Pricing Counterparty Risk Using Good Deal Bounds∗

We develop a method for pricing counterparty risk by using good deal bounds. The method imposes a new restriction in the arbitrage free model by setting upper bounds on the Sharpe ratios of the assets. The potential prices which are eliminated represent unreasonably good deals. The constraint on the Sharpe ratio translates into a constraint on the stochastic discount factor. Thus, one can obtain tight pricing bounds. Previous literature on counterparty risk and good deal bounds involved structural models. We allow for counterparty risk to be given by intensity-based models. Also, previous literature on counterparty risk with intensity models uses pricing directly under the risk neutral measure which is not unique. We provide a link between the objective probability measure and the range of potential risk neutral measures which has an intuitive economic meaning. Also, we study numerically the tightness of the bounds and underline the use of good deal bounds for risk management. In this context, we also study portfolio effects on the good deal bounds prices.