Title: Option-Adjusted Spread (OAS) — What It Is, How It’s Calculated, and How to Use It
Key takeaways
– The option-adjusted spread (OAS) is the constant spread added to a benchmark discount curve (typically Treasury spot rates) that, after adjusting for the effect of any embedded options, makes the present value of a security’s expected cash flows equal its market price.
– OAS separates the value of a fixed-income instrument into two parts: the value of the underlying (option-free) cash flows and the value (cost) of embedded options such as calls, puts, or prepayment options (common in mortgage-backed securities).
– Calculating OAS for securities with embedded options requires modeling interest-rate paths and optionality-triggered cash-flow changes (often via Monte Carlo simulation) and then solving for the spread that equates expected discounted cash flows to market price.
– OAS is more informative than simple yield spreads or the Z‑spread for option-embedded securities, but it depends heavily on model choice and input assumptions (model risk).
Introduction
When a bond has no embedded option, the extra yield an investor earns above risk-free rates can be measured with simple spread measures (e.g., nominal spread, Z‑spread). When optionality exists (issuer callability or borrower prepayment), cash flows are uncertain and depend on future interest-rate paths. The OAS reflects the spread an investor earns after removing (i.e., adjusting for) the effect of those embedded options. It is widely used in pricing and relative-value analysis—especially for mortgage-backed securities (MBS), callable corporate bonds, and structured products.
How OAS works — conceptual overview
– Start with a term (spot) risk-free curve (usually Treasury spot rates or an interpolated money‑market curve).
– Model future interest-rate paths (stochastic models: e.g., Vasicek, Hull‑White, Libor Market Model). For each simulated path, generate the instrument’s cash flows, including optionality-driven changes (calls, prepayments, etc.).
– For a given trial spread s, discount each path’s cash flows using the risk-free spot rates plus the spread s and compute a path present value.
– Compute the expectation (average) of those path present values across all simulated paths: E[PV(rates + s)].
– Adjust s (iteratively) until E[PV] equals the observed market price. That final s is the OAS.
Practical step-by-step: How to calculate OAS
Below is a practical workflow an analyst would follow. In practice you will use pricing software or libraries for the heavy lifting, but knowing the steps helps in setting up models and validating outputs.
1. Gather inputs
– Market price (clean or dirty—be explicit).
– Risk-free spot curve (Treasury spot curve or appropriate benchmark).
– Security terms: coupon, maturity, amortization schedule, call/put features, prepayment conventions/PSA speeds for MBS.
– Volatility and mean-reversion parameters for the chosen interest-rate model.
– Prepayment model (for MBS): historically calibrated PSA, conditional prepayment rates, or borrower behavior model.
2. Choose the interest-rate model
– Short-rate models (Vasicek, Hull‑White) or multi-factor models (LIBOR market model) are common.
– The model must be consistent with the current term structure (calibrated to the market curve) and, ideally, to observed rate volatilities that drive option values.
3. Simulate forward interest-rate paths
– Use Monte Carlo simulation to generate many (thousands to tens of thousands) possible future rate paths.
– For each path, derive forward rates and discount factors at all cash‑flow dates.
4. Generate path-specific cash flows
– For each simulated path, compute the security’s cash flows given path-specific rates and the rules for the embedded option (e.g., issuer calls when rates drop below a threshold; higher prepayments when rates fall).
– This yields a set of cash flows for each path.
5. Discount cash flows and compute path PVs
– For a guessed spread s, discount each path’s cash flows using spot rates + s and obtain a present value for that path.
6. Average across paths and iterate to solve for s
– Compute the mean of the path PVs: E[PV(s)].
– Adjust s (root-finding/search methods: bisection, secant, Newton–Raphson) until E[PV(s)] equals market price. The resulting s is the OAS.
7. Validate and run sensitivity checks
– Run alternative prepayment calibrations, different volatility levels and interest-rate model specifications.
– Compute OAS under plausible scenarios and produce a sensitivity (“OAS breakpoints”) table.
Illustrative (very simplified) example
This toy example is only meant to illustrate mechanics, not replace professional pricing systems.
Security: a 2‑period instrument with a face of 100 and a coupon of 5% (annual). Market price = 98. Treasury flat spot rate r = 1%.
Two scenarios (prepayment-related) with equal probability:
– Scenario A (50%): no prepayment → CF1 = 5, CF2 = 105.
– Scenario B (50%): full prepayment after year 1 → CF1 = 105, CF2 = 0.
Expected cash flows by date:
– E[CF1] = 0.5*5 + 0.5*105 = 55
– E[CF2] = 0.5*105 + 0.5*0 = 52.5
We seek spread s such that:
98 = 55/(1+0.01+s) + 52.5/(1+0.01+s)^2
Solving numerically gives s ≈ 5.4% (540 basis points). This s is the OAS in this simplified setup — it adjusts the discounting of stochastic cash flows to match market price. (Real-world computations are more granular: more paths, finer timing, continuous discounting, and complex prepayment functions.)
OAS versus Z‑spread and other spread measures
– Z‑spread: the constant spread to add to each point on the Treasury spot curve that makes the PV of the (deterministic) promised cash flows equal to market price. It ignores optionality and the fact that cash flows may change with interest rates.
– OAS: adjusts the Z‑spread to remove the embedded option’s value. Conceptually, Z‑spread = OAS + option-value-in-spread-equivalent for securities where the Z‑spread is computed on promised (not path-dependent) cash flows.
– For non‑optioned (option-free) bonds, Z‑spread = OAS.
– Use Z‑spread for quick, static comparisons; use OAS when option effects matter (e.g., MBS, callable issues).
How options and volatility affect OAS
– Embedded call option (issuer option to redeem): reduces upside to investor when rates fall (issuer refinances), so investors demand higher compensation; with the same market price, callable bonds will have lower OAS than their Z‑spread would suggest if option value is ignored.
– Put option (investor can sell back): increases investor protection and reduces required compensation; put-embedded securities usually have higher OAS (or lower option cost).
– Volatility: higher interest-rate volatility increases the expected value of options (both issuer and borrower options), making optionality more valuable to the option holder. For example, higher volatility makes a call option more likely to be exercised, which affects projected cash flows and OAS. In general, greater volatility (other inputs constant) tends to widen the option-related adjustment and thereby change OAS.
– Prepayment risk (for MBS): lower rates typically increase prepayments (mortgage refinancing), shortening expected life and reducing investor yield; OAS captures that prepayment-adjusted compensation required by investors.
Interpreting OAS
– Higher OAS (all else equal) suggests greater compensation for credit, liquidity, or other non‑Treasury risks after accounting for option effects.
– Use OAS for relative-value comparison across securities with similar optionality profiles and model assumptions.
– Beware: differences in OAS can come from model choices and assumptions as much as from true value differentials.
Limitations and pitfalls
– Model risk: OAS depends critically on the interest-rate model, calibration, and prepayment/behavioral models. Different reasonable models can produce materially different OAS values.
– Input risk: volatility estimates, mean reversion, and borrower behavior are estimated from historical data and may not predict future behavior.
– Liquidity, transaction costs, and supply/demand distortions are not captured directly in OAS.
– The numerical solution can be sensitive to discretization, number of Monte Carlo paths, and optimization tolerances.
Tools and software
– Market terminals: Bloomberg displays OAS for many products (functionality varies by security). Traders and portfolio managers commonly reference Bloomberg OAS as a standard market number.
– Libraries and packages: QuantLib, proprietary bank pricing engines, in-house models. These let you implement Monte Carlo, interest-rate trees, or analytic approximations.
– Spreadsheet prototyping: feasible for simple toy examples, but not recommended for production due to path/complexity needs.
Practical checklist for investors and analysts
1. Confirm market price conventions (clean vs dirty) and use consistent discounting.
2. Use an up‑to‑date spot curve and ensure your model is calibrated to it.
3. Choose an interest-rate model you understand; document calibration and assumptions.
4. Implement a realistic prepayment or call/put exercise model and stress-test it.
5. Run sufficient Monte Carlo paths and check convergence.
6. Produce sensitivity analyses: OAS vs volatility, OAS vs PSA/prepayment speed, OAS vs model parameters.
7. Compare your OAS to market quotes (Bloomberg, dealers) and investigate material differences.
8. Remember to include liquidity and transaction-cost considerations in investment decisions even if not included in OAS.
Bottom line
OAS is a powerful, widely used measure that adjusts yield spreads for the effects of embedded options. It’s essential when valuing MBS and callable/puttable bonds because it converts complicated, path-dependent cash flows into a single spread number that can be compared across securities. But OAS is model-dependent; its usefulness depends on careful model selection, sensible calibration, and thoughtful sensitivity analysis.
Sources and further reading
– “Option-Adjusted Spread (OAS),” Investopedia — https://www.investopedia.com/terms/o/optionadjustedspread.asp
– Fabozzi, Frank J., Fixed Income Analysis (CFA Institute Investment Series). (See chapters on mortgage-backed securities and option valuation.)
– QuantLib open-source library — for implementing curve bootstrapping, interest-rate models, and Monte Carlo pricing.
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.