Static Hedging of Defaultable Contingent Claims: A Simple Hedging Scheme Across Equity and Credit Markets

Abstract

This paper proposes a simple scheme for static hedging of defaultable contingent claims. It generalizes the techniques developed by Carr and Chou (1997), , and Takahashi and Yamazaki (2009a) to credit-equity models. Our scheme provides a hedging strategy across credit and equity markets, where suitable defaultable contingent claims are accurately replicated by a feasible number of plain vanilla equity options. Another point is that shorter maturity options are available to hedge longer maturity defaultable contingent claims. Through numerical examples, it is shown that the scheme is applicable to both structural and intensity-based models.

Recovering subjective probability distributions

“…Static replication strategies composed of available options in markets are an accepted approach in both academia and practice. For example, Takahashi and Yamazaki (2009a, 2009b), Ohsaki and Yamazaki (2011), and Carr and Wu (2014) developed replication methods for long‐term options or defaultable bonds by a static portfolio of plain vanilla options. Variance swaps and their subspecies are replicable by a static option portfolio combined with dynamic trading of the underlying asset.…”