MODELLING THE BID AND ASK PRICES OF ILLIQUID CDSs
CDS (credit default swap) contracts that were initiated some time ago frequently have spreads and/or maturities that are not available on the current market of CDSs, and are thus illiquid. This article introduces an incomplete-market approach to valuing illiquid CDSs that, in contrast to the risk-neutral approach of current market practice, allows a dealer who buys an illiquid CDS from an investor to determine ask and bid prices (which differ) in such a way as to guarantee a minimum positive expected rate of return on the deal. An alternative procedure, which replaces the expected rate of return by an analogue of the Sharpe ratio, is also discussed. The approach to pricing just described belongs to the good-deal category of approaches, since the dealer decides what it would take to make an appropriate expected rate of return, and sets the bid and ask prices accordingly. A number of different hedges are discussed and compared within the general framework developed in the article. The approach is implemented numerically, and example plots of important quantities are given. The paper also develops a useful result in linear programming theory in the case that the cost vector is random.