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Fixed Income Securities, 4th Edition
book

Fixed Income Securities, 4th Edition

by Bruce Tuckman, Angel Serrat
September 2022
Beginner content levelBeginner
560 pages
17h 36m
English
Wiley
Content preview from Fixed Income Securities, 4th Edition

APPENDIX TO CHAPTER 14Corporate Debt and Credit Default Swaps

A14.1 CUMULATIVE DEFAULT AND SURVIVAL RATES

Proposition: If the hazard rate is constant at normal lamda, then the cumulative survival probability to time t, upper C upper S left-parenthesis t right-parenthesis, is e Superscript minus normal lamda t, and the cumulative default probability, upper C upper D left-parenthesis t right-parenthesis, is 1 minus e Superscript minus normal lamda t.

Proof: The probability of no default to time t plus normal upper Delta t, upper C upper S left-parenthesis t plus normal upper Delta t right-parenthesis, is the probability that there is no default to time t and no default from then to time t plus normal upper Delta t. Mathematically,

(A14.1)

Taking the limit of the right‐hand side of (A14.2) as approaches zero ...

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