Using Option-Adjusted Bond Prices to Estimate Default Probabilities
Summary
The document raises a methodological question about estimating risk-neutral default probabilities for US corporate bonds when observed prices include embedded optionality. The author has bond prices and related measures such as yields, option-adjusted spreads, duration, and maturity, and is considering repricing the bonds using option-adjusted yields before extracting default probabilities.
The motivation is to distinguish default compensation from the effects of embedded options, particularly when comparing risk-neutral default estimates with real-world probabilities to study default risk premia. The document does not provide an answer, a pricing procedure, or evidence that repricing from option-adjusted yields produces a reliable default probability estimate. It also leaves unspecified the credit and interest-rate models, recovery assumptions, and consistency requirements needed for such extraction. It is useful as a research question about separating credit risk from optionality, but it does not establish that the proposed approach is prudent or that the resulting probabilities measure expected-loss compensation alone.
Key ideas
- Observed corporate bond prices may reflect embedded optionality as well as default risk.
- The author proposes repricing bonds using option-adjusted yields before estimating risk-neutral default probabilities.
- The intended analysis is to compare risk-neutral and real-world default probabilities to study default risk premia.
- The document does not answer whether the proposed method is appropriate or provide a validated extraction method.
- Model choices and assumptions such as recovery and interest-rate treatment remain unspecified.
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# Extracting Risk Neutral Default Probabilities using Option Adjusted Bond Prices # Extracting Risk Neutral Default Probabilities using Option Adjusted Bond Prices I am currently in a project trying to quantify default risk premia for US Corporate Bonds. The data I have consists of bond prices, and other information (i.e. YTM, OAS, Effective Duration, Maturity etc.).The data includes bond prices with optionality and non-optionality. Now, I want to extract risk neutral default probabilities from the bonds at every point in time, but since the given prices incorporates possible optionalities , trying to quantify default risk premia from the extracted RN default probabilities (and comparing against real world DPs from another source) may not give me a true measure of the compensation for expected loss. Now, the data also has information on option adjusted yields, or the yield of a bullet bond after stripping out the optionality. What I am thinking is to reprice the bonds using these option adjusted yields and then use those prices to extract risk neutral default probabilities. My question is, will this be a prudent approach to take? ## Answer by Shabir Ali (score 0) https://quant.stackexchange.com/a/85884 The standard route is a hazard-rate bootstrap rather than working with OAS directly: - For each bond, compute the z-spread against a risk-free discount curve (SOFR these days) — this is the option-adjusted spread with the option model reduced to a parallel shift. - Postulate a piecewise-flat default-intensity (hazard) curve on tenor knots (say 1, 2, 3, 5, 7, 10Y) and a recovery assumption (40% is the common crude default; the CDS market convention). - Bootstrap the hazards so that model par CDS spreads — priced under ISDA standard conventions from the hazard curve — reproduce each bond-implied z-spread at the knots. - The survival curve S(t) = exp(−∫h) gives you the risk-neutral default probabilities: P(default by t) = 1 − S(t). Two honesty notes: the result is risk-neutral (includes risk premia, so it overstates physical default odds), and bonds with floating-rate coupons or thin print history will produce garbage knots — gate or drop them rather than interpolating through. Disclosure: I build/run Basisline, which publishes exactly these outputs — bootstrapped hazards and par spreads for US single-name issuers from TRACE prints, methodology documented at the link, free JSON tier included.
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