Valuation models

Loans

Term loans with bullet, linear, level or scheduled amortization and voluntary prepayments, revolvers with drawn interest and commitment fees on the undrawn, floating at the forward plus a margin with an index floor, the discount margin solved from a price, average life, PV01 and CS01.

Inputs

CurrencyOutstandingMaturity inyMargin over the index%PaidPrepayments% a yearPriceDiscount curveDiscount curve: flat rate% cc

Floor on the indexSolve the discount margin from a price

Results

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Methodology

Conventions

Interest on the outstanding at a fixed rate, or the curve's forward (floored) plus a margin; a revolver also pays a fee on the undrawn amount.
Contractual amortization (bullet, linear, level or a schedule) scaled down by voluntary prepayments at a constant annual rate.
Discounted on the curve plus the discount margin, which a price solves for.

References

Taylor and Sansone, The Handbook of Loan Syndications and Trading

Formulas

Value: V = Σ (Iᵢ + Fᵢ + Aᵢ + PPᵢ) P(tᵢ) e^(−s tᵢ)
Prepayment: p = 1 − (1 − c)^(1/f)
Fee: Fᵢ = f (C − D) τᵢ