A Robust Method to Retrieve Option Implied Risk Neutral Densities for Defaultable Assets

Abstract

Risk neutral densities recovered from option prices can be used to infer market participants’ expectations of future stock returns and are a vital tool for pricing illiquid exotic options. Although there is a broad literature on the subject, most studies do not address the likelihood of default. To fill this gap, in this paper we develop a novel method to retrieve the risk neutral probability density function from call options written on a defaultable asset. The primary advantage of the method is that default probabilities inferred by the model can be analytically expressed and, if available, can be incorporated as an input in a ‡flexible, robust and easily implementable manner.

Keywords: option pricing, no-arbitrage constraints, risk neutral density, state price density

JEL Classification: C58, G13