A Mean Field Game Model of Credit Derivatives Markets

Abstract

The modern credit market is enormous, in both the basic cash bond market and in the credit derivatives markets, with trillions of dollars in notional outstanding. These markets, and in particular the credit derivatives markets, are also of extreme interest to regulators because of their role in the 2008 financial crisis and several other large financial disasters, with regulators in recent years making a strong push for requirements that credit market trades be cleared centrally in order to improve liquidity and transparency. The credit derivatives markets can be challenging to analyze, for a variety of reasons. In particular, liquidity within the credit market as a whole can be difficult to find, particularly in many low-credit securities. We use a mean field game (MFG) approach to model a representative one-contract credit derivative market, with the understanding that such a framework can be applied to specific segments of the credit derivatives markets with higher liquidity and a larger number of market participants. Our model specifies two types of investors: hedging and speculative, with very different motivations. We derive and analyze the equilibrium of this system using both analytic and numerical methods, and formulate a characterization of the equilibrium in an extended model where we also consider the participation of a large bulge bracket bank.