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It is approximately equal to the percentage change in price for a given change in yield, and may be thought of as the elasticity of the bond's price with respect to discount rates. For example, for small interest rate changes, the duration is the approximate percentage by which the value of the bond will fall for a 1% per annum increase in ...
In the case where the only discount rate one has is not a zero-rate (neither taken from a zero-coupon bond nor converted from a swap rate to a zero-rate through bootstrapping) but an annually-compounded rate (for example if the benchmark is a US Treasury bond with annual coupons) and one only has its yield to maturity, one would use an annually ...
In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps. [ 1 ] A bootstrapped curve , correspondingly, is one where the prices of the instruments used as an input to the curve, will be an exact output , when these same instruments ...
When the yield curve is flat, the capital gain is predicted to be much less, and there is little variability in the bond's total returns over time. As market rates of interest increase or decrease, the impact is rarely the same at each point along the yield curve, i.e. the curve rarely moves up or down in parallel.
Of course, the yield curve is most unlikely to behave in this way. The idea is that the actual change in the yield curve can be modeled in terms of a sum of such saw-tooth functions. At each key-rate duration, we know the change in the curve's yield, and can combine this change with the KRD to calculate the overall change in value of the portfolio.
Yield to put (YTP): same as yield to call, but when the bond holder has the option to sell the bond back to the issuer at a fixed price on specified date. Yield to worst (YTW): when a bond is callable, puttable, exchangeable, or has other features, the yield to worst is the lowest yield of yield to maturity, yield to call, yield to put, and others.
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. OAS is hence model-dependent.
A Technical Note on the Smith-Wilson Method, The Financial Supervisory Authority of Norway, (1 July 2010) Lagerås, Andreas & Lindholm, Mathias. (2016). Issues with the Smith-Wilson method. Insurance: Mathematics and Economics. 71. 10.1016/j.insmatheco.2016.08.009. Smith, A. and Wilson, T. (2000). Fitting Yield Curves with Long Term Constraints.