The Limits of Continuous Finance, Network Risk and the Prisoners’ Dilemma

Modern notions of Market Risk are based on the notion of stochastic calculus which is essentially atheoretical about the nature of the shocks that cause changes in asset prices. For example the whole notion of derivatives pricing using techniques such Ito’s Lemma is based on essentially continuous or discrete random changes in asset prices. Enter the Crisis of 2008/2009. The limitations of such models is made clear as the structural relationships between banks comes to the fore in deciding market trading. We are bank A – do we trade with Bank B? We may have exposure to subprime assets through CDOs and other securitized assets. We don’t know how big that exposure is. Bank B may have exposure to subprime assets. B may have exposures to Banks C and D…None of them know what their exposure is. If we transact with Bank B, we take on counterparty risk, which may be much increased by this unknown exposure (credit ratings don’t help much here). Better is to take government money and not take that exposure. Hence interbank funding dries up, and credit spreads rise dramatically. Transaction/Partnering with other members of your network simply becomes too expensive and too risky. This is much like the classic “Prisoners Dilemma” problem where risk aversion and ignorance about others actions produce a suboptimal solution.
What was consequence of this dilemma? High counterparty exposures allow defaults to propagate through the network of counterparties, one by one, the effects increasing as too big/interconnected to fail (TBTF) institutions’ failure are amplified into a failure of the network as a system. Not surprisingly the regulatory response is one of “macroprudential and systemic risk management” and of course call for break up of institutions whose individual failure could cause system wide problems (e.g., the Volcker Rule etc). But let’s go back, it follows that truly understanding systemic effects requires transparency of the underlying exposures (much like having the prisoners in the prisoners’ dilemma be able to communicate). This is one reason (another is reduced settlement risks) for the rise of centralized clearing (CCP), where one entity has transparency into the network and is able to interject using margin requirements, capital injections when the network looks vulnerable. Suddenly risk management for CCPs becomes critical to managing systemic risk for the entire network.