Government spot rate curve

A Z-spread can be calculated relative to any benchmark spot rate curve in the same manner. The question arises what does the Z-spread mean when the benchmark is not the euro benchmark spot rate curve (i.e., default-free spot rate curve) This is especially true in Europe where swaps curves are commonly used as a benchmark for pricing. When the government spot rate curve is the benchmark, we indicated that the Z-spread for nongovernment issues captured credit risk, liquidity risk, and any option risks. When the benchmark is the spot rate curve for the issuer, for example, the Z-spread reflects the spread attributable to the issue s liquidity risk and any option risks. Accordingly, when a Z-spread is cited, it must be cited relative to some benchmark spot rate curve. This is essential because it indicates the credit and sector risks that are being considered when the Z-spread is calculated. Vendors of analytical systems such Bloomberg commonly allow the user to select a benchmark. 

The zero-volatility or static spread is the spread that when added to the government spot rate curve will make the present value of the cash flows equal to the bond s price plus accrued interest. When spread is defined in this way, spread dnration is the approximate percentage change in price for a 100 basis point change in the zero-volatility spread holding the government spot rate curve constant. 

We can compare fitted yield curves to an actual spot rate curve wherever there is an active government (risk-free) zero-couprai market in operation. In the United Kingdom, a zero-couprai bmid market was introduced in December... 

To value a nongovernment bond, the arbitrage-free value is found by adding a suitable spread to the government spot rates. A spot rate curve can be created using any benchmark such as LIBOR. 

The nominal spread for the nongovernment bond is 148.09 basis points. Let s use the information presented in Exhibit 3.15. The second column in Exhibit 3.15 shows the cash flows for the 7%, 5-year nongovernment issue. The third column is a hypothetical benchmark spot rate curve that we will employ in this example. The goal is to determine the spread that, when added to all the Treasury spot rates, will produce a present value for the non-government bond equal to its market price of 101.9141. 

What does the Z-spread represent for this nongovernment security Since the Z-spread is relative to the benchmark euro spot rate curve, it represents a spread required by the market to compensate for all the risks of holding the nongovernment bond versus a government bond... 

In an arbitrage-free model, the initial term structure described by spot rates today is an input to the model. In fact such models could be described not as models per se, but essentially a description of an arbitrary process that governs changes in the yield curve, and projects a forward curve that results from the mean and volatility of the current short-term rate. An equilibrium term structure model is rather more a true model of the term structure process in an equilibrium model the current term structure is an output from the model. An equilibrium model employs a statistical approach, assuming that market prices are observed with some statistical error, so that the term structure must be estimated, rather than taken as given. 

The term structure of interest rates is the spot rate yield curve spot rates are viewed as identical to zero-coupon bond interest rates where there is a market of liquid zero-coupon bonds along regular maturity points. As such a market does not exist anywhere the spot rate yield curve is considered a theoretical construct, which is most closely equated by the zero-coupon term structure derived from the prices of default-free liquid government bonds. 

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