Nonparametric Estimation of the Leverage Effect Using Information from Derivatives Markets
University of Montreal
University of Chicago - Booth School of Business
May 21, 2014
Chicago Booth Research Paper No. 13-83
We consider a new nonparametric estimator of the leverage effect, which uses the data on stock prices as well as a certain volatility instrument, such as the CBOE volatility index (VIX) or Black-Scholes implied volatility. The theoretical justification for the new estimator exploits the relationship between the volatility instrument and the spot volatility, together with a certain invariance property of the spot correlation. We derive the asymptotic distribution of the estimator. We compare this instrument-based estimator with the nonparametric price-only leverage estimator, for which we also derive the asymptotic distribution. The instrument-based estimator has a faster rate of convergence. We demonstrate in simulations and empirically that the instrument-based estimator is substantially more precise than the price-only estimator. Finally, we use the new estimator to provide time series of monthly leverage effects of the S&P 500 index from 2003 to 2012 using two different volatility instruments. We also find that the credit risk, liquidity, and the debt-to-equity are important determinants of the leverage effect.
Number of Pages in PDF File: 46
Keywords: semimartingale, spot correlation, VIX, implied volatility, high frequency data
JEL Classification: G12, C22, C14working papers series
Date posted: November 26, 2013 ; Last revised: August 19, 2014
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