We price vulnerable derivatives - i.e. derivatives where the counter-
party may default. These are basically the derivatives traded on the OTC
markets. Default is modeled in a structural framework. The technique
employed for pricing is 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, tight
pricing bounds can be obtained. We provide a link between the objec-
tive probability measure and the range of potential risk neutral measures
which has an intuitive economic meaning. We also provide tight pricing
bounds for European calls and show how to extend the call formula to
pricing other nancial products in a consistent way. Finally, we numeri-
cally analyze the behavior of the good deal pricing bounds
