Exchangeables and equity-linked default

Crank-Nicolson in the share price with a default hazard, constant for an exchangeable into another company's shares or rising as the share falls (Andersen-Buffum) with the shares jumping to zero on default; conversion at any time, issuer calls and holder puts; bond floor, parity, premium, delta, vega, CS01 and the issuer spread implied by a price.

Inputs

Default model

Notional

Maturity

Coupon%

Paid

Conversion price

Share price

Share vol%

Dividend yield%

Issuer spread%

Recovery%

Hazard exponent p

Callable from

Call price

Put date

Put price

CurrencyCurve

Curve: flat rate% cc

Results

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Methodology

Conventions

Crank-Nicolson in the log share price with a default hazard; the holder converts at any time.
Andersen-Buffum: hazard λ(S) = λ₀ (S₀/S)^p, and the shares jump to zero on default (a convertible into the issuer's own shares).
Exchangeable: a constant issuer hazard; the shares do not jump on the issuer's default.
On default the holder recovers the recovery rate of face; calls and puts bound the value.

References

Andersen and Buffum (2003)
Ayache, Forsyth and Vetzal (2003)

Formulas

PDE: V_t + (r − q + ηλ)S V_S + ½σ²S² V_SS − (r + λ)V + λRN = 0