Abstract
We price vulnerable options - i.e. options where the counterparty may default. These are basically options 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, one can obtain tight pricing bounds. We provide a link between the objective 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 financial products in a consistent way. Specific examples for exchange options and barrier options are computed. Finally, we analyze numerically the behaviour of the good deal pricing bounds interval and analyze the factors that impact its size.