamic pricing model that accounts for embedded options.
There is a time dimension to the analysis of bond values. A 10-year bond at purchase becomes a 9-year bond a year later, and the year after it becomes an 8-year bond, etc. Each year the bond moves incrementally closer to maturity, resulting in lower volatility and shorter duration and demanding a lower interest rate when the yield curve is rising.
The current yield refers only to the yield of the bond at the current moment. It does not reflect the total return over the life of the bond, or the factors affecting total return, such as: the length of time over which the bond produces cash flows for the investor (the maturity date of the bond),
To avoid the impact of the next coupon payment on the price of a bond, this cash flow is excluded from the price of the bond and is called the accrued interest. In finance, the dirty price is the price of a bond including any interest that has accrued since issue of the most recent coupon payment.
An alternative approach to modeling (American) bond options, particularly those struck on yield to maturity (YTM), employs modified equity-lattice methods. [35] Here the analyst builds a CRR tree of YTM, applying a constant volatility assumption, and then calculates the bond price as a function of this yield at each node; prices here are thus ...