Six option-style teaching estimates — and an illustrative residual diagnostic.
A credit's quoted spread is one blended number. The engine maps selected covenant and credit terms into payoff lines, applies a stated teaching estimate to each line, then compares the total with the quoted-spread input. It does not produce a market price or legal conclusion.
What this is — and is not
Every claim uses one of three labels. Development stages such as parametric, state-path or mark-constrained describe implementation inside a label; they are not extra valuation labels.
The engine never touches market data. The quoted spread is an input you supply. That is deliberate: it keeps this an analytics and teaching instrument, not a pricing service.
Inputs: paths and terms
Two things go in. State paths — a set of scenarios for the credit over its life, each a sequence of dated points carrying EBITDA, net debt, leverage, enterprise value, cumulative net income and free cash flow. And the selected payoff assumptions — the make-whole spread and non-call schedule, builder percentage, covenant level, ECF trigger, portability threshold and quoted spread. The corporate model is the path generator; this engine applies the teaching estimate. It does not parse or interpret an agreement.
The annualisation convention
The current decomposition uses a teaching annualisation shortcut:
A production spread-equivalent conversion instead requires the risky premium-leg denominator:
RiskyPV01 changes the denominator only; it does not upgrade the numerator's evidence label. The shortcut is one reason every current output remains a teaching estimate.
The six lines
| Line | What it represents | How it is estimated |
|---|---|---|
| Merton credit-risk put | Put-like default exposure below the debt face. | Expected discounted shortfall of enterprise value below the debt face at the horizon, across paths; cross-checked against the closed-form Black-Scholes put on the initial enterprise value. |
| Builder basket | A path-dependent call the sponsor holds on cumulative retained earnings — capacity to leak value out. | Expected discounted leakage capacity. Reported as an upper bound; see the bracket below. |
| Equity cure | The sponsor's right to inject equity and cure a covenant breach — a knock-in that costs the lender its remedy. | PV-weighted breach quarters (leverage above the maintenance covenant) × the lender's remedy per breach. |
| ECF cash sweep | A lender-held strip: mandatory paydown of a share of free cash flow above a leverage trigger. It reduces the lender's required spread. | Expected discounted swept cash above the trigger, scaled to the lender's benefit. Enters the total with a negative sign. |
| Make-whole call | The borrower's right to refinance early — an American call on the loan's value. | A Cox-Ross-Rubinstein binomial American-call lattice on loan value at the loan-value volatility, net of the make-whole offset. |
| Portability | The right for debt to survive a change of control without triggering the put — a knock-out. | Probability of a change of control × the chance leverage sits at or below the portability threshold × the change-of-control put value. The gate is at/below opening leverage. |
The builder bracket
The builder basket is almost always the dominant line, and its size depends on how you model the sponsor's extraction. So the engine never reports one builder number. It reports a bracket of three:
- Terminal capacity — the full discounted capacity at the horizon. This is the upper bound: it assumes the sponsor could extract the whole basket at the end.
- Leverage-gated accrual — capacity that accrues only in periods when leverage sits at or below a dividend gate. Lower, and closer to how the basket is actually reachable.
- Arithmetic-Asian / uniform extraction — the average capacity over the life, a lower bound representing steady extraction.
Under the current illustrative inputs, the residual stays negative across the bracket. That is a sensitivity result from this path set and these assumptions, not a conclusion about traded relative value.
The residual
Sum the six signed teaching estimates and set the total next to the quoted-spread input:
A negative residual means the teaching estimate exceeds the quoted-spread input under the selected assumptions; a positive residual is the mirror. Neither sign is an investment recommendation, legal conclusion or relative-value claim.
Re-weighting to supplied targets
The optional layer finds the minimum-relative-entropy re-weighting of the uploaded paths that reproduces selected target moments, then re-runs the six teaching estimates. It asks whether the residual diagnostic changes when the path weights are forced to match those targets.
The technique is weighted Monte Carlo: among all path weightings that hit the targets, choose the one closest to the equal-weight prior. Matching moments is not enough to establish an arbitrage-free risk-neutral measure.
Three targets ship in v1: a forward moment, a default probability, and an asset / EV volatility. Diagnostics include effective sample size, relative entropy and target residuals. The engine does not verify whether an input is market-implied, historical or a management assumption.
The re-weighted output remains a teaching estimate. A calibrated risk-neutral price requires instrument-backed calibration, an arbitrage-consistent measure, contract-specific cash flows and exercise, survival/recovery consistency, and RiskyPV01 conversion.
Limits and model risk
This is a teaching estimate, and the bounds ship with the output. Every Monte Carlo line carries a standard error. The builder line carries its bracket. The whole decomposition carries a volatility-band strip. The engine does not calibrate to market instruments, establish a risk-neutral measure, read a document, parse a covenant stack or determine contract-specific availability. It applies simplified option-style arithmetic to the paths and terms you give it.