LoanBook OAS Engine
The OAS Engine calculates the spread over the Treasury curve that accounts for the borrower's embedded prepayment option. A static spread prices one prepayment path; OAS prices the fact that prepayment behavior changes with interest rates. This makes OAS the institutional standard for relative value comparison across loans with different coupons, terms, and prepayment characteristics.
Methodology
The engine uses a one-factor Hull-White short-rate model fitted to a zero curve bootstrapped from current Treasury par yields. On each simulated rate path the prepayment model sets the speed for that path: faster when rates fall (more refinancing incentive), slower when rates rise. Credit losses on Residential loans also respond to each path through the default and severity models.
For each simulated rate path: 1. Project monthly cashflows through LoanBook's canonical cashflow engine, with the path's prepayment and default speeds 2. Discount the cashflows using the simulated short rates plus the trial OAS 3. Calculate the present value of all cashflows on this path
The OAS is the constant spread that makes the average present value across all paths equal to the market price.
The Z-Spread reported with the OAS is solved on the same Hull-White run at the path-mean prepayment speed, so the two reconcile by construction. Option Cost is the larger of Z-Spread minus OAS and zero, and Credit Cost (CDR times loss severity) is subtracted from OAS to give COAS.
Rate-insensitive assets show an Option Cost near zero, which is the correct result: a lease curtails at the same speed on every path, and a floater that resets within 12 months reprices its coupon. Fixed-rate commercial real estate with no rate reset takes its payoff date from the CRE Payoff Model on every path, so a long loan can carry a real Option Cost.
Key Parameters
| Parameter | Value |
|---|---|
| Mean Reversion Speed (a) | 0.10 (10%) |
| Volatility (σ) | 0.01 (100bp annualized) |
| Monte Carlo Paths | 200 in production pricing |
| Time Steps | 360 (monthly for 30 years) |
| Rate Shock Range | -300bp to +300bp (7 scenarios) |
Inputs
Loan cashflow parametersBalance, note rate, remaining term, servicing fee, loan agePrepayment assumptionCPR, or model-derived from the LoanBook Prepay ModelDefault assumptionCDR and loss severity, or model-derivedMarket pricePurchase price as percentage of parTreasury curveCurrent Treasury par yields, bootstrapped to a zero curve (auto-fetched)Outputs
OASOption-Adjusted Spread in basis pointsZ-SpreadSpread solved on the same Hull-White run at the path-mean prepayment speed, in basis pointsOption CostThe larger of Z-Spread minus OAS and zero: the value of the prepayment optionCredit Cost and COASCDR times loss severity in basis points, and OAS net of itEffective DurationPrice sensitivity to rate changesEffective ConvexityChange in duration for rate changesCalibration
Hull-White parameters (mean reversion speed a = 0.10, volatility σ = 0.01) are set in the model configuration. The zero curve is bootstrapped from the current Treasury par curve on every run.
References
- Hull, J. & White, A. (1990). "Pricing Interest-Rate-Derivative Securities." Review of Financial Studies.
- Fabozzi, F. (2006). "Fixed Income Mathematics." McGraw-Hill.
- Tuckman, B. & Serrat, A. (2011). "Fixed Income Securities." Wiley.
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