27.11 CDS Rate continued When default can happen at any time this becomes T q(o()+()]+x(T) Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 27.11 CDS Rate continued When default can happen at any time this becomes ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 T 1 垐 T q t v t R A t R dt s q t u t e t dt u T − − = + +
27.12 Approximate CDs Spread y be the yield on bond issued by reference entity with maturity T x be the yield on risk-free bond with maturity t a be average value of A(t) a* be average value for A(t)if reference bond is a par-yield bond with maturity T y x)1-kiaR S≈ 1-R(1+a* Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 27.12 Approximate CDS Spread • Let – y be the yield on bond issued by reference entity with maturity T – x be the yield on risk-free bond with maturity T – a be average value of A(t) – a* be average value for A(t) if reference bond is a par-yield bond with maturity T ( ) ( )( ) 1 垐 ˆ 1 1 * y x R aR s R a − − − − +
27.13 Alternative uses of the formula To calculate CDs spreads from the probabilities of default and expected recovery rate To bootstrap the probabilities of default from Cds spreads and expected recovery rates Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 27.13 Alternative Uses of the Formula • To calculate CDS spreads from the probabilities of default and expected recovery rate • To bootstrap the probabilities of default from CDS spreads and expected recovery rates
27.14 Sensitivity to Recovery rate Vanilla cds is not very sensitive to the recovery rate providing the same recovery rate is used to estimate default probabilities and calculate payoffs Binary swaps, which provide a fixed payoff in the event of a default, are much more sensitive to recovery rates Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 27.14 Sensitivity to Recovery Rate • Vanilla CDS is not very sensitive to the recovery rate providing the same recovery rate is used to estimate default probabilities and calculate payoffs • Binary swaps, which provide a fixed payoff in the event of a default, are much more sensitive to recovery rates
27.15 First-to-default swaps Similar to a reqular cds Several reference entities and reference bonds First entity to default triggers a payoff Settlement is same as ordinary CDs Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 27.15 First-to-default swaps • Similar to a regular CDS • Several reference entities and reference bonds • First entity to default triggers a payoff • Settlement is same as ordinary CDS