The use of compound options for credit risk modelling

When a company experiences credit-rating downgrades, its equity inevitably drops by a sizable amount as well as the prices of the derivative contracts written on the company’s equity and debt react accordingly. Stemming from the works of Merton (1974), Geske (1977) and Geske (1979), a new structural model of default is introduced. As the reference firm is assumed to have issued n bonds maturating at different future dates, the firm’s equity is modelled as an n fold compound option written on the firm’s assets and struck at the face values of the bonds outstanding. This framework is used across the chapters of the thesis, each constituting a different and original piece of research. The first paper, ‘The Impact of Credit Risk on Equity Options’ analyses the effect of credit risk on equity options. In order to conduct the analysis, a measure of impact of credit risk option contracts is introduced. Consistently with the theory and economic intuition, the option contracts which are mostly affected by changes in the underlying default risk are put options. I further document that their pricing is consistent with the probability of default embedded in the credit default swaps written on the same reference entity. It is also shown that the implied volatilities estimated á la Black-Scholes tend to average out the effect of credit risk over the moneyness space, leading to potential biases when applied for risk management purposes. The second paper, ‘Credit Spreads, Leverage and Volatility: A Cointegration Approach’ documents the existence of a cointegration relationship between credit spreads, leverage and equity volatility for a large set of US companies. It is shown that accounting for the long-run equilibrium dynamic is essential to correctly explain credit spread changes. Once credit these variables are correctly modelled, the fit of the regressions sensibly increases if compared to the results of previous research. The third paper, ‘The Option-implied Asset Volatility Surface’ provides a simple way to estimate the option-implied asset volatility surface. To describe the properties of the surfaces, principal component analysis is conducted both across the moneyness and the time-to-maturity dimension, as well as on the overall surface. Finally, the joint evolution of the smirk and the slope of the surface is modelled as a Vector Autoregressive model with exogenous variables. Both slope and smirk appear to be jointly autocorrelated