questions about Pricing a CDS Index Option

When using the cdsprice function to price a CDS index option, adjustments for the forward spreads are needed, as indicated in the following link: http://www.mathworks.com/help/fininst/credit-default-swap-option.html#btyv_kx-1.

However, I don't understand the calculation for the FEP:

FEP = Spread_OptionExpiry * (cdsrpv01(ZeroData,ProbData,Settle,CDSMaturity)... - cdsrpv01(ZeroData,ProbData,Settle,CDSMaturity,'StartDate',OptionMaturity))

From the formula in the text, shouldn't we have

FEP= Spread_OptionExpiry * RPV01_OptionExpiry ?

Obviously, the difference is why we don't set 'CleanRPV01' to false here in function cdsrpv01 for the FEP calculation as we did above for the RPV01_OptionExpiry.

Thanks,

[Bruno Pop-Stefanov]

Xinping,

I am currently looking into it and I'll get back to you soon.

-Bruno

Answer 1

[Bruno Pop-Stefanov]

Xinping,

After looking further, it turns out that the documentation page is, indeed, incorrect in that the pre-computed RPV01s are used to compute the forward spread but the FEP is computed using clean RPV01s.

The line:

"...RPV01s, which will be used later in the computation of the FEP and the adjusted forward spread."

should be changed to

"...RPV01s, which will be used later in the computation of the adjusted forward spread."

Apparently, this comes from the fact that there are several different models for the CDS index option. It's not standardized yet. This page was probably created from different sources, which use different models.

I informed my colleagues and the page should be updated for a future release, using a different model for the FEP and using clean RPV01s for the forward spread.

In the meantime, I would recommend to rely on O'Kane's book, "Modelling Single-name and Multi-name Credit Derivatives" (Wiley, 2008).