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- 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.

- When are static superhedging strategies optimal? (2004)
- This paper deals with the superhedging of derivatives and with the corresponding price bounds. A static superhedge results in trivial and fully nonparametric price bounds, which can be tightened if there exists a cheaper superhedge in the class of dynamic trading strategies. We focus on European path-independent claims and show under which conditions such an improvement is possible. For a stochastic volatility model with unbounded volatility, we show that a static superhedge is always optimal, and that, additionally, there may be infinitely many dynamic superhedges with the same initial capital. The trivial price bounds are thus the tightest ones. In a model with stochastic jumps or non-negative stochastic interest rates either a static or a dynamic superhedge is optimal. Finally, in a model with unbounded short rates, only a static superhedge is possible.

- What is the impact of stock market contagion on an investor's portfolio choice? (2009)
- Stocks are exposed to the risk of sudden downward jumps. Additionally, a crash in one stock (or index) can increase the risk of crashes in other stocks (or indices). Our paper explicitly takes this contagion risk into account and studies its impact on the portfolio decision of a CRRA investor both in complete and in incomplete market settings. We find that the investor significantly adjusts his portfolio when contagion is more likely to occur. Capturing the time dimension of contagion, i.e. the time span between jumps in two stocks or stock indices, is thus of first-order importance when analyzing portfolio decisions. Investors ignoring contagion completely or accounting for contagion while ignoring its time dimension suffer large and economically significant utility losses. These losses are larger in complete than in incomplete markets, and the investor might be better off if he does not trade derivatives. Furthermore, we emphasize that the risk of contagion has a crucial impact on investors' security demands, since it reduces their ability to diversify their portfolios.

- Tractable hedging - an implementation of robust hedging strategies : [This Version: March 30, 2004] (2004)
- This paper provides a theoretical and numerical analysis of robust hedging strategies in diffusion–type models including stochastic volatility models. A robust hedging strategy avoids any losses as long as the realised volatility stays within a given interval. We focus on the effects of restricting the set of admissible strategies to tractable strategies which are defined as the sum over Gaussian strategies. Although a trivial Gaussian hedge is either not robust or prohibitively expensive, this is not the case for the cheapest tractable robust hedge which consists of two Gaussian hedges for one long and one short position in convex claims which have to be chosen optimally.

- The dynamics of crises and the equity premium (2014)
- There has been a considerable debate about whether disaster models can rationalize the equity premium puzzle. This is because empirically disasters are not single extreme events, but long-lasting periods in which moderate negative consumption growth realizations cluster. Our paper proposes a novel way to explain this stylized fact. By allowing for consumption drops that can spark an economic crisis, we introduce a new economic channel that combines long-run and short-run risk. First, we document that our model can match consumption data of several countries. Second, it generates a large equity risk premium even if consumption drops are of moderate size.

- Pricing two trees when mildew infests the orchard: how does contagion affect general equilibrium asset prices : [version: March 11, 2011) (2011)
- This paper analyzes the equilibrium pricing implications of contagion risk in a two-tree Lucas economy with CRRA preferences. The dividends of both trees are subject to downward jumps. Some of these jumps are contagious and increase the risk of subsequent jumps in both trees for some time interval. We show that contagion risk leads to large price-dividend ratios for small assets, a joint movement of prices in the case of a regime change from the calm to the contagion state, significantly positive correlations between assets, and large positive betas for small assets. Whereas disparities between the assets with respect to their propensity to trigger contagion barely matter for pricing, the prices of robust assets that are hardly affected by contagion and excitable assets that are severely hit by contagion differ significantly. Both in absolute terms and relatively to the market, the price of a small safe haven increases if the economy reaches the contagion state. On the contrary, the price of a small, contagion-sensitive asset exhibits a pronounced downward jump.

- 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.

- Is jump risk priced? - What we can (and cannot) learn from option hedging errors : [This version: November 26, 2004] (2004)
- When options are traded, one can use their prices and price changes to draw inference about the set of risk factors and their risk premia. We analyze tests for the existence and the sign of the market prices of jump risk that are based on option hedging errors. We derive a closed-form solution for the option hedging error and its expectation in a stochastic jump model under continuous trading and correct model specification. Jump risk is structurally different from, e.g., stochastic volatility: there is one market price of risk for each jump size (and not just \emph{the} market price of jump risk). Thus, the expected hedging error cannot identify the exact structure of the compensation for jump risk. Furthermore, we derive closed form solutions for the expected option hedging error under discrete trading and model mis-specification. Compared to the ideal case, the sign of the expected hedging error can change, so that empirical tests based on simplifying assumptions about trading frequency and the model may lead to incorrect conclusions.

- 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.

- Equilibrium asset pricing in networks with mutually exciting jumps (2014)
- We analyze the implications of the structure of a network for asset prices in a general equilibrium model. Networks are represented via self- and mutually exciting jump processes, and the representative agent has Epstein-Zin preferences. Our approach provides a exible and tractable unifying foundation for asset pricing in networks. The model endogenously generates results in accordance with, e.g., the robust-yetfragile feature of financial networks shown in Acemoglu, Ozdaglar, and Tahbaz-Salehi (2014) and the positive centrality premium documented in Ahern (2013). We also show that models with simpler preference assumptions cannot generate all these findings simultaneously.