Valuation models

Contingent CDS, risk participations and recovery swaps

Contingent CDS and risk participation agreements on an interest rate swap, the exposure at each date a European swaption on the rest of the swap, weighted by default probabilities into the CVA, with the fair fee and exposure profile; and recovery swaps that lock in a recovery rate.

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Methodology

Conventions

  • The loss on the counterparty's default is the swap's positive value then: a European swaption on the rest of the swap.
  • The protection is a strip of those swaptions weighted by default probabilities: the CVA.
  • A recovery swap exchanges a fixed recovery for the realised one on default.

References

  • Gregory, The xVA Challenge
  • O'Kane, Modelling Single-name and Multi-name Credit Derivatives, ch. 6 and 10

Formulas

Exposure
EPE(t) = N A(t) [(K − F)Φ(d) + σ√t φ(d)]
Protection
PV = π (1 − R) Σ EPE(tₖ) [Q(tₖ₋₁) − Q(tₖ)]
Recovery swap
V = N (R_lock − E[R]) ∫ D (−dQ)