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Register a new userThe Computational Complexity of Financial Networks with Credit Default Swaps
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The 2008 financial crisis has been attributed to excessive complexity of the financial system due to financial innovation. We employ computational complexity theory to make this notion precise. Specifically, we consider the problem of clearing a financial network after a shock. Prior work has shown that when banks can only enter into simple debt contracts with each other, then this problem can be solved in polynomial time. In contrast, if they can also enter into credit default swaps (CDSs), i.e., financial derivative contracts that depend on the default of another bank, a solution may not even exist. In this work, we show that deciding if a solution exists is NP-complete if CDSs are allowed. This remains true if we relax the problem to $varepsilon$-approximate solutions, for a constant $varepsilon$. We further show that, under sufficient conditions where a solution is guaranteed to exist, the approximate search problem is PPAD-complete for constant $varepsilon$. We then try to isolate the origin of the complexity. It turns out that already determining which banks default is hard. Further, we show that the complexity is not driven by the dependence of counterparties on each other, but rather hinges on the presence of so-called naked CDSs. If naked CDSs are not present, we receive a simple polynomial-time algorithm. Our results are of practical importance for regulators stress tests and regulatory policy.
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We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net value of the contract at the relevant default times. We allow for correlation between the default times of the investor, counterparty and underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models. We then specialize our analysis to Credit Default Swaps (CDS) as underlying portfolio, generalizing the work of Brigo and Chourdakis (2008) [5] who deal with unilateral and asymmetric counterparty risk. We introduce stochastic intensity models and a trivariate copula function on the default times exponential variables to model default dependence. Similarly to [5], we find that both default correlation and credit spread volatilities have a relevant and structured impact on the adjustment. Differently from [5], the two parties will now agree on the credit valuation adjustment. We study a case involving British Airways, Lehman Brothers and Royal Dutch Shell, illustrating the bilateral adjustments in concrete crisis situations.
Recently, incomplete-market techniques have been used to develop a model applicable to credit default swaps (CDSs) with results obtained that are quite different from those obtained using the market-standard model. This article makes use of the new incomplete-market model to further study CDS hedging and extends the model so that it is capable treating single-name CDS portfolios. Also, a hedge called the vanilla hedge is described, and with it, analytic results are obtained explaining the striking features of the plot of no-arbitrage bounds versus CDS maturity for illiquid CDSs. The valuation process that follows from the incomplete-market model is an integrated modelling and risk management procedure, that first uses the model to find the arbitrage-free range of fair prices, and then requires risk management professionals for both the buyer and the seller to find, as a basis for negotiation, prices that both respect the range of fair prices determined by the model, and also benefit their firms. Finally, in a section on numerical results, the striking behavior of the no-arbitrage bounds as a function of CDS maturity is illustrated, and several examples describe the reduction in risk by the hedging of single-name CDS portfolios.
We propose a novel credit default model that takes into account the impact of macroeconomic information and contagion effect on the defaults of obligors. We use a set-valued Markov chain to model the default process, which is the set of all defaulted obligors in the group. We obtain analytic characterizations for the default process, and use them to derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupled with default contagion could have the leading component of the total default risk.
We test the hypothesis that interconnections across financial institutions can be explained by a diversification motive. This idea stems from the empirical evidence of the existence of long-term exposures that cannot be explained by a liquidity motive (maturity or currency mismatch). We model endogenous interconnections of heterogenous financial institutions facing regulatory constraints using a maximization of their expected utility. Both theoretical and simulation-based results are compared to a stylized genuine financial network. The diversification motive appears to plausibly explain interconnections among key players. Using our model, the impact of regulation on interconnections between banks -currently discussed at the Basel Committee on Banking Supervision- is analyzed.
Academics and practitioners have studied over the years models for predicting firms bankruptcy, using statistical and machine-learning approaches. An earlier sign that a company has financial difficulties and may eventually bankrupt is going in emph{default}, which, loosely speaking means that the company has been having difficulties in repaying its loans towards the banking system. Firms default status is not technically a failure but is very relevant for bank lending policies and often anticipates the failure of the company. Our study uses, for the first time according to our knowledge, a very large database of granular credit data from the Italian Central Credit Register of Bank of Italy that contain information on all Italian companies past behavior towards the entire Italian banking system to predict their default using machine-learning techniques. Furthermore, we combine these data with other information regarding companies public balance sheet data. We find that ensemble techniques and random forest provide the best results, corroborating the findings of Barboza et al. (Expert Syst. Appl., 2017).
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