{
  "id": "fc6d8d8d-d4b8-5466-9bc2-355e0289061b",
  "slug": "option-adjusted-spread",
  "term": "Option-Adjusted Spread",
  "aliases": [],
  "category": "Fixed Income",
  "category_slug": "fixed-income",
  "difficulty": "advanced",
  "definition": "Option-Adjusted Spread (OAS) is the constant spread added to the risk-free zero-coupon yield curve that makes the theoretical price of a bond with embedded options — such as callable bonds or mortgage-backed securities — equal to its observed market price, after accounting for the value of the embedded option through a model-derived adjustment.",
  "key_takeaways": [
    "OAS strips out the value of embedded options from the bond's nominal yield, leaving a pure credit and liquidity spread.",
    "A higher OAS indicates cheaper relative valuation (wider spread to Treasuries, net of option cost) and greater expected excess return.",
    "OAS requires an interest rate model (typically Hull-White or Libor Market Model) to generate scenarios for future rate paths.",
    "Callable bonds have lower OAS than otherwise identical non-callable bonds because the call option has positive value to the issuer.",
    "For MBS, OAS analysis must model prepayment behavior across hundreds of interest rate scenarios to produce a stable spread measure."
  ],
  "detailed_explanation": "The Option-Adjusted Spread is the fixed income analyst's primary tool for comparing the relative value of bonds with embedded options — callable corporate bonds, putable bonds, and mortgage-backed securities — to bonds without such features. A callable bond's nominal yield (YTM) includes compensation for the investor's short call position, but the nominal yield spread conflates credit risk, liquidity risk, and option risk. OAS separates these components by explicitly modeling and removing the value of the embedded option.\n\nThe OAS calculation proceeds through three steps. First, an interest rate model is calibrated to current market rates and volatility — typically a short-rate model such as Hull-White (with mean reversion and volatility parameters) or a more complex Heath-Jarrow-Morton framework. Second, the model generates a large number of interest rate paths (typically 500–5,000 Monte Carlo paths) spanning the bond's remaining life. Third, along each path, the expected cash flows of the callable bond are computed — accounting for the possibility of the issuer calling the bond if rates fall sufficiently below the coupon (modeled using a specific call exercise rule). The OAS is then the single constant spread added to each spot rate along each path that equates the average present value of modeled cash flows to the observed market price.\n\nInterpretation is intuitive: a bond with OAS = 120 bps offers investors 120 bps of expected excess return over Treasuries per annum, after paying for the value of the embedded call option. A comparable non-callable bond of the same issuer might trade at a Z-spread (zero-volatility spread, which ignores optionality) of 150 bps — the 30 bp difference represents the value of the call option. If the non-callable bond's spread subsequently tightens to 140 bps while the callable's OAS remains at 120, the callable has cheapened on a relative value basis.\n\nFor MBS, OAS analysis is substantially more complex because the embedded 'option' is the homeowner's prepayment right — which is driven by refinancing economics (the gap between the pool's coupon and current market mortgage rates) and non-economic factors (housing turnover, divorce, relocation). Prepayment models — such as those produced by Bloomberg, Andrew Davidson & Co., or in-house by major dealers — translate interest rate scenarios into expected prepayment speeds (measured in CPR, or Constant Prepayment Rate). The OAS for an agency MBS pool, after being stripped of prepayment option value, represents the pure liquidity and convexity risk premium demanded by investors — typically ranging from 5 to 30 bps for high-quality agency pass-throughs.\n\nFor high-yield callable bonds, OAS and asset-swap spread (ASW) together inform credit spread decomposition. The difference between OAS and ASW reflects the relative value of the call option in the swap market versus the Treasury market. Rising-star credits — issuers whose bonds are expected to be upgraded from high-yield to investment grade — often have particularly interesting OAS dynamics as investors anticipate not just spread tightening but also call risk (issuers refinance at lower rates upon upgrade), compressing future OAS levels and potentially triggering call provisions.",
  "example": "A callable corporate bond issued by a BBB-rated company has a 10-year maturity, a 5.50% coupon, and is callable at par in 3 years. The bond trades at $98.50 in the market. Using a Hull-White interest rate model calibrated to the current Treasury curve and swaption volatility surface, the OAS calculation generates 1,000 rate paths. Across all paths, the issuer exercises the call option in approximately 40% of scenarios where 3-year rates fall below 4.0% (the issuer's estimated refinancing rate). After modeling call cash flows and discounting along each path, the constant OAS that equates the model price to $98.50 is found to be 145 bps. A comparable non-callable 10-year bond from the same issuer trades at a Z-spread of 180 bps. The implied option cost = 180 − 145 = 35 bps, representing the annual yield give-up the callable bondholder accepts in exchange for the call premium (the higher coupon) embedded in the callable structure.",
  "formula": "OAS = Constant spread s.t. Market Price = E[Σ CF(pathᵢ) / Π(1 + r(pathᵢ,t) + OAS)] across all Monte Carlo paths",
  "formula_latex": null,
  "interactive_type": "model",
  "calculator_id": null,
  "related_terms": [
    "asset-swap-spread",
    "basis",
    "bond",
    "call-option",
    "callable-bond",
    "convexity",
    "corporate-bond",
    "credit-risk",
    "credit-spread",
    "exchange",
    "high-yield-bond",
    "implied-repo-rate",
    "interest-rate",
    "investment-grade",
    "liquidity"
  ],
  "backlinks": [
    "coupon-rate",
    "reinvestment-risk",
    "yield-to-call",
    "yield-to-worst"
  ],
  "cross_references": [
    "basis",
    "bond",
    "call-option",
    "callable-bond",
    "convexity",
    "corporate-bond",
    "credit-risk",
    "credit-spread",
    "exchange",
    "interest-rate",
    "investment-grade",
    "liquidity",
    "liquidity-risk",
    "mean-reversion",
    "option",
    "premium",
    "present-value",
    "relative-value",
    "risk-premium",
    "spot-rate"
  ],
  "tags": [
    "level:advanced",
    "cat:fixed-income"
  ],
  "asset_classes": [
    "fixed-income"
  ],
  "regulators": [],
  "see_also": [],
  "sources": [],
  "wordcount": 838,
  "checksum": "f7cbef5d2eed52a1",
  "version": "2026.05.03",
  "license": "CC-BY-4.0",
  "updated_at": "2026-09-07T02:15:24+00:00",
  "_links": {
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    "graph": "https://hedgefund.wiki/api/v1/graph/option-adjusted-spread",
    "category": "https://hedgefund.wiki/api/v1/categories/fixed-income",
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    "html": "https://hedgefund.wiki/#/terms/option-adjusted-spread"
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}