Valuation models

Credit-linked notes, asset swaps and bond TRS

Notes that carry a reference entity's (and the issuer's) default, par and market asset swap spreads against the z-spread, and bond TRS with default ending the swap, fair funding spread, PV01 and CS01.

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Methodology

Conventions

  • Credit-linked notes pay while the reference (and the issuer) survive, and the recovery on default.
  • Asset swaps: par packages cost 100 with floating on face; market packages cost the price with floating on it.
  • Bond TRS: the receiver gets coupons and price change, pays floating plus a spread; default ends the swap.

References

  • O'Kane, Modelling Single-name and Multi-name Credit Derivatives, ch. 11 and 12
  • Schönbucher, Credit Derivatives Pricing Models

Formulas

CLN
P = 100 [Σ cⱼ τⱼ D Q + D(T)Q(T) + ∫ R D (−dQ)]
Par ASW
s = (P_rf − P_dirty) / (100 A)
TRS fair spread
s* = (TR − P₀ Σ fⱼ τⱼ D Q) / (P₀ Σ τⱼ D Q)