# OAS for bond valuation

The option-adjusted spread (OAS) is the constant spread added to all the one-period forward rates that makes the arbitrage-free value of a risky bond equal to its market price. But if OAS is the yield stripped of option value, how could this be the case, why would OAS show the market value if it doesnt count the option value?

It’s a spread for the underlying (option-free) bond. so if we look at this, the red R1 R2 in Z spread is the rate that doesnt include option, while the OAS R1 R2 include option?

Now thinking about it, is it ok to say OAS is only used for valuation comparison, but when you really want to calculate the innate price, Z spread is still the right way to go but OAS gives you an idea the option free bond is over or underpriced?

The OAS calculates the value of the bond assuming the put/call rules are exercised in the future given the rates in the binomial tree. Thus this is the spread you are getting on the bond due to the potential of getting the option exercised against you in the future (in the case of a callable bond). Therefore you can compare this spead to other option free bonds/ or other bonds with embedded options for valuation purposes to see if they are over/undervalued assuming some level of interest rate volatility.

You never want to compare z-spreads when comparing bonds with options. This is NOT CORRECT - because volatility is what makes options valuable. Think about one of the inputs into BSM - its volatility. Thats what gives options value. The z-spread assumed zero volatility which would mean it assumes that all put/call options on bonds are wothless which is incorrect. Therefore the correct measure when valuing a bond with embedded options is the OAS - not the z-spread.

The formula they have in the OAS row is incorrect. They’re adding the OAS to spot rates; the OAS is added to forward rates. And the cash flows are adjusted for the exercise of the option.

The point to understand – the _ absolutely critical idea underlying OAS _ – is that the OAS methodology _ removes the effect of embedded options _. The embedded options are gone. Poof! No more options! Pfft! You’re left with a straight – _ option-free _ – bond. And you’re computing the spread for that straight, option-free bond.

It’s OK as long as you understand the difficulties you’re facing in applying it.

To discount a bond with options using the z-spread, you have to adjust the expected cash flows at each date. How do you propose to do that accurately?

Ok, so here is the key part, if the OAS removes the valune of embedded option, how can it reflect the price of the option embedded instrument

It doesn’t.

It assumes that the option is valued correctly in the market price of the bond.