1-2 1 path dependence pathwise analysis forward pathwise node A B C D E F A B D A B E A C E A C F 2 3 A B C 1-3 1
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1 reference rate pure floater risk free pure floater An Exposition on Pricing and Spread Analysis of Floaters - DI: - - Fax: Kenichi.Tatsumi@gakushuin.ac.jp
2 1-2 1 path dependence pathwise analysis forward pathwise node A B C D E F A B D A B E A C E A C F 2 3 A B C 1-3 1
3 r0 r1 r2 r3 r0 `_ 1+ r0i_ 1+ r1ij / `_ 1+ r0i_ 1+ r1i_ 1+ r2ij -1R0=_ 1 + r0i R1= _ 1+ r0i_ 1+ r1i R2= _ 1+ r0i_ 1+ r1i_ 1+ r2i R3= _ 1+ r0i_ 1+ r1i_ 1+ r2i_ 1+ r3i 12 / R0 R1e R1e - R2e 2 R2 R2e -2 R3e 3 R3e R3e - R3e -3 e v e - v av e, 1 + av vr vr r0 r1e r1e - r2e 2 r2 r2e -2 r3e 3 r3e r3e - r3e -3 v v v a e v, 1 + av Re 2 v - R - R - Re 2 v v - Re - Re v 3 Re v - Re v Re 4v R 2 - v 2vR
4 2 quoted margin 3 range note IAN indexed amortization note Fabozzi-Mann [P.]index duration callable capped floater
5 2 OAS 3 ratchet bond callable capped floater IAN 2 simple margin spread for lifeadjusted simple marginadjusted total margin OAS option adjusted spread 2-1
6 w 1 w = # + _ - i w 2-2 adjusted simple margin quoted margin q P 1 simple margin, spread for life P q 100 _ Pi = * + q4 100 P P q 2 P adjusted price $ C # 100 -_ P + AI ir. ~ = P - # 1 + ~ # R- C = AI = r = ~ = R = 2-3 adjusted total margin
7 100 _ i = + q R 100 * _ i 4 Fabozzi-Mann [ ] 2-4 discounted margin 3 OAS 3-1 OAS OAS option adjusted spread OAS OAS OAS MBS MBS 3-2 OAS OAS OAS OAS 1 burnout 2 OAS OAS
8 OAS 3 OAS C ij P OAS i j N n C ij rij OAS s N n P 1 C ij = N!! _ 1 + rij + s i i = 1 j = OAS 1 OAS OAS OAS OAS rij OAS Bartlett [ ] OAS 2 OAS OAS
9 OAS 3 OAS OAS 3-3 OAS OAS Davidson-Sanders-Wolff-Ching [ ] istatic spread ii zero spread zero volatility spread iii forward spread iv OAS 1 Fabozzi-Ramsey [ ]
10 nominal spread rij 2 Davidson-Sanders-Wolff-Ching [p.] Fabozzi-Ramsey [p.] Davidson-Sanders-Wolff-Ching [ p.]forward cost OAS Fabozzi-Ramsey [ ] OAS Davidson-Sanders-Wolff-Ching [ ] OAS 3-4 OAS 1 OAS Fabozzi-Mann [P.] spread duration = OAS - OAS 2 # # OAS OAS
![]forward cost 3-3-2 OAS Fabozzi-Ramsey [ ] OAS](/docs-images/42/22975743/images/page_10.jpg "Davidson-Sanders-Wolff-Ching [ ] OAS 3-4 OAS 1 OAS Fabozzi-Mann [P.")
11 2 3 OAS OAS Fabozzi-Mann [P.] OAS OAS OAS OAS
12 default risk duration VaR Bierwag-Kaufman Chance Kaufold-Smirlock -1-2
13 Merton, R. 2 Longstaff-SchwartzT Leland-ToftT,p. T recovery rate recovery rate
14 -2-1 V VB exhaustv B = 0 T LelandT T r Z1 Z 2 dv = nvdt + vvdz 1 dr = `p - br jdt + hdz 2 n v p b h dz1 dz 2 tdt Vasicek T r dv = ` n_ V, t i - dj Vdt + vvdz1 n _ Vt, i V d V Kim- Ramaswamy-SundaresanT dv = ` n_ V, t i - dj Vdt + vvdz1 CIR Cox-Ingersoll-Ross / dr = `p - br jdt + hr 12 dz 2 DasT V HJM Heath-Jarrow-Morton dv = nvdt +v VdZ + v VdZ df = pdt + hdz1 f Longstaff- Schwartz T, p. T, p. V VB Leland-Toft T, p.
15 Brennan-Schwartz H _ V, r, Ti T V r T `v / 2jV H + tvhvh + ` h / 2j H + rvh + _ a - br i H - rh = H vv Vr rr V r T a p f _ s; V, VBi VB f _ s; V, VBi F _ s; V, VBi N - 2 F() t = N( h1 ()) t + ( V/ VB ) N( h2 ()) t h1 () t = (- b - av t) vt / h2 () t = (- b + av t) vt / a = ( r - d - ( v / 2))/ v 2 2 b = Ln( V/ VB ) f _ s; V, VBi s f _ s; V, VBi r 71 - F(; s V, VB ) A s s c s c71 - F(; s V, VB ) A s 71 - F( T; V, VB ) A V B T 2-2 credit sensitive notes, spread adjusted notes credit derivatives Jarrow-Lando-TurnbullT Jarrow-TurnbullT K- absorbing
16 t i t + 1 j qij (, t t + 1) qij t i r i () t q (, t t + 1) = r () t q ij i ij T K T 1 - qik (, t T) T T T T qij r i ( 0) r i () 1 r i ( 2) pp.- [ ]Bartlett, W. W., The Valuation of Mortgage-Backed Securites, Irwin,. [ ]Bierwag, G. O. and Kaufman, G. G., "Durations of Non-Default-Free Securities", Financial Analysts Journal, July/August,, pp.-. [ ]Chance,D.M., "Floating rate notes and immunization", Journal of Financial and Quantitative Analysis,,, pp.-. [ ]Chance,D.M., "Default Risk and the Duration of Zero Coupon Bonds", Journal of Finance, XLV,, pp.-. [ ]Davidson, A., Sanders, A., Wolff, L-L. and Ching, A., Securitization, Wiley,. [ ]Fabozzi, F. J. and Ramsey, C., Collateralized Mortgage Obligation, Fank J. Fabozzi Associates,. [ ]Fabozzi, F.J. and Mann, S. V., Floating-Rate Securities, Frank J. Fabozzi Associates,. [ ]Kaufold, H. and Smirlock, M., "The Impact of Credit Risk on the Pricing and Duration of Floatingrate Notes", Journal of Banking and Finance,,, pp.-. [ ]Livingston, M., Bonds and Bond Derivatives, Blackwell,. []
![-. [ ]Chance,D.M., "Default Risk and the Duration of Zero Coupon Bonds", Journal of Finance, XLV,, pp.-. [ ]Davidson, A., Sanders, A., Wolff, L-L. and Ching, A., Securitization, Wiley,. [ ]Fabozzi, F.](/docs-images/42/22975743/images/page_16.jpg "J. and Ramsey, C., Collateralized Mortgage Obligation, Fank J. Fabozzi Associates,. [ ]Fabozzi, F.J. and Mann, S. V., Floating-Rate Securities, Frank J. Fabozzi Associates,. [ ]Kaufold, H.")
IMES DISCUSSION PAPER SERIES Discussion Paper No. 99-J- 9 -J-19 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN
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橡災害.PDF
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