Abstract

http://ssrn.com/abstract=1701685
 
 

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A New Framework for Analyzing Volatility Risk and Premium Across Option Strikes and Expiries


Peter Carr


New York University (NYU) - Courant Institute of Mathematical Sciences

Liuren Wu


City University of New York, CUNY Baruch College - Zicklin School of Business

October 2, 2010


Abstract:     
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

working papers series


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Date posted: November 3, 2010 ; Last revised: July 4, 2013

Suggested Citation

Carr, Peter and Wu, Liuren, A New Framework for Analyzing Volatility Risk and Premium Across Option Strikes and Expiries (October 2, 2010). Available at SSRN: http://ssrn.com/abstract=1701685 or http://dx.doi.org/10.2139/ssrn.1701685

Contact Information

Peter P. Carr
New York University (NYU) - Courant Institute of Mathematical Sciences ( email )
251 Mercer Street
New York, NY 10012
United States
Liuren Wu (Contact Author)
City University of New York, CUNY Baruch College - Zicklin School of Business ( email )
One Bernard Baruch Way
Box B10-225
New York, NY 10010
United States
646-312-3509 (Phone)
646-312-3451 (Fax)
HOME PAGE: http://faculty.baruch.cuny.edu/lwu/
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