Has anyone tried calibrating a reduced form loss model (such as the SPA model or the Schonbucher version) to both the tranche spreads and the index option premiums? The index option premiums are usually consistent with a lognormal distribution of the option payoff (which includes defaults prior to the expiry + the standard CDS option payoff on the remaining notional) as this is the standard model (c.f. Bloomberg documentation, Pedersen's Lehman paper). Therefore, in the case of a default, the index spread must reduce to preserve a lognormal distribution in the payoff. This is exacerbated by the fact that there is a greater default probability at higher spreads.Most indices have low base correlations... especially in the equity tranche. This means that the loss distribution is "largely" constrained to the lower loss tranches. However, when I try to fit a particular parametric form to the default intensity (conditional on a given number of defaults) and hence the transition rates and loss distribution, I cannot find a parametric form which reduces the spread upon default but allows a loss distribution consistent with the tranche spreads.Anyone had any success with this?

Can you share Pedersen's Lehman paper please ?JI don't understand your problemIn fact the first problem is to find the initial default intensity (or default probability p_x(0,T) for all T) which fits the tranche spreadsAfter that you can take a special diffusion for your intensity (HW, ...) but you cannot calibrate the volatility etc, ....Options in the market have short maturity 3m and i think option on equity tranche is not trade because you cannot suppose that there isn't any loss. However, on option on mezzanine 3m you can suppose a lognormal distribution.

Pedersen's Lehman paper is on this forum on the thread "Index CDS Option / CDX (TRACX) Option".Although simplistic, it is the model most used in the market.To explain further:Index options are now available out to 1-year with several strikes. As the payoff contains both the forward CDS and payments for any default prior to expiry, the market premiums should contain information on market expectations of spread distribution + loss distribution. If we further try to use an implied loss distribution generated from tranche spreads, we should be able to imply the spread distribution for a given loss...Anyone had experience with this?