A New Framework for Analyzing Volatility Risk and Premium Across Option Strikes and Expiries
New York University (NYU) - Courant Institute of Mathematical Sciences
City University of New York, CUNY Baruch College - Zicklin School of Business
October 2, 2010
This paper proposes a new theoretical framework for analyzing volatility risk and volatility risk premium embedded in option contracts across different strikes and expiries. The theory starts with the future dynamics of the Black-Scholes implied volatility surface, and derives no-arbitrage constraints on the current shape of the volatility surface. Under the specified proportional volatility dynamics , the shape of the surface can be cast as solutions to a simple quadratic equation. Furthermore, corresponding to the option implied volatility for each contract, the paper defines a new, option-specific expected volatility measure that can be estimated from the historic sample price path of the underlying security. The measure is defined as the volatility input that generates zero expected delta-hedged gains from holding this option and can thus differ across different option strikes and expiries. Applying the new theoretical framework to the S&P 500 index options market, we extract volatility risk and volatility risk premium from the two volatility surfaces, and find that the extracted volatility risk premium significantly predicts future stock returns.
Number of Pages in PDF File: 51
Keywords: Implied volatility surface, realized volatility surface, volatility risk premium, vega-gammavanna-volga, proportional variance dynamics
JEL Classification: C13, C51, G12, G13
Date posted: November 3, 2010 ; Last revised: July 4, 2013
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