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There seems to be a widely accepted view that the market for credit basket contracts is incomplete. In the real-world market, there simply does not exist a set of hedge instruments to construct a self-financing portfolio replicating the payoff of e.g. a First to Default (FtD) contract. Several authors then draw the conclusion that, due to this incompleteness, the pricing measure is not unique and hence there exist a wide range of allowable arbitrage free prices. Incomplete market => Pricing measure not unique. Fine. This I can accept as I do understand that it is difficult to obtain a perfect match for both dimensions maturity and credit obligour in an illiquid market to rebalance the hedge portfolio continuously. However, if we assume that all instruments in the underlying basket are tradable, liquid, shorting is possible etc, isn't the model complete? I.e is it enough with just the instruments in the underlying basket or do I need to assume additional contracts to complete the model?In Risk-Neutral Correlations in the Pricing and Hedging of Basket Credit Derivatives, Walker claims that it is not enough just assuming that all underlying instruments in the basket are tradable, we need additional fictionous instruments to complete the model. He sets up a one period model for a FtD on two underlying risky assets (S1 and S2). The possible states of the world at the end of the period are1) No defaults2) S1 has defaulted3) S2 has defaulted4) S1 and S2 have defaultedIncluding the risk free asset B in the model, we have 4 outcomes but only 3 building blocks. The price of the FtD can not be fully replicated without including an additional asset. I'm not sure I agree with this model. Is state #4 really relevant? What if we make the period short enough, wouldn't that exclude outcome 4? In addition, what is the price of the FtD at outcome 4 when the risky assets have different recoveries? Without state 4 the model would be complete with just S1, S2 and B and we would have concluded that we don't need to assume additional instruments. It would be interesting to hear anyone's thought about this.Thanks. Edit: The article by Walker has been published in The Journal of Credit Risk which gives it some form of credibility.

You could make a model assumption that defaults cannot be simultaneous, but I think that would make your model impractical. The important question is do you have enough time to rebalance in between the two defaults? If S1 and S2 are close to default, the default of one could push the other into default; or it could make the markets illiquid enough for a day or two during which S2 defaults independently. But I'm not entirely disagreeing with you. There may well be useful work that can be done along the lines you indicate.

I am interested in this as well. It certainly does seem hard to be able to set up a hedge for a derivatives whose payoff is based on a huge discontinuity - ie a good bond going into default.

There are three things going on here. First, credit spreads and the associated default probabilities go up and down all the time. They are correlated to market factors like equity prices (low prices increase risk of default) and interest rates (high interest rates increase risk of default).Second, companies sometimes default. I think defaults are usually a suprise. In other works, most of the volatility in single-name default probability evolution occurs in sizeable jumps. Issuers can evolve smoothly from 1% to 10% chance, but generally they'll go from 10% to 100% with most of the move in a couple of jumps.Third, defaults affect the market perception of other issuer default probabilities. I think this effect is larger (in the sense of creating more total credit risk) than the general evolution. I think this reflects both hidden variables, so a default gives the market information about underlying credit quality, and contagion of default.

Edit: This is a reply to your first post, Aaron. Thanks for your comments, really appreciated.Stubborn as I am, I still want to hold the model assumption of continuously tradable basket members intact. I realize that the discussion then becomes purely academic but my ambition at this stage is just to get a feeling for what is needed to create a complete model. The model is not complete in the sense that I cover all possible risk factors and their dynamics, what I'm aiming for is to create a simple model where we have enough assumptions to avoid an incomplete market. QuoteThe important question is do you have enough time to rebalance in between the two defaults?Yes, very good point. My first thought was: couldn't this be a consequence of working with intensity based models? As opposed to a merton style model where the credit quality of the asset is continuously observable, the default in intensity based models is modeled as a jump process and the discontinuous payout (thanks OMD for the word) is impossible to hedge. However after giving a little thought I realized that the payoff of the FtD is perfectly possible to replicate given 3 or 4 contracts in the model below, which in fact can be regarded as an intensity based model.No I still wonder if it's possible somehow to avoid simultaneous default events in the model, without just explicitly assuming it - that seems to be the key. I realize that two assets with a linear correlation of 1 and with equal value for some credit quality measure would not fit in such a model, but that's a situation I would be happy to ignore.