【正文】 Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Chapter 26 Credit Risk Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Credit Ratings ? In the Samp。P rating system, AAA is the best rating. After that es AA, A, BBB, BB, B, and CCC ? The corresponding Moody’s ratings are Aaa, Aa, A, Baa, Ba, B, and Caa ? Bonds with ratings of BBB (or Baa) and above are considered to be “investment grade” Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Information from Bond Prices ? Traders regularly estimate the zero curves for bonds with different credit ratings ? This allows them to estimate probabilities of default in a riskneutral world Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Typical Pattern (See Figure , page 611) Spread over Treasuries Maturity Baa/BBB A/A Aa/AA Aaa/AAA Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull The RiskFree Rate ? Most analysts use the LIBOR rate as the riskfree rate ? The excess of the value of a riskfree bond over a similar corporate bond equals the present value of the cost of defaults Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Example (Zero coupon rates。 continuously pounded) M a tu r ity( y e a r s)Ri sk f r e ey ieldCorpo r a teb o n d y ield1 5% 5 .2 5 %2 5% 5 .5 0 %3 5% 5 .7 0 %4 5% 5 .8 5 %5 5% 5 .9 5 %Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Example continued Oneyear riskfree bond (principal=$1) sells for Oneyear corporate bond (principal=$1) sells for or at a % discount This indicates that the holder of the corporate bond expects to lose % from defaults in the first year e ? ? ?0 05 1 0 951229. .e ? ? ?0 0525 1 0 948854. .Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Example continued ? Similarly the holder of the corporate bond expects to lose or % in the first two years ? Between years one and two the expected loss is % e ee? ? ? ?? ?? ?0 05 2 0 0550 20 05 2 0 009950. .. .Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Example continued ? Similarly the bond holder expects to lose % in the first three years。 % in the first four years。 % in the first five years ? The expected losses per year in successive years are %, %, %, %, and % Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Summary of Results (Table , page 612) Ma turity (ye ars ) Cu mu l. Lo ss . % Loss Du ring Y r ( %) 1 0. 24 97 0. 24 97 2 0. 99 50 0. 74 53 3 2. 07 81 1. 08 31 4 3. 34 28 1. 26 47 5 4. 63 90 1. 29 62 Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Recovery Rates (Table , page 614. Source: Moody’s Investor’s Service, 20xx) Cla s s Me an (%) SD (%) Seni or Secured Seni or Unsecured Seni or Subo rdinated Subo rdinated 8 Junio r Subo rdinated Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Probability of Default 0 . 0 2 5 9 2 4 a n d 0 . 0 2 5 2 9 4 , 0 . 0 2 1 6 6 2 , 0 . 0 1 4 9 0 6 ,0 . 0 0 4 9 9 4 , a r e 5 a n d 4, , 3 2, 1, ye a r sin d e f a u l t of i e sp r o b a b i l i t e x a m p l e , o u r in 0 . 5R a t eR e c IfR a t e R e L o ss% E x p .D e f of P r o bL o ss% E x p . R a t e ) R e (1 D e f . of P r o b .????Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Reason Why This Analysis is Simplistic ? Bonds are assumed to be zerocoupon ? The equation: Prob. of Def. (1Rec. Rate)=Exp Loss% assumes that the claim in the event of default equals the nodefault value of the bond Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull A More Complete Analysis: Definitions Bj: Pric e today of b ond m at urin g at tjGj: Pric e today of b ond m at urin g at tj i f there we re noproba bili ty of defa ultFj( t ): Fo r ward pri ce a t ti m e t of Gj ( t tj)v ( t ): PV of $1 re ce ive d at t im e t with ce rt ai ntyCj( t ): Cla im ma de i f t here is a def ault a t tim e t tjRj( t ): Rec ov er y ra te i n the eve nt of a def a ult at t ime t tj?ij: PV of l oss fr om a def ault a t tim e t i rela ti ve t o G jpi: The ri skneu tr al pro babil it y of defa ult at t im e tiOptions, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull RiskNeutral Probability of Default Page 616, equations to ? PV of loss from default ? Reduction in bond