Can somebody tell me the formula to be used for adjusting Z spread of a premium/ discounted bond

You can use this for a roughly adjustment:Spread Adjustment = - (Price - 100) x CDS Rate/(1- Recovery)

Hey Mariano , could you give some explanation as to how you derived this ? Also you mean we should interpolate CDS spread to that maturity

The z-spread is just the parallel shift applied to the libor/swap curve that makes the PV of the bond’s cash flow equals to the market value. Is not a tradable spread, assumes a constant spread over the swap curve. Is is a roughly measurement of the issuer’s credit quality. The z-spread do not accounts for a recovery rate explicitly, therefore assume a zero default probability. However, is useful as a relative value measure. CDS spreads are a function of both recovery rate and the term structure of default probabilities. Is a pure measurer of credit risk (ie the IR risk and the pull-to-par effect are removed in a par CDS). If you goal here is to compare bond spread vs CDS spread I suggest you to take a look at alternative measures such as bond-equivalent CDS or par-equivalent CDS spreads. Moreover, take a look at the student forum, this threat has been extensively covered. I am sure you will find interesting things to read. M

Mariano, I am not sure how the formula is derived, but it does not seem right to me. When recovery is 100%, it is effectively the case there is no default, but the adjustment will be infinitely large according to the formula. Should it it be multiply instead of divide?

If the recovery rate is 100%, you would expect the CDS spread to be 0, so you get one of those awkward 0/0 situations. Keep in mind that this is just a rough approximation, and one area where it may not be very good is when the recovery rate approaches 100%.