Prepayment Risk: How Borrower Optionality Reshapes Your Cashflows

A fixed-rate mortgage is not just a loan — it's a loan with an embedded call option. The borrower has the right, but not the obligation, to repay early. When rates drop, that option moves into the money, and borrowers refinance. The bank loses its above-market coupon and must reinvest at lower rates. This is prepayment risk, and for banks with significant mortgage portfolios, it can dominate the IRRBB picture.

The Embedded Option

When a bank originates a 30-year fixed-rate mortgage at 5.5%, it expects to receive that coupon for 30 years. But the borrower can prepay at any time — typically at par, with no penalty (in the US market). This is economically equivalent to the bank being short a call option on a bond.

The option has value to the borrower when current market rates are below the coupon rate. The difference — coupon minus current rate — is called the refinancing incentive:

The bank's problem: when prepayment occurs, it receives par (the principal is repaid) but loses the future stream of above-market coupons. It must reinvest the proceeds at the new, lower market rate. This is the essence of prepayment risk: the bank is forced to reinvest at the worst possible time.

Measuring Prepayment: CPR and SMM

Prepayment speed is measured using two related metrics:

CPR is not constant — it varies with the refinancing incentive, loan age (seasoning), and market conditions. A pool of mortgages originated at 6% will have very different prepayment behavior when market rates are at 4% (high CPR — strong incentive to refinance) versus 7% (low CPR — no incentive).

Typical CPR ranges:

The Logistic S-Curve

The relationship between refinancing incentive and CPR follows a characteristic S-shaped curve — the logistic function:

The S-curve captures three behavioral regimes:

• Low incentive (x < 0): CPR is near the baseline floor — only turnover prepayments occur. No one refinances when market rates are above their coupon.
• Transition zone (0 < x < 200bp): CPR rises steeply. Borrowers begin to act on the incentive, but friction (closing costs, qualifying requirements, inertia) means the response is gradual.
• High incentive (x > 200bp): CPR plateaus near the maximum. Nearly everyone who can refinance has done so; the remaining holdouts face credit constraints or are simply unresponsive.

This shape — flat, steep, then flat again — is remarkably consistent across markets and time periods. It's one of the most robust empirical regularities in mortgage analytics, and the logistic function captures it with just three parameters.

Burnout

There is an important complication: burnout. After a sustained period of low rates, the most rate-sensitive borrowers have already refinanced. The remaining pool is composed of "slower" prepayers — those who face barriers or simply don't act. This means the pool's prepayment speed declines even if the incentive remains high.

Burnout has important implications for hedging: after a sustained rate decline, a bank might assume its mortgage portfolio has "stabilized" at a low CPR. But if rates drop further, a new cohort of borrowers crosses their refinancing threshold, and prepayment can re-accelerate — the burnout effect is incentive-specific, not absolute.

Negative Convexity

Prepayment risk creates a phenomenon called negative convexity — the price-yield relationship bends in the wrong direction compared to a non-callable bond:

• When rates fall: A plain bond's price rises significantly (positive convexity). But a prepayable mortgage's price gains are capped — as rates fall, prepayment accelerates, shortening the mortgage's effective maturity and limiting the price increase. The bank receives par on prepaid loans, not the above-par value of the remaining cashflows.
• When rates rise: Prepayment slows, extending the mortgage's effective maturity. The bank is stuck with a longer-duration, below-market coupon asset — duration extends at the worst time.

This double penalty — limited upside, full downside — is the hallmark of negative convexity. It means that duration itself is unstable: the portfolio's sensitivity changes as rates move, making static hedge ratios insufficient. This is why banks with large mortgage books often need options (caps, swaptions) rather than just linear instruments (swaps) to hedge effectively.

Impact on IRRBB

Prepayment assumptions flow through to both IRRBB metrics:

ΔNII impact: Higher CPR means faster principal return, which reduces future interest income from above-market coupons. Under a rates-down scenario, prepayment accelerates, and ΔNII worsens as the bank replaces high-coupon assets with lower-yielding reinvestments.

ΔEVE impact: Prepayment shortens effective duration under falling rates (reducing gains) and extends it under rising rates (amplifying losses). This asymmetry — negative convexity — makes the ΔEVE profile worse in both directions compared to a non-prepayable loan.

The Bigger Picture

Prepayment risk is the second-largest behavioral uncertainty in IRRBB, after NMD deposit decay. It is particularly challenging because it introduces path dependence (burnout), state-dependent duration (negative convexity), and asymmetric P&L profiles — all of which complicate hedging.

For banks with material mortgage portfolios (often 20–30% of total assets), the prepayment model directly affects ΔEVE by hundreds of millions of dollars. The model's three parameters — maximum CPR, slope, and midpoint — should be estimated from historical loan-level data, validated against out-of-sample periods, and stress-tested under extreme rate scenarios. The stakes are too high for rules of thumb.