Valuation models

Index amortizing swaps

Notional amortized by a rate table at each reset after a lockout, with a clean-up, by Monte Carlo on a Hull-White model fitted to the curve. Value against the bullet swap, par rate, expected notional and average life, PV01 and vega.

Inputs

CurrencyNotionalMaturity inyFixed rate%Resets and paymentsLockoutyClean-up below%Hull-White volbpMean reversion%PathsCurveCurve: flat rate% cc

Amortization table, one per line: floating rate, share of the outstanding repaid at that rateFixed rate at par

Results

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Methodology

Conventions

Hull-White short-rate paths fitted to the curve, antithetic, with every reset and payment date on the grid.
At each reset after the lockout the notional falls by the table's share of what is outstanding, read against the period's fixing (linear between levels, flat beyond); below the clean-up the rest is retired.
Both legs pay on the outstanding notional; risk reuses the same paths.

References

Hull, Options, Futures, and Other Derivatives
Brigo and Mercurio, Interest Rate Models

Formulas

Notional: Nᵢ = Nᵢ₋₁ (1 − s(Lᵢ))
Value: V = E[Σ D(tᵢ₊₁) Nᵢ τᵢ (K − Lᵢ)] (receiver)