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2 we discuss building a G2++ quadrinomial tree In section 123, we discuss the two-factor Hull-White model In section 124, we discuss the Heath-Jarrow-Morton (HJM) model in a continuoustime framework In section 125, we discuss pricing discount bond options with a Gaussian HJM model In section 126, we discuss pricing discount bond options in a general HJM framework In section 127, we discuss the single-factor HJM discrete-state model In section 128, arbitrage-free restrictions in a single factor model are given In section 129, we discuss computation of arbitrage-free HJM term structure evolutions In section 1210, an implementation of a single-factor HJM model is given In section 1211, we implement an HJM single-factor tree to value a (synthetic) swap In section 1212, we introduce the two-factor HJM model, while in section 1213 a two-factor HJM implementation is given.

can be found. Let (x) = (et) be the column matrix associated with A = A,-. We may write [[A] - A z [ / ] ] ( ^ ) = ( 0 ) i = 1,2,...,m (A.4.14)

S5.341

which match the conditional mean and variance of yt+1 given (yt, ht2) in the limit. Thus, the tree converges to the continuous-state model (8.37). From equations (8.39) to (8.41), the branching probabilities exist, that is, 0 pu, pm, pd 1 if and only if: | r ( ht2 / 2 ) | 2 n n | r ( ht2 / 2) | 1 min 1 , 2 2 2 2 n 2 n n ht2 (8.43)

In section 1214 we introduce the Ritchken-Sankarasubramanian (RS) model, and in section 1215 the RS short rate process is discussed In section 1216, an improvement of the RS model.

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If continuous compounding is used, then di, j = e ri,j t (11.9)

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upturn in both markets in 1984; the top in bonds in early 1987, preceding the stock market crash of 1987; and both markets rallying together into 1989. To the upper right it can be seen that the breakout by stocks above their 1987 pre-crash highs has not been confirmed by a similar bullish breakout in bonds. Figures 4.4 through 4.9 break the period from 1982 to 1989 into shorter time intervals to provide closer visual comparisons. I'll take a closer look at the events immediately preceding and following the October 1987 stock market crash and will also examine the market events of 1989 in more detail. Figure 4.4 shows the relative action of bonds and stocks at the 1982 major bottom. Notice that as the Dow Industrials hit succeeding lows in March, June, and August of 1982, the bond market was forming rising troughs in the same three months. In August, although both markets rallied together, bonds were the clear leader on the upside. In May of 1983, bonds formed a prominent double top and began to drop. That bearish divergence led to an intermediate stock market peak at the end of the year, which led to a 15 percent downward correction in the equity market. The downward correction in both markets continued into the summer of 1984 (see Figure 4.5). A

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inline double Statistics::mean() const { QL_REQUIRE(sampleWeight_>0.0, Stat::mean() : sampleWeight_=0, insuf cient ); return sum_/sampleWeight_; } inline double Statistics::variance() const { QL_REQUIRE(sampleWeight_>0.0, Stat::variance() : sampleWeight_=0, insuf cient ); QL_REQUIRE(sampleNumber_>1, Stat::variance() : sample number <=1, insuf cient ); double v = (sampleNumber_/(sampleNumber_-1.0)) *(quadraticSum_ sum_*sum_/sampleWeight_)/sampleWeight_; if (fabs(v) <= 1.0e-6) v = 0.0; QL_ENSURE(v >= 0.0, Statistics: negative variance ( + DoubleFormatter::toString(v,20) + ) ); return v; } inline double Statistics::standardDeviation() const { return QL_SQRT(variance()); } inline double Statistics::downsideVariance() const { QL_REQUIRE(sampleWeight_>0.0, Stat::variance() : sampleWeight_=0, insuf cient );

} catch( Exception e ) { e.printStackTrace(); } } } }

a name already exists, you can t use the Name box to change the range to which that name refers. Attempting to do so simply selects the original range. You must use the Define Name dialog box to change the reference for a name.

Good design begins by asking who will use the results, why, and how Since this chapter is about the visualization of data, it will focus only on those performing the analysis and the consumers of their analysis who are people making critical decisions. Data graphics help make arguments, but if essential details are left out, distorted, or hard to see, the consequences can be catastrophic. Before examining speci c data graphics and visualization tools, the construction of a commonly used graph, the scatterplot will be reviewed. Some general principles will be described, along with the basics of graphics design.

CONFIDENCE CONVERT CORREL, PEARSON COS COSH COUNTA COUNTBLANK COUNTIF COUPDAYBS COUPDAYS COUPDAYSNC COUPNCD COUPNUM COUPPCD COVAR CRITBINOM NPER DAYS360 DATE DATEDIF DATEVALUE DAVERAGE DAY DAYS360 DAYS360 DB

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