《金融期货与期权》（英文版）Chapter 26 Credit risk

26.1 Chapter 26 Credit risk Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.1 Chapter 26 Credit Risk

26.2 Credit Ratings In the s&P rating system, AAA is the best rating. After that comes 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 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.2 Credit Ratings • In the S&P rating system, AAA is the best rating. After that comes 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

26.3 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 risk-neutral world Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.3 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 risk-neutral world

26,4 Typical Pattern (See Figure 26.1, page 611) Baa/BBB Spread over Treasuries A/A aa/aa aaa/aaa maturity Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.4 Typical Pattern (See Figure 26.1, page 611) Spread over Treasuries Maturity Baa/BBB A/A Aa/AA Aaa/AAA

26.5 The risk-free rate Most analysts use the LIBOR rate as the risk-free rate The excess of the value of a risk-free bond over a similar corporate bond equals the present value of the cost of defaults Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.5 The Risk-Free Rate • Most analysts use the LIBOR rate as the risk-free rate • The excess of the value of a risk-free bond over a similar corporate bond equals the present value of the cost of defaults

26.6 Example zero coupon rates; continuously compounded) Maturity Risk-free Corporate (years) yield bond yield 5 5.25% 5% 5.50% 5% 5.70% 4 5% 585% 5 5 5.95% Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.6 Example (Zero coupon rates; continuously compounded) Maturity (years) Risk-free yield Corporate bond yield 1 5% 5.25% 2 5% 5.50% 3 5% 5.70% 4 5% 5.85% 5 5% 5.95%

26.7 Example continued One-year risk-free bond(principal=$1)sells for 0.05×1 0.951229 One-year corporate bond(principal=$1) sells for 0.0525×1 =0948854 or at a.2497% discount This indicates that the holder of the corporate bond expects to lose 0.2497% from defaults in the first year Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.7 Example continued One-year risk-free bond (principal=$1) sells for One-year corporate bond (principal=$1) sells for or at a 0.2497% discount This indicates that the holder of the corporate bond expects to lose 0.2497% from defaults in the first year e −  = 0 05 1 0951229 . . e −  = 0 0525 1 0948854 .

268 Example continued Similarly the holder of the corporate bond expects to lose 0.05×20.0550×2 e =0009950 0.05×2 or 0. 9950% in the first two years Between years one and two the expected loss is 0.7453% Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.8 Example continued • Similarly the holder of the corporate bond expects to lose or 0.9950% in the first two years • Between years one and two the expected loss is 0.7453% e e e −  −  −  − = 0 05 2 0 0550 2 0 05 2 0 009950 . . .

26.9 Example continued Similarly the bond holder expects to lose 2.0781% in the first three years 3. 3428%in the first four years; 4.6390% in the first five years The expected losses per year in successive years are 0.2497% 0.7453%,1.0831%,1.2647%,and 1.2962% Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.9 Example continued • Similarly the bond holder expects to lose 2.0781% in the first three years; 3.3428% in the first four years; 4.6390% in the first five years • The expected losses per year in successive years are 0.2497%, 0.7453%, 1.0831%, 1.2647%, and 1.2962%

26.10 Summary of results (Table 26.1, page 612) Maturity Cumul LOss LOSS (years) % During Yr (%) 0.2497 0.2497 0.9950 0.7453 2345 2.0781 1.0831 3.3428 2647 4.6390 1.2962 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull

Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 26.10 Summary of Results (Table 26.1, page 612) Maturity (years) Cumul. Loss. % Loss During Yr (%) 1 0.2497 0.2497 2 0.9950 0.7453 3 2.0781 1.0831 4 3.3428 1.2647 5 4.6390 1.2962