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In the previous example, the price will not rise or fall exactly by the amount predicted by duration because the duration does not remain xed at the original level. Notice that the yield to maturity (r) appears in equation (11.4). This means that as the bond price moves down from 100, the yield rises and the duration changes. When prices fall (rates rise), the modi ed duration declines, so the decline in price is smaller than the original forecast over this range of yields. Similarly, when prices rise (rates fall), the modi ed duration increases, so the rise in price is larger than the original forecast over this range of yields. Figure 11.4 shows the price of a hypothetical 30-year bond with a 5.5 percent coupon at various yields to maturity. Take care in reviewing

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class fill tests(unittest.TestCase): def test numeraire rebased bond(self): env = ppf.market.environment() times = numpy.linspace(0, 2, 5) factors = numpy.array([math.exp(-0.05*t) for t in times]) env.add curve("zc.disc.eur" , ppf.market.curve(times, factors, ppf.math.interpolation. loglinear)) expiries, tenors = [0.1, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0], [0, 90] env.add surface("ve.term.eur.hw" , ppf.market.surface(expiries, tenors, numpy.zeros ((8, 2)))) env.add constant("cv.mr.eur.hw", 0.0) r = ppf.model.hull white.requestor() s = ppf.model.hull white.lattice.state(11, 3.5) sx = s.fill("eur", 0.25, r, env) f = ppf.model.hull white.fill(2.0) PtT = f.numeraire rebased bond(0.25, 1.5, "eur", env, r, sx) exp = \ [1.02531512052 ,1.02531512052 ,1.02531512052 ,1.02531512052 ,1.02531512052 ,1.02531512052 ,1.02531512052 ,1.02531512052 ,1.02531512052 ,1.02531512052 ,1.02531512052] assert seq close(exp, PtT)

0:154 0:454 1:329 0:454 0:155

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SAVOR THE MOMENT Try this exercise: Get a Starburst or some other avorful candy. Unwrap the candy, place it into your mouth and then close your eyes. You will be amazed by the intensity of the avor. Moments in time are like that: When we are fully engaged, the moment is that much sweeter.

Networks have always been essential to Grid environments and, consequently, network services and technologies have been a particularly important topic of discussion within the Grid community. However, network resources have not always been considered what has been termed full participants within Grid environments, or first-class entities : They have not been generally provisioned in accordance with

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Recall from table 2.3 that \ s stands for whitespace (space, tab, or newline) and the + means one or more of the preceding character, which is one or more whitespace characters in this case. Running this code produces output 2.3, which is what we expect.

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The English saw the problem as stemming from ignorance rather than malice and believed the police were better trained than social workers. Further, there was a perception that there is an inherent bias in the role of social worker.

in the coded aperture system. In the following we represent bm (x n) by the generic sampling function fn (x). Our goal in this section is to describe how to estimate f (x) given the discrete measurements. Since at this point we know nothing about the nature of f (x) besides the measurements, all continuous signals that would result in the same measurements are equally likely. In general, there exist in nitely many continuous functions that are consistent with the measured data. Choosing which of these functions to use as the estimated signal is challenging, but as a general rule we might like to start by choosing an estimate that is at least consistent with the measurements. Consistency determines the part of the estimated signal, fest (x), that is, in the Hilbert space V(f) generated by f(x). For each subspace V(f) , L2 (R) there exists a complementary subspace V (f) such that V (f) , L2 (R) V (f) > V(f) {0} V (f) < V(f) L2 (R) (3:123)

reason for SMG to start working in this area was that CDPD, a packet mode service, had been introduced in some US cellular networks. A packet mode service was therefore needed for GSM to be competitive on the world scene. The General Packet Radio Service (GPRS) was then adopted as a phase 21 work item. Work was initially expected to be completed in 1994 but later it was recognised that it could not be nalised before 1996. In the meantime another objective of GPRS had emerged which was to provide an ef cient access to the Internet or other IP networks. This has now become the major stake of GPRS. More details can be found in the dedicated description in 7, Section 8.

6 (4)

It is simply an array with two values stored in association with keys. Each of these values is an array itself. After we have made the array, we can reference it like this:

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