Mortgage Prepayment Risk for Quants

Mortgage prepayment risk is the borrower’s embedded option to refinance, sell, or otherwise repay principal early, which makes mortgage-backed security cash flows path-dependent and rate-sensitive. Unlike a bullet bond, an MBS does not have a fixed maturity cash-flow schedule.

From pool to cash flows

The scheduled balance amortizes; prepayments accelerate its decline. Conditional prepayment rate (CPR) is annualized, while single monthly mortality (SMM) is the monthly fraction of remaining balance prepaid:

SMM = 1 - (1 - CPR)^(1/12)
prepayment_t = SMM_t * balance_after_scheduled_principal

def smm_from_cpr(cpr):
    return 1 - (1 - cpr) ** (1 / 12)

def prepay_cashflow(balance, scheduled_principal, cpr):
    smm = smm_from_cpr(cpr)
    remaining = balance - scheduled_principal
    prepaid = remaining * smm
    return scheduled_principal + prepaid, remaining - prepaid

CPR is a behavioral outcome, not a constant. It depends on refinance incentive, seasoning, burnout, turnover, loan size, geography, credit profile, servicing, and macro conditions.

Negative convexity

When rates fall, refinancing speeds up: principal returns when reinvestment yields are low, shortening duration. When rates rise, prepayments slow: low coupons remain outstanding, extending duration. This adverse asymmetry produces negative effective convexity.

Rate move	Typical prepayment effect	MBS consequence
rates down	faster refinance	contraction, capped upside
rates up	slower refinance	extension, larger duration
volatility up	option more valuable	lower MBS price

Effective duration must reprice cash flows under shocked curves and re-estimated prepayment behavior. Static cash-flow duration is not meaningful risk.

OAS valuation

Option-adjusted spread is the constant spread added to simulated discount rates that equates model PV to market price:

Price_market = E_paths[Σ CF_t(path) exp(-∫(r_path + OAS)dt)]

OAS is only comparable under a shared rate model, volatility surface, prepayment model, and assumptions. A wider OAS may signal cheapness, but may also compensate for unmodeled liquidity or a model that predicts implausibly slow prepayments.

Model validation and hedging

Validate forecast speeds by vintage, coupon, geography, and rate regime, not just aggregate RMSE. Backtest cash-flow distributions and extension tails. Hedge aggregate duration with swaps or Treasuries, then hedge convexity and volatility sensitivity where instruments permit. Dynamic hedging can amplify market moves when many investors extend together.

Prepayment risk is a concentration risk: a portfolio diversified by issuer may still share the same refinance incentive. Correlation estimates should be robust and regime-aware; covariance shrinkage is a useful baseline, but it cannot substitute for scenario design.

Key takeaways

• MBS cash flows depend on borrower behavior and interest-rate paths.
• Falling rates cause contraction; rising rates cause extension and negative convexity.
• OAS is model-dependent; validate speeds and stress hedges under discontinuous behavior.

Building a usable prepayment model

Start with loan-level or cohort-level data, then aggregate only after estimating heterogeneity. Refinance incentive should compare borrower mortgage rate with an available refinance rate after fees, credit constraints, and servicing frictions—not a generic Treasury yield. Include seasoning because newly originated loans do not prepay like seasoned pools, and burnout because borrowers who failed to refinance in prior rallies may be less responsive later.

The model should produce a distribution of cash flows across rate paths. Test calibration not only against average CPR but against tails: the 90th percentile speed in a refinancing wave and the slowest extension paths in a sell-off are economically important. Segment errors by coupon and vintage; aggregate accuracy can hide severe errors in the premium pools that drive portfolio convexity.

Trading and risk limits

Compare OAS across securities only after controlling for collateral, coupon, vintage, prepayment model, and liquidity. A “cheap” security with unusually uncertain speeds may deserve the wider spread. Limit extension exposure by scenario duration rather than current effective duration alone, and include specified-pool pay-ups, dealer liquidity, and hedge slippage in return forecasts.

Mortgage convexity hedging has feedback risk. In a rate sell-off, mortgage investors may receive fixed in swaps or sell duration to offset extension, reinforcing the move. Stress both portfolio P&L and the liquidity of the instruments used to hedge it.