Nonparametric Estimation of the Leverage Effect Using Information from Derivatives Markets
University of Montreal
University of Chicago - Booth School of Business
April 10, 2015
Chicago Booth Research Paper No. 13-83
We consider a new nonparametric estimator of the leverage effect, which uses the stock price as well as a certain volatility instrument, such as the CBOE volatility index (VIX) or the Black-Scholes implied volatility. The theoretical justification for this estimator relies on the relationship between the volatility instrument and the spot volatility, together with a certain invariance property of the spot correlation. In addition, we propose a nonparametric estimator that uses stock prices alone. The instrument-based estimator has a faster rate of convergence, whereas the price-only estimator is valid under weaker assumptions. Finally, we provide a time series of monthly leverage effect estimates of the S&P 500 index from 2003 to 2013 using the VIX as a volatility instrument. We find that the credit risk, illiquidity, and the debt-to-equity ratio are important factors related to the dynamics of the leverage effect.
Number of Pages in PDF File: 59
Keywords: semimartingale, spot correlation, VIX, implied volatility, high frequency data
JEL Classification: G12, C22, C14
Date posted: November 26, 2013 ; Last revised: April 15, 2015
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