coupon effects Fisher Cohen, Kramer and Waugh Ordinary Least Squares OLS log

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2 coupon effecs Fsher Cohen, Kramer and Waugh Ordnary Leas SquaresOLS 3 j τ = a0 a j m a4 log m a5c a6c a7 log C j= τ = a a a [ ] 0 m log m

4 [ a, b] f Pn E f = max f x P x = f P n ( ) ( ) n ( ) a x b n ξ 3

5 4 G F ξ ξ ξ = =, ( ) A ( ) ( ) ( ) k k k e A e A e A 3 3,, = = = ( ) O ξ < = 0 ( ) O ξ = ( ) 0 = f ξ ( ) ( ) ( ) 3 6 = f ξ ξ ξ ξ ξ ( ) ( ) G G FG F f ξ ξ ξ ξ = ( ) ( ) = 6 f ξ ξ ξ ξ ξ ξ ξ ( ) f n n = = ( ) ( ) ( ) ( ) ( ) = = n A A A A D α α α α ( ) ( ) ( ) ( ) ( ) = A A A O A 3 3 3

6 ( ) 0 lm D = D = lm D [ A, B] ( = 0, n) B k ( ) ξ,..., A = ξ < ξ <... < ξ = n B 0 ( ) ( ξ, ξ k ) B k ( ) B k ( ) ( ) D ' = D j= 0 ( ) ( ) l= 0, l j l j D = lm D ( ) ( ) = k k ξ ξ k k k B ( ) = [ max ( ξ j,0)] 5

7 [ A, B] ( = 0, n) ξ 0 n,,, n ξ,..., ξ ( = 3, n, n 3) [ B] ξ A, = { ( )} k n Φ φ k =~ α Dˆ = Φα S = CΦ C P = Sα ε α ( ) = α φ ( ) D k = n k k 6

8 h( ) k ( ) ( ) ( ) h, β = β kφk = φ β k= λ 0 λ h( ) λ λ λ mn GCV T h ( ) d RSS( λ) m n T ) ( p p ) λ h ( ) d = 0 ( λ, θ ) = RSS ( λ ) ( λ ) [ m θk ] 7

9 k ( λ) θ λ n d j ( m m ), j, Q d j = ml θ L L =,..., n j θ = L Q n( j ) L = [ ] Q m L ( ) z (, T ) 8

10 ( T ) Z (, T ) ( ) Z, τ τ τ f (, τ, T ) INST = lm f (, τ, T ) τ T ( T ) z, z (, T ) dsc f f = (, T ) (, τ, T ) = e = e 00 β0 β β τ β 0 f ( TTM ) β 0 T 365 (, T ) ( T ) Z [( T ) z(, T )] [( τ ) z(, τ )] T τ (,τ, T ) = z (, T ) ( T ) z f (, T ) = ( TTM ) INST = T x = β 0 f (, τ, T ) β T e INST TTM τ dx β (, T ) z TTM τ e TTM τ 9

11 β β ( TTM ) f β τ β β τ f ( TTM ) ( TTM ) 0 z z ( TTM ) 3.0%.5%.0%.5%.0% 0.5% 0.0% -0.5% = β 0 β τ TTM e TTM τ β τ TTM e TTM τ TTM τ z( TTM ) β f ( TTM ) = β 0 β e TTM τ β TTM τ e TTM τ

12 ( ) TTM f ( ) TTM z ( ) = 3 0 τ τ τ τ β τ β β β TTM TTM TTM e TTM e TTM e TTM f ( ) = 3 0 τ τ β τ τ β τ β β τ τ τ TTM e TTM TTM e TTM e TTM TTM z TTM TTM TTM

13 ( v / v max ) ( n / n max ) ( e ) ( e ) W = W v v max n n max

14 McCulloch Vascek & Fong Seeley McCulloch Vascek & Fong Seeley Smoohng Nelson & Segel Exend N & S Svensson 3

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24 n Mn ( ) w ˆ P P = Mn n = ( ˆ ) w P P = n j = D j D j D j 3

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37 5 6 = 5, 65 36

38 τ β { x } { x } λ λ λ λ T = [( ) ( )] x x x x λ 4 λ = 0 37

39 λ λ 38

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45 . Blss, R.R., 996, Tesng Term Srucure Esmaon Mehods, Federal Reserve Bank of Alana Workng Paper 96-a.. Bolder, D., Srelsk, D., 999, Yeld Curve Modelng a he Bank of Canada, Bank of Canada Techncal Repor No Bank of Inernaonal Selemen, 999, Zero-Coupon Yeld Curves: Techncal Documenaon. 4. Choudhry, M., 004, Analysng & Inerpreng he Yeld Curve, John Wley & SonsAsaPe. Ld. 5. Danel F. W., 997, Splne Mehods for Exracng Rae Curves from Coupon Bond Prces, Federal Reserve Bank of Alana Workng Paper Fsher, M., Nychka, D., and Zervos, D., 995, Fng he Term Srucure of Ineres Raes wh Smoohng Splnes, Workng Paper 95-, Fnance and Economcs Dscusson Seres, Federal Reserve Board. 7. McCulloch, J. H., 97, Measure he Term Srucure of Ineres Raes, Journal of Busness, p McCulloch, J. H., 975, The Tax-Adjused Yeld Curve, Journal of Fnance, Vol. 3, p Nelson, C. R., Segel, A. F., 987, Parsmonous Modelng of Yeld Curves, Journal of Busness, Vol. 60, p Seeley, J. M., 99, Esmang he Gl-Edged Term Srucure Bass Splne and Confdence, Journal of Busness Fnance and Accounng, Vol.8, p Subramanan, K. V., 00, Term Srucure Esmaon In Illqud Markes, Journal of Fxed Income, Vol., No., p Svensson, L. E. O., 994, Esmang and Inerpreng Forward Ineres Raes: 44

46 Sweden , NBER Workng Paper Seres Vascek, O., 977, An Equlbrum Characerzaon of he Term Srucure, Journal of Fnancal Economcs, Vol. 5, p Vascek, O., Fong, G., 98, Term Srucure Esmaon Usng Exponenal Splnes, Journal of Fnance, Vol.38, p Uned Kngdom Deb Managemen Offce, 000, The DMO s Yeld Curve Model. 6. Yu, I.W., Fung, L., 00, Esmaon of Zero-Coupon Yeld Curve Based on Exchange Fund Blls and Noes n Hong Kong, Hong Kong Moneary Auhory. 45

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