Option Adjusted Spread.

Could somebody please explain me OAS in the simplest way possibe, and just not the overview a little in detail as in the books for level 2.

Would appreciate the help.

thnx :slight_smile:

If you do a search for OAS (in the upper-right corner, just below the logout), you’ll get lots of threads in which it is discussed / explained. There’s a wealth of knowledge there; no need to repeat it (especially as it’s really late here).

The best way to understand OAS is in contrast to z-spread. The z-spread is the amount you have to add to the spot rate curve (i.e. the additional compensation required for risk) in order for the theoretical price of the bond to match the market price. For bonds with embedded options, the market price represents not only the value of the bond, but the value of the embedded option.

Take a callable bond, for example. The market price is lower than the market price of an equivalent non-callable bond due to the embedded short position in the call option. So, the z-spread doesn’t accurately capture the additional risk.

The OAS effectively nets out the effect of the embedded option. So just think of it as the “option-removed” spread. For a bond with no embedded option, the OAS = the Z-spread.



First, you need to understand what a spread is: it’s additional interest that you add to a base interest rate (or rates) – usually, but not always, risk-free rates such as US Treasury rates – to value a risky bond; viewed another way, it’s the addional interest (yield) that an investor earns (or an issuer pays) to accept the additional risk of the bond. For simplicity, let’s assume that the risk-free rates used are for US Treasuries.

If you use Treasury rates to discount the cash flows of a risky bond, you will (generally) get a price that differs from the market price of the risky bond. When you add the appropriate spread (a constant amount) to each of the Treasury rates and discount using these new (adjusted) rates, you get a price that matches the market price for the risky bond.

The most common spreads are:

Nominal Spread : this is simply the difference between the YTM for the risky bond and the YTM for a Treasury of the same maturity. Thus, the nominal spread is the rate added to the Treasury par curve to get the market price of the risky bond. The nominal spread is a poor measure of additional yield because it ignores the term structure of interest rates: all of the bond’s cash flows are discounted at the same rate: the YTM.

Z-Spread : this is the spread added to the Treasury spot curve to get the discount rates that equate the risky bond’s value to its market price. This is a superior measure of additional yield because it takes the term structure of interest rates into account. The “Z” in “Z-spread” abbreviates “zero-volatility”: the spot curve is assumed to be a perfect predictor of future interest rates. The Z-spread is useful for option-free bonds, but not for bonds with embedded options.

OAS : this means “option-adjusted spread”, which really means “option-removed spread”; it is used for bonds with embedded options, but it explicitly removes the value of the embedded options, giving a spread for the remaining, option-free, bond. The OAS is calculated using an interest rate tree (typically a binomial tree): it is the appropriate spread added to each node of the tree so that the discounted cash flows – using some rule to determine if and when the embedded option(s) would be exercised – equate the price to the market value for the bond. Because an interest tree is used – so future interest rates can be above or below the rates in the current spot curve – this is not a “zero-volatility” spread: some positive (i.e., nonzero) volatility of future interest rates is inherent in the calculation (the ups and downs in the tree).

Note that freqently you will see drawings which have the Treasury spot curve, the Z-spread curve (above the spot curve for callable bonds, below it for puttable bonds), and the OAS curve (above or below the spot curve), with the (vertical) distance (spread) between the Z-spread curve and the OAS curve labeled as the “option value” (measured in basis points of additional yield). While this gives a good visualization of the option value, it is inaccurate, because the OAS is not added to the zero-volatility spot curve.

When comparing bonds, you prefer to purchase those with the highest OAS: the highest additional yield (for the option-free bond).


That’s a good explanation for anyone currently reviewing.

Thats exactly what i need here.