Valuation models

Contingent convertibles (AT1)

AT1 and tier 2 CoCos that convert into shares or are written down when a capital trigger (proxied by a share price) is hit, valued as a bond floor less down-and-in forwards on the shares at the conversion price and the coupons cancelled after a trigger or at the issuer's discretion; trigger probability, credit derivatives spread, implied share volatility from a price, delta and vega.

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Methodology

Conventions

  • The capital trigger is proxied by the share price falling to the trigger price.
  • Price = bond floor (coupons and face at the curve plus the senior spread) less the down-and-in forwards on the shares at the conversion price (or the written-down face) less the coupons lost after a trigger or cancelled.
  • AT1s are valued to the first call; the trigger probability is the continuous barrier hitting probability.

References

  • De Spiegeleer and Schoutens (2012)
  • Rubinstein and Reiner (1991)

Formulas

Hit probability
Φ((ln(S*/S) − νT)/σ√T) + (S*/S)^(2ν/σ²) Φ((ln(S*/S) + νT)/σ√T)
Credit derivatives spread
s = (1 − R) λ, λ = −ln(1 − p*)/T