Research

AC3R Research Themes

21st-century risks

Analyzing new threats - from financial contagion to climate crises to pandemics: This theme aims to develop new approaches to conduct modern risk evaluation, responding to the pervasive uncertainty surrounding 21st-century global crises. Modern risks associated with financial-economic instability, environmental changes, technological breakdowns and epidemic outbreaks are characterized by their contagious amplification over time and space, i.e., across markets, regions, and networks. This theme provides new probabilistic, statistical and econometrics methods to fundamentally advance the modeling and measurement of modern shocks and fragilities, with a focus on financial-economic (in)stability.

Social-economic resilience

Understanding how systems recover and adapt: This theme aims to improve our understanding of what makes financial institutions, firms, households and societies resilient to 21st-century risks. The degree of adaptability and innovativeness of human capital along with an equitable allocation of resources and services are suggested as key drivers of resilience, but our understanding of the precise mechanisms is in its infancy. This theme provides modern analyses to bear on the drivers of resilience and adequate measures that enhance socio-economic stability.

Regulation and policy

Designing legal structures to make risks manageable: This theme aims to unravel the modern interplay between the tools of regulators and policymakers, including financial regulation, monetary policy and investment incentives in securing financial-economic stability. It also analyzes the role of financial institutions, and in particular insurers and pension funds, in providing long-term capital and investment commitment.

AC3R Selected Research Articles

Property without law -- Personalized property rights through smart contracts on the Blockchain

Stefan Bechtold, Giuseppe Dari-Mattiacci, Edoardo D. Martino and Gideon Parchomovsky

Emerging technologies for the automatic enforcement of contracts, conventionally referred to as smart contracts, have the potential to realize Professor Alan Schwartz’ ideal of an efficient contract law for sophisticated parties, as they reduce the cost of textualist enforcement, added contingencies, and privately-provided templates, and offer a way to get around mandatory rules relating to such matters as contract modifications, penalty clauses, and substantial performance. They also enable contracting parties to create personalized property rights free of legal restraints. Through automatic enforcement, a contract term can be directly included in contracts with subsequent transferees of the asset. Smart contracts thus turn mere contractual rights into de facto property rights that “run with the (digital) asset.” Breach is made impossible by the very nature of the automatic enforcement system, and notice is assured by distributed and readily accessible ledgers. Compared to traditional property rights, these “property-without-law” rights are more easily customizable ex ante – as they are not bound by the numerus clausus principle – and stronger ex post – because courts cannot modulate enforcement. We document this phenomenon, explore its potential and vulnerabilities, discuss examples in intellectual property, real estate, organizations, and financial contracts, and re-examine the role of property law in a world where technology, rather than law, turns promises into assets.

Spatiotemporal Hawkes processes with a graphon-induced connectivity structure

Justin Baars, Roger J. A. Laeven and Michel Mandjes

We introduce a spatiotemporal self-exciting point process, boundedly finite both over time and space, with excitation structure determined by a graphon. This graphon Hawkes process generalizes both the multivariate Hawkes process and the Hawkes process on a countable network, and despite being infinite-dimensional, it is surprisingly tractable. After proving existence, uniqueness and stability results, we show, both in the annealed and in the quenched case, that any graphon Hawkes process can be obtained as the suitable limit of d-dimensional Hawkes processes. Furthermore, in the stable regime, we establish an FLLN and an FCLT for our infinite-dimensional process, while in the unstable regime we prove divergence. Finally, we exploit a cluster representation to derive fixed-point equations for the respective Laplace functional, for which we set up a recursive approximation procedure. We apply these results to show that, starting with multivariate Hawkes processes converging to stable graphon Hawkes processes, the limits d → ∞ and t →∞ commute.

Achieving safety: Personal, private, and public provision

Enrico C. Perotti and Spyros Terovitis

We study how a primary need for minimum safety affects investment choices. In addition to risky projects, agents may choose to invest in personal assets they can control. Investing in personal assets serves as self-insurance, as they ensure a higher minimum return but offer a lower expected return than the risky project offers. In autarky, investors ensure a minimum return by personal assets, besides investing in the risky project. Private intermediaries and a safe rate arise endogenously to limit inefficient self-insurance, with self-insured investors holding bank equity to safeguard private safe debt. The endogenous conflict over interim risk choices is resolved by demandable debt, forcing early liquidation in states in which the ability of banks to repay debt holders remains uncertain. Our work highlights the unintended consequences of public provision of safety for private provision of safety and aggregate investment, demonstrating that these effects depend critically on whether public provision takes the form of public debt or deposit insurance.

Saddlepoint approximations for Hawkes jump-diffusion processes with an application to risk management

Yacine Aït-Sahalia and Roger J. A. Laeven

We propose a statistical model based on Hawkes processes in which large financial losses can arise in close succession serially as well as cross-sectionally. We derive in closed form saddlepoint approximations to the tails of profit and loss distributions, both marginal and joint, and use them to construct explicit risk measure formulae that account for the fact that a given financial institution’s losses make it more likely that that institution will experience further losses, and that other financial institutions will experience losses as well. These closed-form risk measures can be used for comparative statics, parameter calibration, and setting capital requirements and potential systemic risk charges.

Jump contagion among stock market indices: Evidence from option markets

H. Peter Boswijk, Roger J. A. Laeven, Andrei Lalu and Evgenii Vladimirov

We analyze the contagious propagation of jumps among international stock market indices, using a rich panel of high-frequency stock and options data (692,892 option contracts) over the period 2006–2015. We propose a bivariate option pricing model designed to allow for time and space amplification of jumps in option markets. We develop a semi-parametric estimation procedure, which employs a continuum of moment conditions in GMM with implied states and non-parametric high-frequency spot volatility estimation. A partial-information approach is introduced to reduce the computational complexity arising in the multivariate setting. We find statistical evidence of jump contagion both within and between stock market indices. Our results reveal that jump contagion from the US to the UK is more pronounced than vice versa, whereas the jump contagion effects between the US and Germany stand on equal footing. We illustrate the statistical and economic importance of capturing jump contagion for risk management, option pricing, and scenario analysis. We show that accounting for jump contagion, employing scenarios based on the Global Financial Crisis, leads to an increase of capital requirements in the UK from 6.3% to 8.4% for each unit invested.

Estimating option pricing models using a characteristic function-based linear state space representation

H. Peter Boswijk, Roger J. A. Laeven and Evgenii Vladimirov

We develop a novel filtering and estimation procedure for parametric option pricing models driven by general affine jump-diffusions. Our procedure is based on the comparison between an option-implied, model-free representation of the conditional log-characteristic function and the model-implied conditional log-characteristic function, which is functionally affine in the model’s state vector. We formally derive an associated linear state space representation and the asymptotic properties of the corresponding measurement errors. The state space representation allows us to use a suitably modified Kalman filtering technique to learn about the latent state vector and a quasi-maximum likelihood estimator of the model parameters, for which we establish asymptotic inference results. Accordingly, the filtering and estimation procedure brings important computational advantages. We analyze the finite-sample behavior of our procedure in Monte Carlo simulations. The applicability of our procedure is illustrated in two case studies that analyze S&P 500 option prices and the impact of exogenous state variables capturing Covid-19 reproduction and economic policy uncertainty.

The euro as an institutionally diverse monetary union

Enrico C. Perotti and Oscar Soons

We analyse the causes and consequences of the adoption of a common currency by countries with persistently different institutional quality, as in the euro area. A diverse monetary union has redistributive effects on investment and fiscal capacity across countries and societal groups. A common currency leads to rapid market adjustments while nominal wages lag, and institutional differences persist, resulting in hidden currency revaluations and devaluations. Productive and fiscal capacity benefit in core countries with stronger institutions, while public spending is less constrained in periphery countries with weaker institutions just as their fiscal capacity is reduced by revaluation. Firms and employment gain in core countries, along with savers in periphery countries.

Localizing strictly proper scoring rules

Ramon F. A. de Punder, Cees G. H. Diks, Roger J. A. Laeven and Dick J. C. van Dijk

When comparing predictive distributions, forecasters are typically not equally interested in all regions of the outcome space. To address the demand for focused forecast evaluation, we propose a procedure to transform strictly proper scoring rules into their localized counterparts while preserving the score divergence and strict propriety. This is accomplished by applying the original scoring rule to a censored distribution. Our procedure nests the censored likelihood score as a special case. Among a multitude of others, it also implies a class of censored kernel scores that offers a (possibly multivariate) alternative to the threshold weighted Continuously Ranked Probability Score (twCRPS), extending its local propriety to more general weight functions than single tail indicators. Within this localized framework, we obtain a generalization of the Neyman Pearson lemma, establishing the censored likelihood ratio test as uniformly most powerful. For other tests of localized equal predictive performance, results of Monte Carlo simulations and empirical applications to risk management, inflation and climate data consistently emphasize the excellent power properties of censoring versus other localization methods.

Containing runs on solvent banks: Prioritizing recovery over resolution

Edoardo D. Martino and Enrico C. Perotti

The sudden banking defaults in the spring of 2023 proved current prudential norms insufficient to prevent bank distress. Capital and liquidity norms need to be adjusted. The experience also shows how a lack of credible supervisory tools led to forbearance and finally chaotic public bailouts. An intervention gap arises when viable but undercapitalized banks are at the mercy of runs. Once outflows start to escalate, all that is left is to prepare for resolution and assign losses. We call for new Pillar II – i.e. activated by the supervisor – stabilizing measures, as contingent capital and liquidity tools.

A timely recapitalization option requires stronger supervisory powers to activate a timely going-concern recapitalization, such as by equity conversion of additional Tier 1 contingent convertible debt. One contingent liquidity measure is the automatic activation of redemption charges upon large outflows of uninsured deposits. The goal is to interrupt any self-fulfilling expectation of further outflows. The measure mirrors new US Securities and Exchange Commission norms created for institutional money market funds, the natural benchmark for uninsured corporate deposits. The combination creates a framework for credible interim intervention and a chance to steer solvent banks toward recovery early on rather than settling for forbearance and increasing the probability of resolution and bailouts.

Dynamic return and star-shaped risk measures via BSDEs

Roger J. A. Laeven, Emanuela Rosazza Gianin and Marco Zullino

This paper establishes characterization results for dynamic return and star-shaped risk measures induced via backward stochastic differential equations (BSDEs). We first characterize a general family of static star-shaped functionals in a locally convex Fréchet lattice. Next, employing the Pasch-Hausdorff envelope, we build a suitable family of convex drivers of BSDEs inducing a corresponding family of dynamic convex risk measures of which the dynamic return and star-shaped risk measures emerge as the essential minimum. Furthermore, we prove that if the set of star-shaped supersolutions of a BSDE is not empty, then there exists, for each terminal condition, at least one convex BSDE with a non-empty set of supersolutions, yielding the minimal star-shaped supersolution. We illustrate our theoretical results in a few examples.

Compound multivariate Hawkes processes: Large deviations and rare event simulation

Raviar S. Karim, Roger J. A. Laeven and Michel Mandjes

In this paper, we establish a large deviations principle for a multivariate compound process induced by a multivariate Hawkes process with random marks. Our proof hinges on showing essential smoothness of the limiting cumulant of the multivariate compound process, resolving the inherent complication that this cumulant is implicitly characterized through a fixed-point representation. We employ the large deviations principle to derive logarithmic asymptotic results on the marginal ruin probabilities of the associated multivariate risk process. We also show how to conduct rare event simulation in this multivariate setting using importance sampling and prove the asymptotic efficiency of our importance sampling based estimators.

Robust multiple stopping—A duality approach

Roger J. A. Laeven, John G. M. Schoenmakers, Nikolaus Schweizer and Mitja Stadje

We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights—that is, optimal multiple stopping—for a robust evaluation that accounts for model uncertainty with a dominated family of priors and for general reward processes driven by multidimensional jump-diffusions. Our approach relies on first establishing robust martingale dual representation results for the multiple stopping problem that satisfy appealing almost sure pathwise optimality properties. Next, we exploit these theoretical results to develop upper and lower bounds that, as we formally show, not only converge to the true solution asymptotically, but also constitute genuine prelimiting upper and lower bounds. We illustrate the applicability of our approach in a few examples and analyze the impact of model uncertainty on optimal multiple stopping strategies.