Equity Hybrid Derivatives

CHAPTER 6

Credit Modeling

6.1 INTRODUCTION

The growth witnessed in the credit derivatives market in recent years has led to the introduction of equity hybrid structures that depend on the creditworthiness and the performance of an equity underlying. Convertible bonds constituted the first generation of these structures and are still the most liquid of them, while the equity default swap remains the main innovation in this field.

This chapter presents a methodology to value derivative securities written on equity underlyings subject to credit risk. Arbitrage-free valuation techniques are employed, and the methodology is applied to derivative securities written on assets subject to default risk as well as to pure credit derivative instruments.

6.2 BACKGROUND ON CREDIT MODELING

The risk of default is the financial loss that a counterparty would bear if a reference entity does not honor its commitments. This is in general called a credit event and could range from downgrades by a rating agency to failure to pay debt to complete liquidation. In theory, every financial transaction embeds this kind of risk regardless of the counterparties involved. Estimating the likelihood of occurrence of a credit event is the center of any methodology aiming at modeling credit risk or default risk. However, this is not sufficient for the pricing of contingent claims sensitive to default risk. Indeed, we need to model the loss given default (or recovery), risk-free interest rates, and in the case of ...