Yield Curve Building with Bonds

# Yield Curve Building with Bonds - Yield Curve Modeling...

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Yield Curve Modeling Yield Curve Building with Bonds Copyright © 1996-2006 Investment Analytics

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Copyright © 1996-2001 Investment Analytics Yield Curve Building with Bonds Slide: 2 Yield Curve Building with Bonds ¾ Bootstrap Method ¾ Regression Techniques ¾ Building Emerging Market Yield Curves ¾ Iterative Methods
Copyright © 1996-2001 Investment Analytics Yield Curve Building with Bonds Slide: 3 Bootstrap Method for Bonds ¾ Take treasuries with a succession of maturities and common payment dates ¾ Bond Price = D 1 C 1 + D 2 C 2 + D 3 C 3 + 100D 3 9 Cash flows are known from the bond coupon 9 The curve has already been built out to 2 years using zeros 9 D 1 and D 2 are known, calculate D 3 by bootstrapping C 1 C 2 C 3 Year 1 Year 2 Year 3 Today PV of Cash Flows

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Copyright © 1996-2001 Investment Analytics Yield Curve Building with Bonds Slide: 4 Problems with Bootstrapping ¾ Two bonds with same maturity, may have different yields ¾ More payment dates than bonds ¾ A good solution is to use regression techniques
Copyright © 1996-2001 Investment Analytics Yield Curve Building with Bonds Slide: 5 The Regression Method ¾ Regression: Y = α + β X+ ε 9 Y is variable you want to predict - e.g. Bond Price 9 X is “explanatory” variable - e.g. cash flows 9 β is the multiple to be estimated - discount factor 9 α is typically insignificant and presumed = 0 9 ε is error term: ~ iid No(0, σ 2 ) Normally distributed Zero mean, constant variance σ 2

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Copyright © 1996-2001 Investment Analytics Yield Curve Building with Bonds Slide: 6 Multiple Regression ¾ Expresses linear relationship between a single dependent variable (y) and a series of independent variables (x 1 . . . x n ) ¾ y i = α + β 1 x 1i + β 2 x 2i + . . . + β n x ni + ε i ¾ Determine the coefficients which are “optimal”: 9 Least Squares Estimates Coefficients which minimize the sum of squares of the error terms e i The e i are the differences between the observed values of y and the values of y estimated using the regression equation
Copyright © 1996-2001 Investment Analytics Yield Curve Building with Bonds Slide: 7 Multiple Regression with Bond Data ¾ y is the bond price, and (x 1 . . . x n ) are the cash flows on dates 1 to n. ¾ If α is set to zero, and β 1 . . . β n can be estimated and will be the discount factors. ¾ If we make certain statistical assumptions, we can measure how good the estimates are. ¾ y i = α + β 1 x 1i + β 2 x 2i + . . . + β n x ni + ε i ¾ Price = C 1 D 1 + C 2 D 2 + . . . + C n D n + e i

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Copyright © 1996-2001 Investment Analytics Yield Curve Building with Bonds Slide: 8 Example: Bond Data 1994 1995 1996 1997 1998 1999 2000 2001 2002 Price Cashflow 100.91 107.5 0 0 0 0 0 0 0 103.54 110.25 0 0 0 0 0 0 0 101.49 8.5 108.5 0 0 0 0 0 0 102.37 9 109 0 0 0 0 0 0 100.37 8.25 108.25 0 0 0 0 0 99.74 8 8 108 0 0 0 0 0 99.68 0 0 0 0 99.70 0 0 0 0 94.02 7 7 7 7 107 0 0 0 93.02 6.75 106.75 0 0 0 86.88 5.75 105.75 0 0 86.93
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## This document was uploaded on 11/04/2011 for the course ECON 421 at CUNY York.

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Yield Curve Building with Bonds - Yield Curve Modeling...

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