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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
, , - 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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Nelson Siegel Popular model that has been refined. 2 or 3 parameters to estimate
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online