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In many enterprises, this type of data is kept in separate databases and on separate servers This data as shown Figure 5-1

Example5 l, wc can seethatthe t'unction changes signbetween values -50 clf and 200Thc p l o t o b v i o u s l y s u g g e s t s b e t t e r i n i t ua l s s e s , s a y 0 a n d I 5 0 , b u t t i l r i l l u s t r a t i ' u ' t ' p u r p o s r - ' \ gi e l4 lct's assume clon'thave the bencfitof the plcltand havc madeconservative we guesses Thcrcfble,the initial estimatc the rtx>tr, at thc midpointof the interval of lies 50+ l(x)

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/ value tlrerootis 1421316 means thc value 125calcuNotethattlreexact of This that of lated here a trueDercent has error relative of r,/rI ,,-l 1421316 r2-sx 1 0 0 4 : 1 2 4 3 4 / , l i 1127316 I

FIGURE 5-1

Next wc compute productof the functionvalueat the lower boundandat the midpoint: the : I ( 5 0 )I ( 1 2 - 5:1 - 4 5 1 9 ( - 0 4 0 9 1 1 3 7 1 thanzero,and henceno sign change which is greater occursbetween lower boundand the the midpointConsequently, root mustbe locatecl the upperinterval betweerr and in the 125 200Therefbre, create new intervalby redefining lower boundas 125 we a the

To effectively demonstrate the new market volatility we are discussing, let s look at a few exceptional examples of recent volatility and massive price movement Figure 33 shows the CBOT soybean futures over four years or so with the most striking part of the chart beginning in September 2006 Soybeans began a rally based on fundamental crop issues and massive index and hedge fund buying that culminated in gains of over $1100 per soybean contract The margin on the CBOT soybean futures contract changes as market volatility increases risk, but futures margin requirements exploded during this period At-the-money call options during this period were a full $100 per bushel or more (5,000 bushel contract or $5,000 per

BRACKETING METHODS ROOTS:

fronrxl : At this point,the new intervalextends rnatecau thenbe calculated as l2-5to r, :200 A revised l'ootesti-

5:

r v h i c h r e p r e s e n t s a t r u e p e r c e n t e rlre ,lr:o f3 8 5 % T h e p r o c e s s c a n b e r e p e a t e d t o o b o 1 tain refineilestinrates example, For -0409(0359) -(t|1l : 6 f ( t t s l 11 1 2 - 5:; Therelbre roo( is now irr the lower intervalbetween125and 162-5 upperbound the The tirr is rede[ined l 625anclthe root cstinrate the third iteration calculated as is as

125 1625 * : | 437-5 )

FIGURE 5-2

.

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