The European Credit Default Swap Option (CDSO) pricing model serves the purpose of pricing an option that grants its holder the right, but not the obligation, to enter into a Credit Default Swap (CDS) at some future point in time. The premium to be paid on this forward-start CDS is fixed in advance at some strike level. If the reference entity should default before the forward-start date, the contract is in null and no payments are made.
A closed form solution, which is similar to the Black’s model for interest rate swaption, is implemented within the current credit library framework. The forward credit spread of the underlying CDS is computed using pricing model for CDS and the counterparty risk is handled with default correlation model. Apart from pricing, the model can be employed to back out the implied volatility of the forward credit spread.
It is natural to try to value a CDSO by using an approach similar to that of the valuing a European swaption in interest rate markets. It has been proved that a modified Black future pricing closed form solution can be derived to price CDSO, by which the model follows.
It is important to notice that the CDSO will be in null, if the reference name defaults before the maturity of the option. Sometimes people would be interested in buying protection before the maturity the option along with the CDSO. The fair value of this upfront payment, called knockout value, is the value of protection of the underlying CDS from the settlement date of the option until the start date of the underlying.
When we price the CDOS using this model, we would expect that the volatility could be implied from the market. If there is no liquid option market for a given name, the volatility information could be found by proxy to other names. If the implied volatility cannot be found from the market, a historical analysis, as proposed by Hull and White1, would be used to find a reasonable estimation.
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