Can Tests Based on Option Hedging Errors Correctly Identify Volatility Risk Premia?

38 Pages Posted: 14 May 2004

See all articles by Nicole Branger

Nicole Branger

University of Muenster - Finance Center Muenster

Christian Schlag

Goethe University Frankfurt - Research Center SAFE

Date Written: January 15, 2004

Abstract

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.

Keywords: Stochastic Volatility, Volatility Risk Premium, Discretization Error, Model Error

JEL Classification: G12, G13

Suggested Citation

Branger, Nicole and Schlag, Christian, Can Tests Based on Option Hedging Errors Correctly Identify Volatility Risk Premia? (January 15, 2004). EFMA 2004 Basel Meetings Paper. Available at SSRN: https://ssrn.com/abstract=493462 or http://dx.doi.org/10.2139/ssrn.493462

Nicole Branger (Contact Author)

University of Muenster - Finance Center Muenster ( email )

Universitatsstr. 14-16
Muenster, 48143
Germany
+49 251 83 29779 (Phone)
+49 251 83 22867 (Fax)

HOME PAGE: http://www.wiwi.uni-muenster.de/fcm/fcm/das-finance-center/details.php?weobjectID=162

Christian Schlag

Goethe University Frankfurt - Research Center SAFE ( email )

(http://www.safe-frankfurt.de)
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany
+49 69 798 33699 (Phone)

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