Coupon defined

Another device that finds frequent use is the stirred cell shown in Fig. 20-54. This device uses a membrane coupon at the bottom of the reservoir with a magnetic stir bar. Stirred cells use low fluid volumes and can be used in screening and R D studies to evaluate membrane types and membrane properties. The velocity profiles have been well defined (Schlichting, Boundary Layer Theory, 6th ed., McGraw-Hill, New York, 1968, pp. 93-99). 

With small modifications, ASTM standard G48 can be used to determine a CPT. The test is used as a ranking parameter for the resistance to pitting of high-alloyed austenitic stainless steels. In this method, material coupons are typically exposed for 24 or 72 h to a 6% FeCl3 (=1.11 mole/liter) solution at fixed temperatures (typically with 2.5°C intervals). The CPT is defined as the lowest temperature at which the specimen is attacked by pitting corrosion. 

Surface finish of the test coupon Various manufacturing processes can change the physical form of the metal s initial surface or produce surface films, either of which may influence the eharacteristies of the corrosion deposit that is developed when in contact with water. These effeets may influence or change the mechanism controlling the level of eontamination. The standard sit-and-soak test defines a machined smface that will not be representative of a cast surface, for example. In the first set of eonormative tests, aetual galvanized steel pipe was used to overcome precisely this sort of problem. 

The asset swap is an agreement that allows investors to exchange or swap future cash flows generated by an asset, usually fixed rates to floating rates. It is essentially a combination of a fixed coupon bond and an IRS. We define it thus ... 

The price of a zero-coupon discount at time t is defined in terms of the short-rate r at time t and the current term structure. The price function is not static, and the price of a bond at time t that matures at time T is a function of the short-rate, as we have noted, and separately of the time f. 

A default-free zero-coupon bond can be defined in terms of its current value imder an initial probability measure, which is the Wiener process that describes the forward rate dynamics, and its price or present value under this probability measure. This leads us to the HJM model, in that we are required to determine what is termed a change in probability measure , such that the dynamics of the zero-coupon bond price are transformed into a martingale. This is carried out using Ito s lemma and a transformatiOTi of the differential equation of the bmid price process. It can then be shown that in order to prevent arbitrage, there would have to be a relationship between drift rate of the forward rate and its volatility coefficient. 

The no-arbitrage condition is set by defining the price of a zero-coupon bond that matures at time T in terms of an accumulation factor B(t) which is the value of a money market account that is invested at time 0 and reinvested at time t at an interest rate of r(t). This accumulation factor is defined as Equation (4.31) ... 

The author defines the total value of the firm v(V) as the sum of firm value V, tax benefit from coupon payments TB(V) less the value of bankruptcy costs BC(F). The value is given by Equation (8.23) ... 

The credit spread is defined as the difference between the risky rate of a defaul-table bond and the risk-free rate of a default-free bond. In this case, with bonds priced at par, between coupon and risk-free rate, the pricing is performed like a valuation of a straight bond, including the default risk adjustment. The price is given by Equation (8.25) ... 

Floating-rate notes can include additional features. One example is the inclusion of cap, floor and collar clauses. A floater with cap feature means that the reference rate cannot overcome the threshold rate defined in the indenture. Usually the threshold is expressed in terms of coupon, that is after a coupon threshold (e.g. 6%, reference rate plus quoted margin) the investor receives at maximum the cap level. In this case, the floater is not completely covered by rising interest rates, in which after the threshold the floater trades as a conventional bond. In contrast, a floater with a floor feature represents the minimum coupon level that an investor can receive, hedging to the downside risk of interest rates. If the bond includes both cap and floor, this feature is known as collar or collared floating-rate note. The bond can include also a drop-lock feature that after a threshold it ceases to float. 

We will value our 4-year, 6% coupon bond under three different scenarios. These scenarios are defined by the relationship between the discount rate or required yield and the coupon rate. In the first scenario, we will consider the case when the annual discount rate and the coupon rate are equal. For the second scenario, we will value the bond when the discount rate is greater than the coupon rate. The last scenario assumes the discount rate is less than the coupon rate. 

In other words the 7% gilt, the 6% Bund, and the 4% bonos around which the futures contracts are constructed do not exist. A cash market bond that can be delivered into the contract on maturity has to be identified and converted to match the futures contract specification. In full exchange-based contract specifications, the list of deliverable cash market bonds are well defined and are restrictive. Deliverable bonds in the case of the Bund future will be bonds issued by the Federal Government of Germany and will have a maturity between 8.5 and 10.5 years. Normally, bonds offering early redemption, floating coupons, or some form of convertibility will not be in the list of deliverables. 

Coupon income is defined as follows. From July 4, 2002, the date of the last coupon payment, until the settlement date, September 12, 2002, there are 71 days of accrued interest. Based on a coupon of 5.00% per annum and a 360-day year this amounts to 0.986. ... 

The futnre market price of a zero-coupon bond in this framework can be found by defining the reversion rate, P, the volatility, and the... 

The risk of an investment in securities is often defined as the volatility of prices or returns. The return is measured here as the sum of coupon income and price gains. From an investor s viewpoint it would be advantageous to hold a portfolio of securities the returns of which correlate as little as possible. In real life investors therefore try to keep correlations between securities in their portfolios as low as possible. Correlations for the database from 6/80 to 11/02 are all positive. They range from 0.66 (Treasury 10 year+ and BBB 1-3 years) to 0.99 (A 3-7 years and AA 3-7 years). ... 

Engineering data are defined as coupon tests, subelement tests, and component tests, as well as design and life prediction results. 

The unit in which convexity, as defined by (2.18), is measured is the number of interest periods. For annual-coupon bonds, this is equal to the number of years for bonds with different coupon-payment schedules, formula (2.19) can be used to convert the convexity measure from interest periods to years. 

The coupon process represents the cash flow investors receive while they hold the bond. Assume that a bond s term can be divided into very small intervals of length dt and that it is possible to buy very short-term discount bonds, such as Treasury strips, maturing at the end of each such interval and paying an annualized rate r t). This rate is the short, or instantaneous, rate, which in mathematical bond analysis is defined as the rate of interest charged on a loan taken out at time t that matures almost immediately. The short rate is given by formulas (3.10) and (311). 

In practice, the term structure of coupon bonds is not complete, so the coefficients in (3.33) cannot be identified. To address this problem, McCulloch (1971, 1975) prescribes a spline estimation method that assumes zero-coupon bond prices vary smoothly with term to maturity. This approach defines price as a discount function of maturity, P N), which is a given by (3.34). 

The approach described in Heath-Jarrow-Morton (1992) represents a radical departure from earlier interest rate models. The previous models take the short rate as the single or (in two- and multifactor models) key state variable in describing interest rate dynamics. The specification of the state variables is the fundamental issue in applying multifactor models. In the HJM model, the entire term structure and not just the short rate is taken to be the state variable. Chapter 3 explained that the term structure can be defined in terms of default-free zero-coupon bond prices or yields, spot rates, or forward rates. The HJM approach uses forward rates. 

This chapter considers some of the techniques used to fit the model-derived term structure to the observed one. The Vasicek, Brennan-Schwartz, Cox-Ingersoll-Ross, and other models discussed in chapter 4 made various assumptions about the nature of the stochastic process that drives interest rates in defining the term structure. The zero-coupon curves derived by those models differ from those constructed from observed market rates or the spot rates implied by market yields. In general, market yield curves have more-variable shapes than those derived by term-structure models. The interest rate models described in chapter 4 must thus be calibrated to market yield curves. This is done in two ways either the model is calibrated to market instruments, such as money market products and interest rate swaps, which are used to construct a yield curve, or it is calibrated to a curve constructed from market-instrument rates. The latter approach may be implemented through a number of non-parametric methods. 

As noted above, index bonds differ in whether their principal payments or their coupons or both are linked to the index. When the principal alone is linked, each coupon and the final principal payment are determined by the ratio of two values of the relevant index. U.S. TIPS coupon payments, for instance, are calculated using an accretion factor based on the ratio between two CPI-U levels, defined by equation (12.1). 

TIPS periodic coupon payments and their final redemption payments are both calculated using an inflation adjustment. Known as the inflation compensation, or IC, this is defined as in expression (12.2). 

The simple margin formula may be adjusted to take into account changes in the reference index rate since the last reset date. This is done by replacing the price in (131) with an adjusted price, defined using either (13.2a) or (13.2b) which assume semiannual coupons. 

Yield has been defined in previous chapters as the discount rate that equates the sum of the present values of all a bonds cash flows to its observed market price. A vanilla bond, such as a U.S. Treasury, has m future cash flows—the coupon payments—each having a value C, equal to one-half the coupon rate applied to the face value. C , is the principal payment. The sum total of the bond s discounted cash flows is given by equation... 

Between the short- and long-term horizon dates is one at which the net effect of the change in reinvestment rate on the bond s future value is close to zero. At this date, the bond behaves like a single-cash-flow or zero-coupon security, and its future value can be predicted with greater certainty, no matter what the yield curve does after its purchase. Defining this date as Sh interest periods after the purchase date and Ph as the value of the bond at that point, it can be shown that the bond s rate of return up to this horizon date is the value for rntn that solves equation (16.6). 

The environmental factors that tend to accelerate metal loss include high humidity, high temperature and proximity to the ocean, extended periods of wetness and the presence of pollutants in the atmosphere. The small amount of carbon dioxide normally present in the air neither initiates nor accelerates corrosion. Vernon [57] was the first to study the corrosion rate of steel coupons in the presence of well-defined atmospheres. Atmospheric gases such as CO2, SO2, NO2, HCl, etc. after getting dissolved in the moisture layer on the metal surface, these gases result in a number of ions and ionic species like H", CF, COa , NOa , S04 , etc. They measured corrosion rate was as a function of time, relative humidity and... 

At the RCM held in Sao Paulo in March 1998, racks 2A, 2B, 3A and 3B were received from the IAEA. A test protocol concerning specimen (coupon) preparation and handling, test duration, etc., was defined. The use of site specific alloys was also encouraged. These four racks contained coupled coupons. The coupons were photographed, and the rack was reassembled and introduced into the lEA-Rl reactor pool, close to the spent fuel racks, on 1998-08-25. Racks 2B and 3B were removed on 1999-10-20 and racks 2A and 3A on 2000-09-27, after 13 and 25 months, respectively. 

In order to define the reasons and mechanism of steel corrosion in petroleum products, experiments were done with mild steel coupons in mixtures of distillates and water, under laboratory conditions. After exposure of the coupons in the mixtures during 7 days of intensive agitation, corrosion rates and form were determined. The results show that the critical concentration of water... 

The next step, currently in progress [61], is the use of microsensors built into coupons used in the rotating cage for the determination of localized shear stresses in various locations of the coupons. By defining the exact geometry of the cage and the test vessels, as well as the fluids, the shear stresses will be mapped sis a function of the speed of rotation... 

Metal coupon data are relatively easy to use for materials selection purposes from calculation of corrosion rate and observations on the appearance of the coupon. For nonme-tallic materials, the problem is to define what constitutes failure. For example, when is color change, flaking, swelling, or tackiness acceptable, and when do they indicate potential failure ... 

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