Dynamics of Market Spread of First-to-Default Swap in an Information-Based Approach

In this paper, we employ an information-based credit risk model to analyze the dynamics of the market spread of First-to-Default Swaps (FtDS), which serve as a foundational framework for understanding more complex multi-name credit derivatives. Specifically, we derive stochastic differential equations satisfied by the market FtDS spread and the first-to-default hazard rate process within the information-based credit risk model, enabling an exploration of how these dynamics are driven by the flow of information regarding multiple correlated defaults. Our findings reveal that the market FtDS spread dynamics are influenced by the quality of information about survival conditions, which is quantified as the discrepancy between the conditional expectations of credit factors under different conditions related to the first default event. By establishing a framework to describe the relationship between information flows regarding the correlated defaults and the price dynamics of credit derivatives dependent on these risks, this study seeks to contribute to advancing the theoretical understanding and valuation of complex credit instruments.