Option-adjusted spread is the yield a callable or mortgage-backed bond would offer if its embedded options were stripped away, and it is the only honest way to compare such bonds against straight debt. Option-Adjusted Spread Calculator below does the decomposition. A plain bond's spread over Treasuries is its z-spread, a constant addition to the whole spot curve that makes discounted cash flows equal the market price. That z-spread bundles two things: the pure credit and liquidity premium, and the value of the option the issuer holds. A callable bond gives the issuer the right to redeem early, and that right is worth something to the borrower and costs the lender.
The option value equation
The relationship is arithmetic. Option Value equals Z-Spread minus OAS. Take a bond with a z-spread of 180 basis points and an embedded call option worth 45 basis points. The true option-adjusted spread is 135 basis points. The 45 basis points is the compensation the market demands for the risk that the issuer calls the bond when rates fall, capping your upside. Ignore the option and you overstate the credit compensation by the full 45 basis points.
Binomial interest rate trees
The option value is not observed; it is modelled. Analysts build a binomial interest rate tree, a lattice of possible short rates that branch up and down each period, and walk the bond's cash flows through every path. At each node the model checks whether the issuer would exercise the call. The result is a distribution of possible prices, and OAS is the spread that, added to every path and discounted, reproduces the observed market price on average.
Z-spread versus OAS
The two spreads diverge exactly by the option value. Z-spread ignores optionality entirely, so it overstates compensation on callable bonds and understates it on putable bonds, where the investor holds the option. OAS removes the distortion and isolates the credit and liquidity premium. For a non-callable bond the two are identical, because there is no option to strip. The differential between them is a direct measure of how much optionality the market is pricing.
Why it matters
Compare two bonds with the same z-spread and you may be comparing apples to oranges, because one carries a heavy embedded option and the other carries none. OAS levels the field. A wider OAS means more compensation for credit and liquidity risk after optionality is removed, and that is the number a portfolio manager should rank on. The 45 basis point gap in the worked example is not noise; it is the price of the call.