Analyzing Volatility Risk and Risk Premium in Option Contracts: A New Theory

56 Pages Posted: 3 Nov 2010 Last revised: 8 Jul 2015

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

Date Written: October 2, 2010

Abstract

We develop a new option pricing framework that tightly integrates with how institutional investors manage options positions. The framework starts with the near-term dynamics of the implied volatility surface and derives no-arbitrage constraints on its current shape. Within this framework, we show that just like option implied volatilities, realized and expected volatilities can also be constructed specific to, and different across, option contracts. Applying the new theory to the S&P 500 index time series and options data, we extract volatility risk and risk premium from the volatility surfaces, and find that the extracted risk premium significantly predicts future stock returns.

Keywords: Implied volatility surface; Option realized volatility; Expected volatility surface; Volatility risk premium; Vega-gamma-vanna-volga; Proportional variance dynamics

JEL Classification: C13, C51, G12, G13

Suggested Citation

Carr, Peter and Wu, Liuren, Analyzing Volatility Risk and Risk Premium in Option Contracts: A New Theory (October 2, 2010). Available at SSRN: https://ssrn.com/abstract=1701685 or http://dx.doi.org/10.2139/ssrn.1701685

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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