How do I calculate option-adjusted spread (OAS) step by step?

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AcadiFi · Accepted Answer

Option-adjusted spread is the constant spread added to every 1-year forward rate on the binomial tree such that the recalculated value equals the observed market price. OAS strips out the embedded option's impact, leaving a 'clean' credit-and-liquidity spread comparable across securities. Procedure: (1) Build the binomial tree using benchmark (Treasury) 1-year rates calibrated to the current Treasury curve and an assumed volatility. (2) Value the callable bond with backward induction at zero spread — you get 101.20 in this example. Market price is 98.40, so the model is 'too rich' by 2.80 and OAS must be positive. (3) Iterate: add a trial spread z to every node's rate and revalue. If z = 40 bps yields 99.75, still too high; try z = 70 bps yields 98.35, very close; interpolate to z = 69 bps. (4) The OAS is approximately 69 basis points. Key mechanics during iteration: at each node, discount using (1 + r_node + z) rather than (1 + r_node). The call rule still applies (cap at call price). Because the option decision depends on the path and is re-evaluated at each z, OAS is not simply Z-spread minus option cost — the option value changes with z. Interpretation: OAS of 69 bps means investors demand 69 bps above Treasuries for credit and liquidity risk after accounting for the call. Compare to similar-rated non-callable corporate at 58 bps — our callable is offering 11 bps extra, suggesting either marginal cheapness or compensation for higher credit concerns. OAS narrows when volatility assumption rises (fewer paths, option more valuable, implied spread higher for same price).

How do I calculate option-adjusted spread (OAS) step by step?

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