LoanBook Prepay Model
The Prepay Model calculates the expected Conditional Prepayment Rate (CPR) for loans in all five sectors: Residential, Consumer, Commercial, Government and Lease. Prepayment speed is the single most important variable in whole loan pricing. It determines WAL, BEY, and the amortization of any purchase premium or discount.
Methodology
The model routes each loan to the method for its sector and loan type:
Residential: S-curve refinancing model (Richard & Roll) with two-population burnout (Schwartz & Torous), plus a separate turnover channel for home sales. The S-curve captures the relationship between the borrower's rate incentive (note rate vs. market rate) and prepayment probability. The seasoning ramp applies to the turnover channel only, and a rate lock-in effect slows turnover when market rates are above the borrower's note rate.
Consumer: A refinance S-curve scaled by loan type, plus loan-type turnover. Refinance ability depends on the borrower's credit. HELOC speeds follow the draw and repayment phases.
Auto: ABS-style methodology with lender segmentation (captive finance, bank, credit union, subprime).
Commercial: A fixed-rate commercial real estate loan with no rate reset takes its payoff date from the CRE Payoff Model: the first month in which its probability of still being outstanding falls to 50%, from observed SBA 504 first-lien payoff experience by prepayment protection, loan age and refinance incentive, capped at balloon or maturity. No payoff is projected while yield maintenance, defeasance or a lockout is in force. A loan with a rate reset is priced to its first reset.
Government: Guaranteed portions use the SBA calibrations described in the SBA 7(a) and 504 models. A default on the guaranteed portion is paid at par, so it arrives as involuntary prepayment.
Lease: A lessee who pays off early owes the remaining payment stream less the contract's early payoff discount, so the payoff is a curtailment. Leases curtail at a flat 2.66% CPR, with no rate sensitivity.
Residential and consumer speeds carry multipliers for credit, collateral, seasoning, seasonality and geography. A missing FICO, LTV or DTI makes no adjustment; the model never fills in an assumed value.
Key Parameters
| Parameter | Value |
|---|---|
| CPR Bounds (Residential) | Floor 3%, Cap 65% |
| Residential turnover base | 4.98% annual |
| CRE payoff date | First month survival falls to 50%, capped at balloon or maturity |
| Lease curtailment speed | 2.66% CPR, flat, rate-insensitive |
Inputs
note_rateGross coupon rate (decimal)current_balanceOutstanding principal balanceloan_age_monthsMonths since originationoriginal_ficoFICO score at originationcurrent_ltvCurrent loan-to-value ratiomarket_refi_rateCurrent market refinancing rate for comparable loanloan_sectorResidential, Consumer, Commercial, Government, or LeaseOutputs
cpr_annualAnnualized Conditional Prepayment RatesmmSingle Monthly Mortality (monthly prepay rate)componentsBreakdown by refinance, turnover, burnout, seasoning and multiplierscpr_vectorMonthly CPR projection over remaining lifeCalibration
Residential is calibrated from Fannie Mae Single-Family Loan Performance Data at the loan level, with the turnover level fit jointly to a normal housing market (2016-2019) and a locked-in one (2023-2025). Commercial payoff dates are calibrated from SBA 504 third-party first-lien payoff experience in the FOIA data. Government speeds come from SBA FOIA loan records. The lease speed comes from the lease program's observed early payoffs.
References
- Richard, S. & Roll, R. (1989). "Prepayments on Fixed-Rate Mortgage-Backed Securities." Journal of Portfolio Management.
- Schwartz, E. & Torous, W. (1989). "Prepayment and the Valuation of Mortgage-Backed Securities." Journal of Finance.
- Kalotay, A. et al. (2004). "An Option-Theoretic Prepayment Model for Mortgages." International Journal of Theoretical and Applied Finance.
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