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