Charta is on Google Play: practise on the go. Get the app
Charta

Explain the uses and the challenges of Option Adjusted Spread (OAS), starting from its definition.

FRM® Part I · Financial Markets and Products · Mortgages and Mortgage-Backed Securities · FRM1.FM.18.j

The idea

Option adjusted spread is the constant spread added to the short rates on every simulated path so that the average present value of projected cash flows equals the market price. The Z-spread is the same idea on one static curve with no option effect. OAS = Z-spread − option cost. The option cost is the value of the borrower's prepayment option in spread terms. OAS is used to compare mortgage securities with each other and with other bonds on an option-adjusted basis, and to judge whether a security looks cheap or rich. Its weakness is model dependence, because it relies on the interest rate model, the volatility input and the prepayment model. Higher assumed volatility lowers OAS, and an underestimated prepayment speed on a premium pass-through overstates it. The exam point is that OAS is only as reliable as its models.

Formulas

Option adjusted spread

OAS = Z-spread − option cost

Z-spread
the spread over one static curve, ignoring the prepayment option
option cost
the value of the borrower's prepayment option, in spread terms

Model dependent: higher assumed volatility lowers OAS, and underestimating prepayments on a premium pass-through overstates it.

A practice question

From the question bank, with the reason each wrong option is wrong.

The option adjusted spread (OAS) of an MBS is best defined as:

  1. The yield difference between the MBS and a Treasury of the same maturity.Why not: That is a nominal spread, which does not adjust for the option.
  2. The spread over the static Treasury curve that equates the PV to price, ignoring option exercise.Why not: That is the Z-spread, which excludes the option cost.
  3. The constant spread added to short rates on every path that equates average PV to market price. - correct
  4. The spread that compensates only for credit risk in the pool.Why not: OAS reflects the residual after the option; for agency MBS credit risk is not the main driver.

OAS is solved so that the average PV of cash flows across the paths equals the market price. It is the spread left after the cost of the embedded prepayment option is accounted for.

A harder one

What is the main use of OAS in the analysis of mortgage securities?

  1. Comparing securities with different embedded options on a common basis. - correct
  2. Measuring the probability that borrowers in the pool will default on their loans.Why not: OAS does not estimate default probability.
  3. Providing the exact expected holding-period return over the next year.Why not: OAS is a model-based spread, not a realized or expected return.
  4. Replacing duration as the measure of a security's interest rate sensitivity.Why not: OAS measures value relative to the curve; rate sensitivity comes from effective duration.

Because OAS strips out the effect of the embedded option, it allows comparison between MBS, callable bonds and others for cheapness or richness.

The hardest tier

A model gives these average present values for a pass-through at different spreads added to short rates: 60 bp gives 101.2, 80 bp gives 100.4, 100 bp gives 99.6, and 120 bp gives 98.8. The market price is 100.1. Using linear interpolation, the OAS is closest to:

  1. 92.5 basis pointsWhy not: Interpolates in the wrong direction, measuring from the 100 bp node.
  2. 90.0 basis pointsWhy not: Takes the midpoint of the bracketing spreads and ignores where the price falls.
  3. 87.5 basis points - correct
  4. 80.0 basis pointsWhy not: Picks the nearest grid point without interpolating.

The market price lies between 100.4 (80 bp) and 99.6 (100 bp). OAS = 80 + (100.4 - 100.1) / (100.4 - 99.6) x 20 = 87.5.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

Start free →

More in Mortgages and Mortgage-Backed Securities