Abstract Regulators charged with monitoring systemic risk need to focus on sentiment as well as narrowly defined measures of systemic risk. This chapter describes techniques for jointly monitoring the co-evolution of sentiment and systemic risk. To measure systemic risk, we use Marginal Expected Shortfall. To measure sentiment, we apply a behavioral extension of traditional pricing kernel theory, which we supplement with external proxies. We illustrate the technique by analyzing the dynamics of sentiment before, during, and after the global financial crisis which erupted in September 2008. Using stock and options data for the S&P 500 during the period 2002–2009, our analysis documents the statistical relationship between sentiment and systemic risk.

Keywords Systemic risk, Marginal Expected Shortfall, Pricing Kernel, Overconfidence, Optimism; JEL Codes: E61, G01, G02, G28

Introduction

The report of the Financial Crisis Inquiry Commission (FCIC, 2011) emphasizes the importance of systemic risk and sentiment. These two concepts, and the relationship between them, are important for regulatory bodies such as the Financial Stability Oversight Council (FSOC) who, with the support of the Office of Financial Research (OFR), is charged with the responsibility for monitoring systemic risk throughout the financial system. This chapter describes tools regulators can use to monitor sentiment and its impact on systemic risk.

Abstract From the financial supervisor's point of view, an early warning system involves an ex ante approach to regulation, targeted to predict and prevent crises. An efficient EWS allows timely ex ante policy action and can reduce the need for ex post regulation. This chapter builds on existing microprudential and macroprudential early warning systems (EWSs) to propose a hybrid class of models for systemic risk, incorporating the structural characteristics of the financial system and a feedback amplification mechanism. The models explain financial stress using data from the five largest bank holding companies, regressing institutional imbalances using an optimal lag method. The z-scores of institutional data are justified as explanatory imbalances. The models utilize both public and proprietary supervisory data. The Systemic Assessment of Financial Environment (SAFE) EWS monitors microprudential information from systemically important institutions to anticipate the buildup of macroeconomic stresses in the financial markets at large. To the supervisor, SAFE offers a toolkit of possible institutional actions that can be used to diffuse the buildup of systemic stress in the financial markets. A hazard inherent in all ex ante models is that the model's uncertainty may lead to wrong policy choices. To mitigate this risk, SAFE develops two modeling perspectives: a set of medium-term (six-quarter) forecasting specifications that gives policymakers enough time to take ex ante policy action, and a set of short-term (two-quarter) forecasting specifications for verification and adjustment of supervisory actions. Individual financial institutions may utilize the public version of SAFE EWS to enhance systemic risk stress testing and scenario analysis.

In order to fully understand and analyze systemic risk, it is first necessary to understand the system and its components. This means having a consistent representation of the ‘stuff’ of which the system is made up – the business entities, the contracts between them and the securities that are traded.

Classification is intimately bound up in semantics as we shall see. To create a formal representation of securities contracts for example, one must start by classifying them into different types.

In order to represent the system as a whole – the system within which systemic risk arises – there are two things which need to be represented formally: the components of the system; and the ways in which these inter-relate. Representing the components is relatively simple: this is a matter of formally representing financial instruments and the entities that issue them, trade them and hold positions in them. This is a prerequisite to modeling the overall system as a web of connections between and among those instruments and entities.

A common fallacy is to think that representing financial instruments is a matter of data. Because instruments have a lot of data about them, and because these are maintained in databases, it is frequently assumed that representing those instruments is a data issue, and that solutions to the problems of representing and understanding systemic risk must be technical solutions.

This is not the case. Technical solutions are exactly that – solutions to some problem. In order to develop the right technical solutions, one must first formally set out the problem to be solved.

Accounting and Systemic Risk: An Introduction

During the most recent financial crisis the role accounting played in exacerbating the effects of the crisis seemed to be a regular focus of debate in academic, analyst/investor, media and policy circles. This debate focused on several issues including: the use of fair value accounting, securitization and related entities off-balance sheet treatment, derivatives especially related to credit default swaps and whether accounting exacerbated pro-cyclicality. Barth and Landsman (2010), Laux and Leuz (2010) and Ryan (2008) discuss and provide useful synopses of the academic work on these issues.

Most of the published academic work tried to assess whether the application of fair value actually caused or at least added to the systemic risk. The broad consensus seems to be that it is not possible to demonstrate this association let alone any causation. Many publications and commentators also discuss a need for shifting from opacity to greater disclosures with varying degrees of specificity.

In contemplating what would be useful for this Handbook it seemed important to consider what we could provide that added some insight for our readers. My own view, formed while observing this late 2000's crisis unfolding from inside an investment bank in multiple roles as well as participating indirectly in accounting regulation and academic analysis, suggested that the role accounting played in exacerbating the systemic risk would be hard for academics to validate in the systematic way that is necessary for a credible publication.

Data for Systemic Risk

Whatever models may be constructed to assess systemic risk, they will require data to evaluate. This Part of this book explores the data needs for evaluating systemic risk, and describes the many challenges in meeting these data needs effectively.

Systemic risk models are particularly complicated because they are aggressively non-linear – an entity is either able to meet its contractual obligations or it is not, and which of the two scenarios we are in can affect the solvency of many other entities – and furthermore have heavy interlinkage between model entities so that independence assumptions are almost never possible. In consequence, the common mathematical simplifications, of linearity and independence, cannot be made. This leads to the need for models that are far more complex, potentially require Monte Carlo simulations to solve, and rely upon a large body of data and computation. In short, a large variety of detailed (granular) data is likely to be required, from a range of market participants. The size of this dataset makes computational assessment imperative: its complexity makes purely computational evaluation challenging. The five chapters in this Part together elucidate this challenge and also suggest directions toward a solution.

Abstract This chapter surveys models of counterparty contagion and their application in systemic risk management, emphasizing the network of counterparty relationships. It addresses how counterparty contagion contributes to systemic risk in combination with other sources of risk, and how models of counterparty contagion can be used to attribute systemic risk to participants in the financial system. The article discusses challenges and possible progress to be made in modeling the counterparty network and the dynamics of the financial system.

Introduction

This survey attempts to present a unified view of a mushrooming literature on counterparty contagion and its significance for systemic risk. This literature is so broad as to include mathematical treatments of random graphs, interacting particle systems, and Markov processes, but also financial theorizing about such topics as balance sheet constraints and haircuts in collateralized lending, and also empirical studies of data provided by banking regulators. Contagion is distinguished from correlation between firms that does not feature a causal link; counterparty contagion as mediated by various kinds of bilateral deals is distinguished from other forms of contagion that are intermediated by markets (§20.2).

The intent in producing this Handbook is to familiarize researchers and policy makers with the many aspects of systemic risk. The Handbook contains some 32 chapters prepared by experts from a multitude of academic and professional backgrounds. What will become clear to the reader are both the complexity of systemic risk and the necessity for bringing together multiple academic disciplines to better understand systemic risk and for designing policies to mitigate the impact of a systemic crisis upon the global economy. Recent history has shown us not only the enormous cost of a systemic crisis but also how woefully unprepared and illequipped governments and private markets have been to prevent a systemic crisis or minimize its impact.

The first issue in addressing systemic risk is to define the system. Despite the large volume of recent articles on the topic of systemic risk, there has been little attention paid to what is endogenous to the system and events that are external. The financial system is a system in which humans, their emotions, politics and responses to incentives play a critical role. The topology of the system is extremely complex, dynamic, and not well studied. The system does not recognize national boundaries. Events in the US have impacted the markets across the globe. European debt crisis is impacting the Americas, Africa, and Asia. The common use of the terms “Wall Street” and “Main Street” seems to suggest that the two are separable.

Systemic Risk and Mathematical Finance

The chapters in this part represent a range of approaches to modeling and understanding systemic risk within a mathematical framework. While the subject is still in its infancy, the five chapters here show there are many interesting challenges for mathematicians looking to enter this area.

Rogers and Zaczkowski construct a continuous-time equilibrium model to demonstrate how financial markets affect the ‘real’ economy, particularly through random shocks. Their investigation includes simulating the parts of this economy to show where regulations are needed to control systemic risk.

Grasselli and Ismail also model the economy in an agent-based manner. They focus on interbank lending and with numerical solutions analyze the formation of banking systems and their needs and design for investors. This chapter adapts the tools of network models and cellular automata and shows their importance for the systemic risk problem.

The two chapters by Garnier, Papanicolaou and Yang and by Fouque and Sun, bring large deviation analysis to bear on stochastic models where firms are connected to other firms in a mean-field manner. The models are different, but similar in spirit and aim to capture the small probability with which the interconnectedness can bring down the whole.

The chapter of Choi and Douady takes a dynamical systems approach in which a financial crisis such as the recent one is related to the onset of chaos in the system. Within this framework, they are able to interpret specific crises and the effects of policies such as quantitative easing.

Abstract This chapter begins by describing the current financial information processing environment in a typical financial services firm. Then it points to the many places in this environment where data of value for systemic risk assessment can be found. This leads to an assessment of the data elements that are likely to be found with moderate ease and those that will likely be more difficult to obtain. These will be compared with the data collection mandates being undertaken by the systemic risk regulator and financial market utilities. This assessment of disparate data will set the stage for a discussion of data integration in later chapters of this Part.

Introduction

The global financial crisis highlighted the need for greater availability and transparency of standardized information to assess and monitor systemic risk. During the crisis, regulators and others needed timely information to monitor the health of financial firms, understand their exposures, and assess concentrations and interconnections between firms and within markets. This information was not always readily available. As a result, there has been an intensifying focus on information related to systemic risk oversight.

Systemic risk oversight looks at the risks to the overall financial system and the interactions between financial institutions and between markets. Such oversight has the potential to broaden the regulatory view from the traditional “microprudential” focus on individual institutions to a broader “macroprudential” focus on the financial system and on the potential for contagion in the financial system.

Abstract It has been pointed out in the macroeconomics and financial risk literature that risk-sharing by diversification in a financial network may increase the systemic risk. This means roughly that while individual agents in the network, for example banks, perceive their risk of default or insolvency decrease as a result of cooperation, the overall risk, that is, the risk that several agents may default simultaneously, or nearly so, may in fact increase. We present the results of a recent mathematical study that addresses this issue, relying on a mean-field model of interacting diffusions and its large deviations behavior. We also review briefly some recent literature that addresses similar issues.

Keywords systemic risk, mean field, large deviations, dynamic phase transitions; MSC Codes: 60F10, 60K35, 91B30, 82C26

Introduction

Systemic risk is the risk that a large number of components of an interconnected financial system fail within a short time thus leading to the overall failure of the financial system. What is particularly interesting is that the onset of this overall failure can occur even when the individual agents in the system perceive that their own individual risk of failure is diminished by diversification through cooperation. This phenomenon is described and put into a broader perspective in Haldane's recent presentation (Haldane, 2009), which was the starting point of our own work (Garnier et al., 2012). In this review we first introduce and describe our model for the role of cooperation in determining systemic risk.

Abstract Since the summer of 2007, the financial system has faced two major systemic crises. European banks have been at the center of both crises, particularly of the European sovereign debt crisis. This chapter analyzes the systemic risk of European banks across both crises exploiting the specific institutional nature of the European banking system. We employ the “Systemic Expected Shortfall” concept developed in Acharya et al. (2010) which creates a systemic risk index among financial institutions based on their individual contribution to the capital shortfall of the financial system.We analyze which banks are most systemic in Europe using this measure and its relationship to bank stock returns in cross-sectional tests. We then construct a systemic risk ranking of European banks and European countries as of June 2007 and calculate an estimate of the expected capital shortfall at that point of time. Our market-data based systemic risk measures suggest that markets demanded more capital from banks with high exposures to particularly peripheral countries in Europe, that is, banks’ sovereign debt holdings have been a major contributor to systemic risk. Finally, using hand-collected data of sovereign debt holdings and impairments, we provide estimates of how much capital was needed in the Fall of 2011 to restore confidence in the European banking sector.

Introduction

Since the summer of 2007, the financial system has faced two major systemic crises. While the financial crisis of 2007 to 2009 had its origin in the US housing market, the European sovereign debt crisis that started in 2010 is the result of excessive sovereign debt financed by the banking system.

Algorithmic Trading

Over recent decades, advances in information technology have had a significant impact on the way in which financial markets are functioning. The traditional trading pits were abandoned and replaced by electronic order books. Orders can now be routed to electronic exchanges within fractions of a second from all over the world. This has led to an increased competition between exchanges and to the introduction of new types of trading platforms such as dark pools. As another consequence, it is now possible for computer programs to execute trades without involving humans. This type of trading is called algorithmic trading. In this Part, several aspects of algorithmic trading will be highlighted in two chapters.

The first of the chapters is by C.-A. Lehalle. It starts by giving an overview of the current, fragmented state of electronic markets in Europe and the United States, paying particular attention to the “mechanics” of the various novel trading platforms and to the new phenomenon of high-frequency market making. Highfrequency traders are now an essential part of electronic markets and hold a major share in all market transactions. Their presence has led to strongly increasing updating frequencies of limit order books and to a decrease of tick sizes. Today's trading speeds are so high that the transmission time of signals between the trader's computer and the exchange becomes a critical quantity. Markets therefore are increasingly depending on the performance of the hardware, and the software, components of trading systems.

Abstract A great deal of academic and theoretical work has been dedicated to optimal liquidation of large orders these last twenty years. The optimal split of an order through time (‘optimal trade scheduling’) and space (‘smart order routing’) is of high interest to practitioners because of the increasing complexity of the market micro structure because of the evolution recently of regulations and liquidity worldwide. This chapter translates into quantitative terms these regulatory issues and, more broadly, current market design.

It relates the recent advances in optimal trading, order-book simulation and optimal liquidity to the reality of trading in an emerging global network of liquidity.

Market microstructure modeling and payoff understanding are key elements of quantitative trading

As is well known, optimal (or quantitative) trading is about finding the proper balance between providing liquidity in order to minimize the impact of the trades, and consuming liquidity in order to minimize the market risk exposure, while taking profit through potentially instantaneous trading signals, supposed to be triggered by liquidity inefficiencies.

The mathematical framework required to solve this kind of optimization problem needs:

• a model of the consequences of the different ways of interacting with liquidity (such as the market impact model (Almgren et al., 2005; Wyart et al., 2008; Gatheral, 2010));

• a proxy for the ‘market risk’ (the most natural of them being the high frequency volatility (Aït-Sahalia and Jacod, 2007; Zhang et al., 2005; Robert and Rosenbaum, 2011));

• and a model for quantifying the likelihood of the liquidity state of the market (Bacry et al., 2009; Cont et al., 2010).

Behavioral Finance: Introduction

Behavioral finance is the application of psychology to financial decision making and financial markets. This section consists of three chapters whose content provides perspectives and tools to facilitate the integration of psychological variables into the analysis of systemic risk.

FCIC Report

To set the stage for the issues discussed in this part of the Handbook, consider a series of comments made by the Financial Crisis Inquiry Commission (FCIC) in connection with regulatory failures that occurred before and during the financial crisis that erupted in 2008. In its report, the FCIC draws attention to a series of issues that include the mistaking of concentrated risk for diversification, the lack of a comprehensive framework for assessing systemic risk, and the failure to appreciate the role played by the bubble in housing prices. The following series of excerpts, taken from page xxi of the FCIC report, provide the FCIC's perspective.