Time-Changed Birth Processes and Multi-Name Credit Derivatives

Abstract

A credit investor such as a bank granting loans to firms or an asset manager buying corporate bonds is exposed to correlated corporate default risk. A multi-name credit derivative is a financial security that allows the investor to transfer this risk to the credit market. In this article, we study the valuation and risk analysis of multi-name derivatives. To capture the complex economic phenomena that drive the pricing of these securities, we introduce a time-changed birth process as a probabilistic model of correlated event timing. The self-exciting property of a time-changed birth process captures the feedback from events that is often observed in credit markets. The stochastic variation of arrival rates between events captures the exposure of firms to common economic risk factors. We derive a closed-form expression for the distribution of a time-changed birth process, and develop analytically tractable pricing relations for a range of multi-name derivatives valuation problems. We illustrate our results by calibrating a tranche forward and option pricer to market rates of index and tranche swaps.