Valuation models

Single-name CDS options

Knock-out payers and receivers on the forward CDS off the name's credit curve, by Black on the forward spread or by a CIR++ stochastic default intensity fitted exactly to the curve and simulated to expiry, with the implied Black vol, CS01, vega and the payoff at expiry.

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Methodology

Conventions

  • Single-name options knock out if the name defaults before expiry: both forward legs carry survival to expiry.
  • Black: lognormal forward spread. CIR++: a CIR intensity plus a shift that fits the credit curve exactly, simulated to expiry.

References

  • O'Kane, Modelling Single-name and Multi-name Credit Derivatives, ch. 9
  • Brigo and Mercurio, Interest Rate Models, ch. 22

Formulas

Forward spread
F = PV_prot(tₑ, T) / RPV01(tₑ, T)
Payer (Black)
V = N RPV01 [F N(d₁) − K N(d₂)]
CIR++
λ = x + φ(t), dx = κ(θ − x)dt + σ√x dW