  In this work we consider three problems of the standard market approach to
pricing of credit index options: the definition of the index spread is not
valid in general, the usually considered payoff leads to a pricing which is not
always defined, and the candidate numeraire one would use to define a pricing
measure is not strictly positive, which would lead to a non-equivalent pricing
measure.
  We give a general mathematical solution to the three problems, based on a
novel way of modeling the flow of information through the definition of a new
subfiltration. Using this subfiltration, we take into account consistently the
possibility of default of all names in the portfolio, that is neglected in the
standard market approach. We show that, while the related mispricing can be
negligible for standard options in normal market conditions, it can become
highly relevant for different options or in stressed market conditions.
  In particular, we show on 2007 market data that after the subprime credit
crisis the mispricing of the market formula compared to the no arbitrage
formula we propose has become financially relevant even for the liquid
Crossover Index Options.
