Hi all,Can some one please explain what the OAS (Option adjusted spread) means when there is no optionality involved - i.e, If I have a 10 government Bond paying 5% semi annually with no optionality and I calculate the OAS of that Bond against a 6M Libor curve - what does the OAS mean? How do I calculate it? Any references would also be appreciated.Thanks.

When people talk about OAS they usually mean OAS to a curve, so they would say OAS to Libor or OAS to Treasury. I've never heard about "OAS to 6M Libor", so I don't know. OAS to Libor in your case works the following way. All the future cash flows on your bond are known, so the bond' MV is just a sum of discounted future cash flows. If you pricing a product with respect to Libor, you shoud use Libor discount factors, let's call them d_t. So in a Libor world you bond should costMV=\sum CF_t \cdot d_tbut you bond is from a Treasury world so its market value MV_0 will not equal MV, you have to correct by OAS which is defined by the following equationMV_0=\sum CF_t \cdot d_t \cdot e^{OAS \ cdot t}(In case you don't know \cdot just puts a multiplication sign in Latex ). Simply speaking, OAS is by what you need to shift Libor by a parallel shift so that MV=MV_0.I know I was a little confusing, so feel free to ask further questions.

6M curve probably means the curve is constructed using swaps that fund vs 6M libor. Euro swaps curve is one such curve, for example.

QuoteOriginally posted by: syaekHi all,Can some one please explain what the OAS (Option adjusted spread) means when there is no optionality involved - i.e, If I have a 10 government Bond paying 5% semi annually with no optionality and I calculate the OAS of that Bond against a 6M Libor curve - what does the OAS mean? How do I calculate it? Any references would also be appreciated.Thanks.not sure what the others above are saying...to me, the answer to your question is simple: as OAS is the spread investors would pay/subtract wrt 6Mo LIBOR to compensate for the optionality (convexity) embedded in bond, the OAS in your example would be zero ... unless the gov bond in your example is backed by mortgage cash flows which have prepayment feature (exhibit negative convexity).best way to calculate oas is to do a simulation of bond cash flows over many paths I, where I = 6mLibor + s, and choose s such that the avg of all discounted cash flows equals current market price. then, s is your OAS. if your bond has no optionality, then s will be very close to zero, but not exactly zero due to inconsistencies in your term structure model vs. market implied yield curve paths.wrote this quickly but i hope it makes sense. let me know if you have questions.

I have one more questionFor a simple callable bond, which is calculated ascallable bond market price=underlying vanilla bond (discounted at Libor +OAS) -- value of call optionLet us say the value of call option is computed by,say, some swaption calculator,Do you compute this swaption using Libor curve only, or do you use the same shift in Libor+OASfor discounting in the calculation of this swaption.

OAS = Z spread (if no options in the bond)

if you govt is not USA, then the bonds may have fancy options, so your OAS is adjustment to them

Hi,I try to value call on the bond. The main problem is this callable bond is not quoted, so I don't have bond's market price. I have Hull-White tree model to calculate value of the option but I don't know what credit spread should I use. Should I use OAS? If yes how can I determine how big it is if I don't have market price? Or maybe should I use some term structure of credit spread? Has anyone ever heard of using Hull-White model with time dependent credit spread? Many thanks for all replies.

QuoteOriginally posted by: zuwdzordzHi,I try to value call on the bond. The main problem is this callable bond is not quoted, so I don't have bond's market price. I have Hull-White tree model to calculate value of the option but I don't know what credit spread should I use. Should I use OAS? If yes how can I determine how big it is if I don't have market price? Or maybe should I use some term structure of credit spread? Has anyone ever heard of using Hull-White model with time dependent credit spread? Many thanks for all replies.Hi,concerning the time dependent credit spread. I havent heard this. You have (at least) two main streams of modelling i would say. You have to decide if you want a stochastic credit spread or not. If you have a stochastich spread then you can take for example the books of tavella/rundall on finite difference methods and solve a 2 factor pde for the bond and the option price.If you like to see the option only as an interest rate option (which seem to me many people like to think this way) then you stick with a one factor pde for the bond price. You obtain swaption formulas where you discount the fix side (the bond side) of the swap (underlying the swaption) with this additional credit spread. You have to take care to get the correct interest rate vols in this case. Anyway this is only a workaround as in fact bond are more often driven by the credit spread. And this is definitly volatileIf you look at callable floaters you will find yourself in a complete mess if you stick to the swaption valuation of the bond option. You end up with a silly swaption that makes no sense from the perspective of an interest rate option

I have one more questionFor a simple callable bond, which is calculated ascallable bond market price=underlying vanilla bond (discounted at Libor +OAS) -- value of call optionLet us say the value of call option is computed by,say, some swaption calculator,Do you compute this swaption using Libor curve only, or do you use the same shift in Libor+OASfor discounting in the calculation of this swaption.

 As far as i know, the option needs to be priced at Libor + OAS as well.