Systemic Risk: An Asymptotic Evaluation

Abstract

The systemic risk (SR) has been shown to play an important role in explaining the …nancial turmoils in the last several decades and understanding this source of risk has been a particular interest amongst academics, practitioners, and regulators. The precise mathematical formulation of the SR is still scrutinised, but the main purpose is to evaluate the …nancial distress of a system as a result of the failure of one component of the …nancial system in question. Many of the mathematical de…nitions of the SR are based on evaluating expectations in extreme regions and therefore, Extreme Value Theory (EVT) represents the key ingredient in producing valuable estimates of the SR and even its decomposition per individual components of the entire system. Without doubt, the prescribed dependence model amongst the system components has a major impact over our asymptotic approximations. Thus, this paper considers various well-known dependence models in the EVT literature that allow us to generate SR estimates. Interestingly, our …ndings reveal sensible results. That is, the SR has a signi…cant impact under asymptotic dependence, while weak tail dependence, known as asymptotic independence, produces an insigni…cant loss over the regulatory capital.

Asymptotics for Systemic Risk With Dependent Heavy-Tailed Losses

“…In this section, we use a transparent definition by Acharya et al (2012) to model the SR, see also Acharya et al (2017), Brownlees and Engle (2017), Asimit and Li (2018). Assume that there are n lines of businesses or legal entities with potential net loss variables Z 1 , ..., Z n , which may depend on each other since these n lines operate in similar macroeconomic environments.…”

“…In the wake of the financial crisis and the collapses of Lehman Brother and AIG, systemic risk (SR), considered as the risk of collapse of an entire financial system, has been widely used to explain the recent financial turmoils for insurance/actuarial and financial industries; some recent papers include Acharya et al (2012Acharya et al ( , 2017, Adrian and Brunnermeier (2016), Brownlees and Engle (2017), and Asimit and Li (2018), among many others. This topic is of particular relevance to insurers who play a significant role in the economy as suppliers of protection against financial and economic risks.…”

“…Asymptotic evaluations of the MES were investigated in Asimit and Li (2016). A variate of variants on MES including Conditional Tail Expectation, Marginal Mean Excess, and their asymptotic approximations have appeared in the insurance and actuarial science literature, see Asimit et al (2011), Hua and Joe (2011), Das and Fasen (2018), Asimit and Li (2018). The determinants found in the literature provide us a guidance for dependent heavy-tailed losses in our model.…”

Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations

“…Calculating or estimating systemic risk allocations given an unconditional joint loss distribution is in general challenging since analytical calculations often require to know the joint distribution of the marginal loss and the aggregated loss, and crude Monte Carlo estimation suffers from the rare-event characters of the crisis event. For computing CoVaR, CoES and MES, Mainik and Schaanning (2014), Bernardi et al (2017) and Jaworski (2017) derived formulas based on the copula of the marginal and the aggregated loss; Asimit and Li (2018) derived asymptotic formulas based on extreme value theory; and Girardi and Ergün (2013) estimate CoVaR under a multivariate GARCH model. Chiragiev and Landsman (2007), Dhaene et al (2008), Furman and Landsman (2008) and Vernic (2006) calculated Euler allocations for specific joint distributions.…”