KIC000008

KIC000008 - Nice flexible form to estimate shapes and no...

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, , - Cubic for Spot Rates Almost everyone makes continuous compounding assumptions when deriving these curves given the complications for compounding with daily rules, ect. ret) = r o + at + bt' + ct' When t=Othen r 0 is the instantaneous spot rate. Piecewise Cubic for Spot Rates ret) = /(l + all + b/ +c/ r(IO)+a,(I-IO)+b,(I-IO)' +c,(I-IO)' r(20) + a,(I- 20) + b, (I - 20)' + C,(I- 20)' 1~10 IOSIS20 20:5:/::;30 What's a Spline? At each point where we switch over from one piece to the other, there is some discontinuity We don't like discontinuity since it causes jumps in forward rates. The piecewise we defined does not have jumps in the spot rate, but has jumps in the slope of the spot rate. All a spline does is ensure smoothness between the switchover points or knot points in the slope and the slope of the slope. All this implies is that there is some binding condition between the coefficients between the two adjacent sections. 4

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Nelson Siegel Popular model that has been refined. 2 or 3 parameters to estimate
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Unformatted text preview: Nice flexible form to estimate shapes and no spline is needed. 2 parameters has problems capturing certain shapes, hence the development of the 3 parameter model. de!) = e-r (r)1 Fitting the Curve With splines need to oe careful of under or over fitting, i.. e. where we pick the switch points or knots. All that's left is to find the parameters given the data, So you need some criteria for this. like allnear regressjon, you can minimize squared errors between the actual datil and the implied data point from the function, The spot curve will give you a fitted yield (price] for a bond and you can observe the yield in the market. MinimiZing the root mean squared error between the yield (price) and fitted yield (price) is one WilY to do it: RMSE~ 1 ~(y .)' N f:: ,-Y, Exhibit 5-6 from Fabozzi (6 th edition) 5...
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This note was uploaded on 09/06/2011 for the course FIN 428 taught by Professor Hood during the Fall '11 term at Iowa State.

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KIC000008 - Nice flexible form to estimate shapes and no...

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