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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
Empirical evidence suggests that even those firms presumably most in need of monitoringintensive financing (young, small, and innovative firms) have a multitude of bank lenders, where one may be special in the sense of relationship lending. However, theory does not tell us a lot about the economic rationale for relationship lending in the context of multiple bank financing. To fill this gap, we analyze the optimal debt structure in a model that allows for multiple but asymmetric bank financing. The optimal debt structure balances the risk of lender coordination failure from multiple lending and the bargaining power of a pivotal relationship bank. We show that firms with low expected cash-flows or low interim liquidation values of assets prefer asymmetric financing, while firms with high expected cash-flow or high interim liquidation values of assets tend to finance without a relationship bank. JEL - Klassifikation: G21 , G78 , G33
When performance measures are used for evaluation purposes, agents have some incentives to learn how their actions affect these measures. We show that the use of imperfect performance measures can cause an agent to devote too many resources (too much effort) to acquiring information. Doing so can be costly to the principal because the agent can use information to game the performance measure to the detriment of the principal. We analyze the impact of endogenous information acquisition on the optimal incentive strength and the quality of the performance measure used.