Title:Two talks on the structure of financial derivatives
Clearing Payments in Financial Networks with Credit Default Swaps (20 minutes practice talk for EC)
We consider the problem of clearing a system of interconnected banks that have been exposed to a shock on their assets. Eisenberg and Noe (2001) and Rogers and Veraart (2013) showed that when banks can only enter into debt contracts with each other, then there always exists a unique Pareto efficient clearing payment vector and it can be computed in polynomial time.
In the present paper, we show that the situation changes radically when banks can also enter into credit default swaps (CDSs). We first prove the surprising result that with CDSs, there may not even be a clearing vector at all. This implies that the value of a contract may not be well-defined. Furthermore, we prove that even determining whether a clearing vector exists is computationally infeasible in the worst case (NP-hard). We then develop a new analysis framework to derive constraints on the contract space under which these problems are alleviated. Our results can be used to inform the discussion on different policy proposals. We show that routing all contracts via a central counterparty would not even guarantee existence. In contrast, we show that banning “naked” (speculative) CDSs would re-establish an existence guarantee for a unique Pareto efficient clearing payment vector.
An Axiomatic Framework for No-Arbitrage Relationships in Financial Derivatives Markets (10 minutes practice talk for LOFT)
No-arbitrage relationships are statements about prices of financial derivative contracts that follow purely from the assumption that no market participant can make a risk-free profit. They are a fundamental tool of modern finance and basis to all modern market models. The ever-growing complexity of financial derivatives impairs the effectiveness of conventional approaches based on expected payments for understanding these relationships. In this paper, we introduce the Logic Portfolio Theory (LPT), a new framework in typed first-order logic with higher-order functions that allows users to prove no-arbitrage relationships based on the syntactic structure of contracts. We first show that LPT is rich enough to replace informal or stochastic arguments by proving the well-known put-call parity and Merton’s theorem inside the theory. This also yields the most general versions of these no-arbitrage relationships to date. We second show that LPT is general enough to encompass both a simple stochastic model and a purely cash flow oriented model.