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- Internationally cross-listed stock prices during overlapping trading hours : price discovery and exchange rate effects (2001)
- We analyze exchange rates along with equity quotes for 3 German firms from New York (NYSE) and Frankfurt (XETRA) during overlapping trading hours to see where price discovery occurs and how stock prices adjust to an exchange rate shock. Findings include: (a) the exchange rate is exogenous with respect to the stock prices; (b) exchange rate innovations are more important in understanding the evolution of NYSE prices than XETRA prices; and (c) most (but not all) of the fundamental or random walk component of firm value is determined in Frankfurt.

- Money-back guarantees in individual pension accounts : evidence from the German pension reform (2002)
- The German Retirement Saving Act instituted a new funded system of supplementary pensions coupled with a general reduction in the level of state pay-as-you-go old-age pensions. In order to qualify for tax relief, the providers of supplementary savings products must offer a guarantee of the nominal value at retirement of contributions paid into these saving accounts. This paper explores how this "money-back" guarantee works and evaluates alternative designs for guarantee structures, including a life cycle model (dynamic asset allocation), a plan with a pre-specified blend of equity and bond investments (static asset allocation), and some type of portfolio insurance. We use a simulation methodology to compare hedging effectiveness and hedging costs associated with the provision of the money-back guarantee. In addition, the guarantee has important implications for regulators who must find an appropriate solvency system for such saving schemes. This version June 17, 2002 . Klassifikation: G11, G23, G28

- Has there always been underpricing and long-run underperformance? : IPOs in Germany before World War I (2000)
- This paper provides empirical evidence on initial public offerings (IPOs) by investigating the pricing and long-run performance of IPOs using a unique data set collected on the German capital market before World War I. Our findings indicate that underpricing of IPOs has existed, but has significantly decreased over time in our sample. Employing a mixture of distributions approach we also find evidence of price stabilization of IPOs. Concerning long-run performance, investors who bought their shares in the early after-market and held them for more than three years experienced significantly lower returns than the respective industry as a whole. Earlier versions of this paper were presented at the ABN-AMRO Conference on IPOs in Amsterdam, the Annual Meetings of the European Finance Association, the Annual Meetings of the Verein für Socialpolitik, the IX Tor Vergata International Conference on Banking and Finance in Rome, and at Johann Wolfgang Goethe-University in Frankfurt.

- Asset Pricing Under Uncertainty About Shock Propagation (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.

- Is jump risk priced? - What we can (and cannot) learn from option hedging errors (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.

- Can tests based on option hedging errors correctly identify volatility risk premia? : [Version 15 Januar 2004] (2004)
- This paper provides an in-depth analysis of the properties of popular tests for the existence and the sign of the market price of volatility risk. These tests are frequently based on the fact that for some option pricing models under continuous hedging the sign of the market price of volatility risk coincides with the sign of the mean hedging error. Empirically, however, these tests suffer from both discretization error and model mis-specification. We show that these two problems may cause the test to be either no longer able to detect additional priced risk factors or to be unable to identify the sign of their market prices of risk correctly. Our analysis is performed for the model of Black and Scholes (1973) (BS) and the stochastic volatility (SV) model of Heston (1993). In the model of BS, the expected hedging error for a discrete hedge is positive, leading to the wrong conclusion that the stock is not the only priced risk factor. In the model of Heston, the expected hedging error for a hedge in discrete time is positive when the true market price of volatility risk is zero, leading to the wrong conclusion that the market price of volatility risk is positive. If we further introduce model mis-specification by using the BS delta in a Heston world we find that the mean hedging error also depends on the slope of the implied volatility curve and on the equity risk premium. Under parameter scenarios which are similar to those reported in many empirical studies the test statistics tend to be biased upwards. The test often does not detect negative volatility risk premia, or it signals a positive risk premium when it is truly zero. The properties of this test furthermore strongly depend on the location of current volatility relative to its long-term mean, and on the degree of moneyness of the option. As a consequence tests reported in the literature may suffer from the problem that in a time-series framework the researcher cannot draw the hedging errors from the same distribution repeatedly. This implies that there is no guarantee that the empirically computed t-statistic has the assumed distribution. JEL: G12, G13 Keywords: Stochastic Volatility, Volatility Risk Premium, Discretization Error, Model Error

- 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.

- Can tests based on option hedging errors correctly identify volatility risk premia? (2004)
- Tests for the existence and the sign of the volatility risk premium are often based on expected option hedging errors. When the hedge is performed under the ideal conditions of continuous trading and correct model specification, the sign of the premium is the same as the sign of the mean hedging error for a large class of stochastic volatility option pricing models. We show, however, that the problems of discrete trading and model mis-specification, which are necessarily present in any empirical study, may cause the standard test to yield unreliable results.