Convex instruments

The relationship is reduced as maturity is increased because of the low liquidity of futures markets beyond two to five years, increased futures execution risk, and increased interest rate volatility. The convexity problem when using futures contracts (nonconvex instruments) to hedge interest rate swap positions (convex instruments) is more pronounced for long-term transactions, resulting in reduced hedge efficiency. The convexity issue is addressed in detail later in this chapter. 

Atomic emission from the plasma is focused on to the entrance slit of the monochromator using a combination of convex or plano-convex lenses or a concave mirror. The combination of focusing optics, monochromator and detector is generally referred to as a spectrometer, although the heart of the device is the monochromator. A monochromator is an instrument that... 

Lenses were known in ancient times, and by the fifteenth century their use in spectacles was common. It was not until the seventeenth century, however, that a convex and a concave lens were put together in a tube to form the first crude microscope. Galileo used one of the first instruments, and he was amazed to discover the compound eyes of insects. Stelluti... 

There are available microprocessor controlled solvent delivery modules which can generate the required gradient profile, be it stepwise, linear, convex, concave or simply isocratic. Up to four solvents can be selected. A detailed discussion of the instrumentation is presented in Chapter 6. The pumping systems and accessories are equally adaptable to use with open tubular chromatography as with high pressure systems. 

Cap prices can also be valued analytically using the Hull-White model. The cap prices calculated using the implied volatilities of interest rate caps and the Black-Scholes model serve as the calibrating instruments. After the Hull-White model has been calibrated, the parameters a and o that minimize a goodness-of-fit measure can be used to solve for the convexity bias. 

As we mentioned earlier, it is difficult for credit portfolio managers (where the market is overwhelmingly noncallable) to actively manage convexity of their holdings. However, preferring higher coupon instruments and premium bonds over lower coupon and discount bonds tends to increase the convexity of the portfolio and in turn increases its total return. 

Ramsden eyepiece An eyepiece for optical instruments consisting of two identical plano-convex lenses with their convex faces pointing towards each other. They are separated by a distance of two thirds of the focal length of either lens. 

Bond traders wishing to hedge the interest rate risk of their bond positions have several tools to choose from, including other bonds, bond futures, and bond options, as well as swaps. Swaps, however, are particularly efficient hedging instruments, because they display positive convexity. As explained in chapter 2, this means that they increase in value when interest rates fall more than they lose when rates rise by a similar amount—just as plain vanilla bonds do. 

Bucket elevators, belt conveyor, and pneumatic conveying system These shall be run only when the level in silos at delivery end goes down to a preset level. Instruments shall be provided to monitor the levels provision of convex mirrors shall also be made to observe the levels (of open silos). The conveying systems shall never run idle, or insufficiently loaded. Ensure that flow of material is smooth at feed point (e.g. all buckets are properly filled up there is no spillage of materials from belts). 

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