# 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?

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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.

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I wonder who has the other side of the option. Designated Primary Market Makers, according to the FAQ. –  chrisaycock Mar 10 '11 at 19:13
@Chris -- My bad. I had only scanned the FAQ. –  Richard Herron Mar 10 '11 at 20:14
"Another option could be to think about no arbitrage with any CDS and swaps that are already written on the underlying." A retail trader will not be able to hedge their CBOE options with a CDS, so I don't think that it makes sense to use CDS spreads to price these things. –  quant_dev Mar 19 '11 at 17:47
@quant_dev -- Could someone who does buy/sell CDS trade in the CEBO market? Do we expect the CEBO market to have huge limits to arbitrage? –  Richard Herron Mar 19 '11 at 23:54
Would they be interested? Trading with retail investors brings its own set of problems (e.g. different regulatory regime). –  quant_dev Mar 21 '11 at 20:27

Since there is no recovery value, any credit default model should be suitable, were I suppose reduced form models would be more appropiate.

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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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The delta is the first derivative of the Black-Scholes value with respect to the spot price. –  chrisaycock Mar 10 '11 at 17:11