General Equilibrium with Contagion Effects

Projekt Start: 03/2013
Status: Beendet
Forscher: Nicole Branger, Patrick Grüning, Holger Kraft, Christoph Meinerding, Christian Schlag
Kategorie: Financial Markets, Transparency Lab, Systemic Risk Lab
Finanziert von: LOEWE

Topic and Objectives

Stock market meltdowns like the Wall Street Crash of 1929 or the burst of the Dotcom Bubble do not happen at a single day. For instance, on the "Black Thursday", October 24, 1929, U.S. markets fell by 11% at the opening bell. Until November 13, 1929, the Dow Jones Industrial Average decreased further to 198.69 from 305.85 on October 23, 1929. Such a series of adverse events is generally referred to as financial contagion. Since contagion affects the economic conditions for some time period, the question arises how contagion influences the financial market equilibrium in an economy: How is the threat of contagion reflected in prices today, and how do prices change if contagion hits the economy? Do we observe differential pricing in the cross-section if assets differ in their propensity to trigger contagion or in their degree of robustness against contagion risk? How does the threat of contagion affect second moments of returns like volatilities or correlations?

Several approaches to model contagion have been suggested. One strand of literature models contagion as simultaneous Poisson jumps in all assets, while other important contributions use (hidden) Markov chains. Recently, self-exciting processes have also been discussed in the literature. Typically, Markov chain models distinguish between good ("boom") and bad ("depression") states of the world, where in a bad state the probabilities and/or correlations for/between losses are higher than in good states. A typical assumption in these models is that agents are not able to observe the current state of the economy.

In this project, we analyze the impact of contagion risk on asset prices and asset price dynamics in a general equilibrium model with multiple assets. In order to capture contagion effects, we design an appropriate hidden Markov chain model with learning. Recent asset pricing literature has shown that one has to assume stochastic differential utility in order to match key asset pricing figures like the equity premium or the risk-free rate. This complicates the solution of the model significantly. From a methodological point of view, our research thus links to different strands of literature: on the one hand, we build on general equilibrium asset pricing theory with multiple goods and assets. On the other hand, we apply results about nonlinear filtering of a hidden Markov chain in a jump-diffusion framework. Methodologically, the innovation of this project lies in the combination of highly sophisticated asset pricing techniques (stochastic differential utility, multiple Lucas trees, latent state variables) with involved methods from filtering theory (nonlinear filtering of default intensities, hidden Markov chains, self-exciting processes).

On the economic side, we study how the threat of contagion affects prices and price dynamics. First, we explore whether an extra risk premium for contagious jumps is earned in equilibrium and how the threat of contagion affects the risk-free rate in the economy. Second, we study the effect of the shock propagation mechanism on second moments, in particular return volatilities and return correlations of the two risky assets.

Results

Our calibrated model matches empirical figures about the countercyclicality of volatilities and correlations extremely well. The risk of "financial contagion" or "shock propagation" and the imperfect observability of the state of the economy together endogenously create countercyclical second moments of returns in equilibrium. In terms of their beliefs about the state of the economy it seems to take investors a rather long time to regain confidence after negative shocks. To capture this stylized fact in the model we assume that the transition from the bad back to the good state is not linked to a particular upward move in endowments, so that this type of regime switch is unobservable, and the investor learns about it only gradually over time. So she needs a rather long stretch of "good" observations in the sense of an absence of downward jumps, before she is becoming confident enough that the economy is again back in the good state. The representative agent in our economy has recursive preferences and a preference for early resolution of uncertainty. Therefore, equilibrium prices and returns depend on the estimated (i.e., filtered) probability p of being in the good state, which the investor continuously updates by observing the output streams of the two trees. Unlike in usual Hidden Markov Models, the estimate p exhibits countercyclical volatility in that it is much more volatile close to 0, i.e., when the investor is relatively certain to be in the bad state, than compared to when it is close to 1. We show that these dynamics can only be generated in a model with uncertainty about shock propagation. Since in our equilibrium model the estimated state is a key input, model-generated return volatilities and correlations are countercyclical as well because of the shock propagation feature in our model.

Besides, our model can match a lot of other stylized facts about asset returns. E.g., our model is able to produce large jump risk premia due to the shock propagation feature, i.e., due to the fact that jumps in one asset can cause a switch to a regime with higher overall jump intensities. Moderate jump sizes around -6% in the output streams are sufficient to generate a reasonable equity premium, so that we do not have to rely on a "Peso problem" type of story. Our model thus provides a possible solution to a famous critique of disaster models. This critique states that disaster models need very extreme one-period consumption growth shocks to generate a high equity premium, whereas consumption disasters in the data often stretch out over many years. This issue is also discussed in more detail in SAFE Working Paper No. 11.

Zugehörige publizierte Papers

Autor(en) Titel Jahr Forschungs­bereich Keywords
Nicole Branger, Holger Kraft, Christoph Meinerding The Dynamics of Crises and the Equity Premium
Review of Financial Studies
2016 Financial Markets, Transparency Lab, Systemic Risk Lab General Equilibrium, Asset Pricing, Recursive Preferences, Long-Run Risk, Disaster Models
Nicole Branger, Holger Kraft, Christoph Meinerding Partial Information about Contagion Risk, Self-Exciting Processes and Portfolio Optimization
Journal of Economic Dynamics and Control
2014 Financial Markets, Transparency Lab, Systemic Risk Lab Asset Allocation, Contagion, Nonlinear Filtering, Hidden State, Self-exciting Processes

Zugehörige Working Papers

Nr. Autor(en) Titel Jahr Forschungs­bereich Keywords
28 Nicole Branger, Holger Kraft, Christoph Meinerding Partial Information about Contagion Risk, Self-Exciting Processes and Portfolio Optimization 2013 Financial Markets, Transparency Lab, Systemic Risk Lab Asset Allocation, Contagion, Nonlinear Filtering, Hidden State, Self-exciting Processes
11 Nicole Branger, Holger Kraft, Christoph Meinerding The Dynamics of Crises and the Equity Premium 2013 Financial Markets, Transparency Lab, Systemic Risk Lab General Equilibrium, Asset Pricing, Recursive Preferences, Long-Run Risk, Disaster Models
34 Nicole Branger, Patrick Grüning, Holger Kraft, Christoph Meinerding, Christian Schlag Asset Pricing Under Uncertainty About Shock Propagation 2013 Financial Markets, Transparency Lab, Systemic Risk Lab General Equilibrium, Contagion Risk, Partial Information, Filtering, Recursive Utility

 

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