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#### Institute

- How does contagion affect general equilibrium asset prices? : [Version: March 13, 2013] (2013)
- This paper analyzes the equilibrium pricing implications of contagion risk in a Lucas-tree economy with recursive preferences and jumps. We introduce a new economic channel allowing for the possibility that endowment shocks simultaneously trigger a regime shift to a bad economic state. We document that these contagious jumps have far-reaching asset pricing implications. The risk premium for such shocks is superadditive, i.e. it is 2.5\% larger than the sum of the risk premia for pure endowment shocks and regime switches. Moreover, contagion risk reduces the risk-free rate by around 0.5\%. We also derive semiclosed-form solutions for the wealth-consumption ratio and the price-dividend ratios in an economy with two Lucas trees and analyze cross-sectional effects of contagion risk qualitatively. We find that heterogeneity among the assets with respect to contagion risk can increase risk premia disproportionately. In particular, big assets with a large exposure to contagious shocks carry significantly higher risk premia.

- When do jumps matter for portfolio optimization? : [Version 29 April 2013] (2013)
- We consider the continuous-time portfolio optimization problem of an investor with constant relative risk aversion who maximizes expected utility of terminal wealth. The risky asset follows a jump-diffusion model with a diffusion state variable. We propose an approximation method that replaces the jumps by a diffusion and solve the resulting problem analytically. Furthermore, we provide explicit bounds on the true optimal strategy and the relative wealth equivalent loss that do not rely on results from the true model. We apply our method to a calibrated affine model and fine that relative wealth equivalent losses are below 1.16% if the jump size is stochastic and below 1% if the jump size is constant and γ ≥ 5. We perform robustness checks for various levels of risk-aversion, expected jump size, and jump intensity.

- Partial information about contagion risk, self-exciting processes and portfolio optimization : [Version 18 April 2013] (2013)
- This paper compares two classes of models that allow for additional channels of correlation between asset returns: regime switching models with jumps and models with contagious jumps. Both classes of models involve a hidden Markov chain that captures good and bad economic states. The distinctive feature of a model with contagious jumps is that large negative returns and unobservable transitions of the economy into a bad state can occur simultaneously. We show that in this framework the filtered loss intensities have dynamics similar to self-exciting processes. Besides, we study the impact of unobservable contagious jumps on optimal portfolio strategies and filtering.

- Asset pricing under uncertainty about shock propagation : [version 18 november 2013] (2013)
- We analyze the equilibrium in a two-tree (sector) economy with two regimes. The output of each tree is driven by a jump-diffusion process, and a downward jump in one sector of the economy can (but need not) trigger a shift to a regime where the likelihood of future jumps is generally higher. Furthermore, the true regime is unobservable, so that the representative Epstein-Zin investor has to extract the probability of being in a certain regime from the data. These two channels help us to match the stylized facts of countercyclical and excessive return volatilities and correlations between sectors. Moreover, the model reproduces the predictability of stock returns in the data without generating consumption growth predictability. The uncertainty about the state also reduces the slope of the term structure of equity. We document that heterogeneity between the two sectors with respect to shock propagation risk can lead to highly persistent aggregate price-dividend ratios. Finally, the possibility of jumps in one sector triggering higher overall jump probabilities boosts jump risk premia while uncertainty about the regime is the reason for sizeable diffusive risk premia.