Can tests based on option hedging errors correctly identify volatility risk premia?

  • 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

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Author:Nicole BrangerORCiDGND, Christian SchlagORCiDGND
Document Type:Working Paper
Year of Completion:2004
Year of first Publication:2004
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/10/06
Tag:Optionspreistheorie; Risikoprämie; Statistischer Test; Stochastischer Prozess; Theorie; Volatilität
Discretization Error; Model Error; Stochastic Volatility; Volatility Risk Premium
Issue:Version 15 Januar 2004
Page Number:38
This paper was formerly titled 'Is Volatility Risk Priced? | Properties of Tests Based on Option Hedging Errors'. Earlier versions were presented at Arizona State University, at the 35th Annual Meeting of the Money, Macro, and Finance Research Group conference in Cambridge, at the EIASM Workshop on Dynamic Strategies in Asset Allocation and Risk Management in Brussels, at the 2003 annual congress of the Verein für Socialpolitik in Zurich, at the 10th Annual Meeting of the German Finance Association in Mainz, at the annual meetings of European Investment Review in Geneva, and at the 2003 MathFinance Colloquium in Frankfurt.
Source:EFMA 2004 Basel Meetings Paper., Version 15 Januar 2004
Institutes:Wirtschaftswissenschaften / Wirtschaftswissenschaften
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
Licence (German):License LogoDeutsches Urheberrecht