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Home / Financial Tools / Mortgage-Backed Security Prepayment & Option-Adjusted Spread (OAS) Model

Graduate-Level Modeling · Structured Fixed Income & Mortgage Analytics

Mortgage-Backed Security Prepayment & Option-Adjusted Spread (OAS) Model

A static spread ignores the one thing that actually makes a mortgage bond different from a regular bond: the borrower gets to prepay whenever it benefits them most, and the investor pays for that right whether they realize it or not.

How To Use This Model

Reading This Tool

Build a mortgage pool's PSA prepayment curve, simulate a full Vasicek short-rate model across hundreds of interest rate paths with rate-dependent refinancing behaviour, and solve for the Option-Adjusted Spread that makes the model's average discounted price match a market price you specify.

The gap between the simple static spread and the full OAS is a real, quantifiable number: the option cost, exactly what the borrower's right to prepay early is actually costing the mortgage bond investor.

Mortgage Pool

Prepayment Assumptions

Interest Rate Model (Vasicek)

Pricing

Refinancing sensitivity controls how much the PSA multiplier accelerates for every 1 percentage point the simulated rate falls below the pool's WAC, capturing the classic prepayment burnout behaviour a static PSA assumption can't.

Spread Decomposition

Static (Zero-Volatility) Spread

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Option-Adjusted Spread (OAS)

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Option Cost

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Model Price Check At Solved OAS

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Spread Bridge: Static Spread To OAS

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Prepayment Profile

Weighted Average Life (Base Case)

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CPR At Month 30 (Base PSA)

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First Year Interest Collected

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Months To 50% Paydown

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PSA Prepayment Curve (CPR By Month)

Weighted Average Life Across PSA Speeds

Sample Simulated Short-Rate Paths

Pool Balance Decline Across A Sample Of Rate Paths

What The Option Cost Is Actually Paying For

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Why Static Spread Alone Can Be Dangerously Misleading

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What "Burnout" Means And Why It Matters

Real MBS pools don't keep prepaying at the same accelerated rate forever, even when rates stay low. The borrowers most eager and able to refinance do so quickly, leaving the remaining pool disproportionately full of borrowers who, for whatever reason (credit issues, small remaining balance, apathy), never refinance even when it would clearly benefit them. This tool models the rate-dependent acceleration but not full path-dependent burnout, real OAS models often add a burnout factor tied to how much of the pool has already prepaid.

Structured Fixed Income & Mortgage Analytics

The Core Formulas

PSA CPR(m) = min(0.06, 0.002m)·PSA%, for m < 30, flat at 0.06·PSA% after
SMM = 1 − (1−CPR)1/12
Path-Dependent PSA Multiplier = min(Cap, Base·[1 + Sensitivity·max(0, WAC−rt)×100])
Model Price(OAS) = (1/Npaths)·Σpaths Σm CFm / Π(1+(rt+OAS)/12)
Option Cost = Static Spread − OAS

When To Actually Use This Model

  • Teaching mortgage-backed security analytics, prepayment modeling and OAS methodology in a fixed income or structured products course.
  • Understanding, quantitatively, why an MBS trading at an attractive static spread can still be a poor risk-adjusted investment once the embedded prepayment option is priced in.
  • Building intuition for how rate volatility and refinancing sensitivity assumptions each separately drive the option cost.

Key Assumptions & Limitations

  • This tool models a single, current-coupon pool, real MBS analytics run this across many pools with different WAC/WAM combinations and vintage-specific prepayment behavior.
  • The refinancing incentive function here is a simplified linear response, real prepayment models (e.g., Andrew Davidson, BlackRock's proprietary models) fit dozens of parameters to historical prepayment data by loan characteristic.
  • Uses a single-factor Vasicek short-rate model for path generation, production OAS systems typically use a full arbitrage-free term structure model calibrated to the current yield curve, similar to the Hull-White approach shown in this site's short-rate model suite.

Foundational References

Fabozzi, F. J. The Handbook of Mortgage-Backed Securities. Oxford University Press.

Hayre, L. (Ed.). Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed Securities. Wiley.

Want the short-rate model suite behind this on its own?

Open The Short-Rate Model Suite →