Vulnerable Options and Good Deal Bounds - A Structural Model

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 deal. 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. Finally, we analyze numerically the behaviour of the good deal pricing bounds.

Keywords: incomplete markets, counterparty risk, good deal bounds, vulnerable options

JEL Classification: G13