Consistent Pricing of CMS and CMS Spread Options - UniCredit ...

copulas and rich enough to produce a natural joint distribution with skew and heavy tails, but
simple enough to maintain tractability.
Extensive numerical tests showed that the standard model recovers spread option prices strikewise
very well, but is inconsistent with the CMS cap market and produces distortions in CMS
spread digitals.
We further numerically analysed the extended model, ie. the effect of a Power-Gaussian copula.
The Power-Gaussian copula smoothed out jumps/kinks present in the correlation skew implied by
the standard model. As a result, CMS spread digital prices were smooth in the extended model,
but the inconsistency to the CMS cap market remained (due to the normal marginals).
Finally, we tested our new model. We found that CMS caps, and as a consequence CMS
floors, swaps and SABR swaptions, were accurately recovered (due to the SABR-like skewed-t
distribution). For lower maturities, the CMS spread option market could be recovered as well, for
higher maturities, high strike spread cap prices were too high, indicating a possible inconsistency
in the CMS and CMS spread market.
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