Benchmark interest rate

Once we estimate the cash flows for a fixed-income security, the next step is to determine the appropriate interest rate for discounting each cash flow. Before proceeding, we pause here to note that we will once again use the terms interest rate, discount rate, and required yield interchangeably throughout the chapter. The interest rate used to discount a particular security s cash flows will depend on three basic factors (1) the level of benchmark interest rates (2) the risks that the market perceives the securityholder is exposed to and (3) the compensation the market expects to receive for these risks. 

As we have seen, duration is a measure of the change in a bond s value when interest rates change. The interest rate that is assumed to shift is the government rate which serves as the benchmark interest rate. However, for nongovernment instruments, the yield is equal to the government yield plus a spread to the government yield curve. This is why nongovernment... 

Interest rate or term structure risk stems from movements in the benchmark interest rate curve. Excluding exchange rate risk, it is the main source of risk for most investment-grade bonds. Any reasonable model will include markets that are stable and actively traded. A typical coverage, taken from JP Morgan GBI Broad Index, is shown in Exhibit 23.1. Note the presence of two emerging markets. 

Calcnlation of the interest rates at which NPV=0 can be tedious. Computer software exists to do this job, but quite accurate estimates can be obtained simply by calculating some benchmark values, plotting a graph of interest rate vs. NPV and then interpolating to obtain the reqnired value of /. 

There is still a consistency problem if we want to price interest rate derivatives on zero bonds, like caplets or floorlets, and on swaps, like swaptions, at the same time within one model. The popular market models concentrate either on the valuation of caps and floors or on swaptions, respectively. Musiela and Rutkowski (2005) put it this way We conclude that lognormal market models of forward LIBORs and forward swap rates are inherently inconsistent with each other. A challenging practical question of the choice of a benchmark model for simultaneous pricing and hedging of LIBOR and swap derivatives thus arises. ... 

The option-adjusted spread (OAS) is the most important measure of risk for bonds with embedded options. It is the average spread required over the yield curve in order to take into account the embedded option element. This is, therefore, the difference between the yield of a bond with embedded option and a government benchmark bond. The spread incorporates the future views of interest rates and it can be determined with an iterative procedure in which the market price obtained by the pricing model is equal to expected cash flow payments (coupons and principal). Also a Monte Carlo simulation may be implemented in order to generate an interest rate path. Note that the option-adjusted spread is influenced by the parameters implemented into the valuation model as the yield curve, but above all by the volatility level assumed. This is referred to volatility dependent. The higher the volatility, the lower the option-adjusted spread for a callable bond and the higher for a putable bond. 

The most actively traded government securities for various maturities are called benchmark issues. Yields on these issues serve as reference interest rates which are used extensively for pricing other securities. Exhibit 1.2 is a Bloomberg screen of the benchmark bonds issued by the government of the Netherlands. European government bonds will be discussed in Chapter 5. As an illustration of a corporate bond. Exhibit 1.3 shows a Bloomberg Security Description screen for 4.875% coupon bond issued by Pirelli SPA that matures on 21 October 2008. 

The minimum interest rate that an investor should require is the yield available in the marketplace on a default-free cash flow. For bonds whose cash flows are denominated in euros, yields on European government securities serve as benchmarks for default-free interest rates. In some European countries, the swap curve serves as a benchmark for pricing spread product (e.g., corporate bonds). For now, we can think of the minimum interest rate that investors require as the yield on a comparable maturity benchmark security. 

The zero-volatility spread, also referred to as the Z-spread or static spread, is a measure of the spread that the investor would realize over the entire benchmark spot rate curve if the bond were held to maturity. Unlike the nominal spread, it is not a spread at one point on the yield curve. The Z-spread is the spread that will make the present value of the cash flows from the nongovernment bond, when discounted at the benchmark rate plus the spread, equal to the nongovernment bond s market price plus accrued interest. A trial-and-error procedure is used to compute the Z-spread. 

Interest Rate Swaps as the Benchmark Curve ter Eure Bevies... 

As we have seen, interest rate swaps are valued using no-arbitrage relationships relative to instruments (funding or investment vehicles) that produce the same cash flows under the same circumstances. Earlier we provided two interpretations of a swap (1) a package of futures/forward contracts and (2) a package of cash market instruments. The swap spread is defined as the difference between the swap s fixed rate and the rate on the Euro Benchmark Yield curve whose maturity matches the swap s tenor. 

First, as mentioned earlier, there is usually no universal benchmark in a given market. Again, a possible approach, used in Barra s models, is to introduce a swap spread factor that describes the average spread between sovereign and swap rates and can conveniently allow spread risk to be expressed with respect to the LIBOR/swap curve when interest rate risk factors are originally based on the sovereign yield curve. 

Each corporate bond will only be exposed to one of these factors, with an exposure that will typically increase with the bond s maturity. A rule of thumb is that it will be comparable to the bond s exposure to the shift factor. The spread risk of almost all AAA, AA, and A rated bonds will be less than their interest rate risk, and it is only for BBB rated bonds and in some very specific market sectors such as Energy and Telecoms that spread risk starts exceeding benchmark risk. Spread risk is by far the dominant source of systematic risk for high-yield instruments. 

Fortunately for the investment community, there are alternatives to calculating tracking error that give an accurate idea of where a portfolio s risks lie. These methods start with understanding the exposures of a portfolio relative to its benchmark, along several dimensions such as duration, term structure, rating, sector, and issuer. They then create interest rate and credit spread scenarios for different future time periods and perform a what-if analysis on the portfolio and the benchmark for these scenarios. These scenarios should encompass both expected and extreme conditions (best and worst case) in order to generate a return profile, both absolute and relative to the index, as well as to identify key thresholds. 

The asset swap spread is equal to the underlying asset s redemption yield spread over the government benchmark, minus the spread on the associated interest rate swap. The latter, which reflects the cost of convert-... 

IDNs do expose investors to interest rate risk. If the rate differential moves in the opposite direction from the one desired, the coupon is reduced and the yield may fall below that available on the benchmark bond. 

Option-adjusted spread analysis uses simulated interest rate paths as part of its calculation of bond yield and convexity. Therefore an OAS model is a stochastic model. The OAS refers to the yield spread between a callable or mortgage-backed bond and a government benchmark bond. The government bond chosen ideally will have similar coupon and duration values. 

Thus OAS is a general stochastic model, with discount rates derived from the standard benchmark term structure of interest rates. This is an advantage over more traditional methods in which a single discount rate is used. The calculated spread is a spread over risk-free forward rates, accounting for both interest-rate uncertainty and the price of default risk. As with any methodol-ogy, OAS has both strengths and weaknesses however, it provides more realistic analysis than the traditional yield-to-maturity approach. Hence, it has been widely adopted by investots since its introduction in the late 1980s. 

In October 2008, the Sichuan Government announced various preferential loan policies for households to rebuild their house or buy a new house. For households taking out a bank loan to purchase a new house, the minimum interest rate was adjusted to 0.6 of the benchmark lending interest rate, and the minimum down payment was reduced to 10 %. And for rebuilding, buying or strengthening a house received a 1 % point discount on their interest rate. 

It may however, be noted that these values for different parameters are influenced by purity, morphology and particle size of the sample. The calculated values of VOD for FOX-7 and RDX are 9090ms 1 and 8940 ms 1 respectively (Cheetah Thermochemical Code). Based on these results, it was concluded that FOX-7 is better than RDX which is used as a benchmark explosive for comparison with other explosives. Consequently, it is an attractive ingredient for application in high performance IM compliant explosive formulations. FOX-7 also increases the burning-rate in propellants and as a natural consequence, is of interest for high performance propellants. 

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