Pricing Credit Event Binary Options with Default Models
Summary
The document discusses valuing a binary contract that pays a fixed amount if a specified credit event occurs before expiry and nothing otherwise. Its quoted premium is described as an approximate market-implied chance of bankruptcy. One proposed approach uses a binomial tree: estimate default probabilities over successive intervals with a KMV–Merton model, assign probabilities to the tree branches, and discount the resulting payoffs at the risk-free rate. A reduced-form credit model is also suggested as a possible fit.
The discussion offers checks and caveats rather than a complete pricing recipe. Prices could be compared with related credit default swaps or swaps to assess no-arbitrage consistency, and a deep out-of-the-money put’s delta is mentioned as a rough comparison rather than an established equivalence. Observed premiums may include a liquidity component. The answer acknowledges limited first-hand experience with the model and leaves open who takes the opposite side, so calibration, contract details, and market frictions remain important.
Key ideas
- A credit event binary pays according to whether a defined default event occurs before expiry.
- A binomial tree can combine interval default probabilities with discounting to value the payoff.
- KMV–Merton or reduced-form credit models are possible sources of default probabilities.
- Related credit swaps can provide a no-arbitrage comparison, while liquidity may affect traded premiums.
- A put delta is only a possible reference point and is not shown to equal the binary premium.
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Full text
# How would one price a "credit event binary option"? # How would one price a "credit event binary option"? CBOE has introduced credit event binary options, kind of as a retail trader's CDS. These binary options are worth $1 if there is a credit event (ie, bankruptcy) before expiration, and $0 if there is no credit event (ie, solvency) at expiration. The option's premium is quoted in pennies and indicates the chance of a bankruptcy during the option's lifetime (eg, $0.11 is 11% chance). How would someone price one of these options? My gut is that the premium should be similar to the delta of a deeply out-of-the-money put option. Any other thoughts? ## Answer by Richard Herron (score 5, accepted) https://quant.stackexchange.com/a/685 I would see if a binomial tree gives reasonable answers (i.e., can you get close to the CEBOs with high volume). You could determine the probability of default over a given interval using the KMV-Merton model. Then use the probability over each of these intervals to determine the probabilities for each of the branches (since the payoff is in default, the tree will be very one-sided). Then discount each of branches back at your risk-free rate. I don't have first-hand experience calculating the KMV-Merton model, but it's pretty common, so I think you should be able to find code out there for it (it's calculated iteratively). Another option could be to think about no arbitrage with any CDS and swaps that are already written on the underlying. But given that your CEBO are traded, there may also be a liquidity premium wrapped up in them. Looking quickly at the website, it doesn't look like retail investors can sell protection. Is that right? I wonder who has the other side of the option. ## Answer by Owe Jessen (score 2) https://quant.stackexchange.com/a/686 Since there is no recovery value, any credit default model should be suitable, were I suppose reduced form models would be more appropiate. ## Answer by Ralph Winters (score 0) https://quant.stackexchange.com/a/684 The CBOE site states that the premium will approximately reflect the probability of bankruptcy. Usually the delta reflects the probability that the OTM option will be ITM, so I am not sure what is involved in the premium calculation. However, If you can compute the delta, you can compare it to the premium to see if is over/under valued. -Ralph Winters
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