A random walk down the options market


  • We thank Peter Christoffersen, Jin-Chuan Duan, Kris Jacobs, Jangkoo Kang, Chris Lamoureux, Moshe Milevsky, Chris Telmer, Jason Wei, Shu Yan, participants of finance seminars at the University of Arizona, National University of Singapore, the Third International Conference of Financial Markets, and the International Symposium on Risk Management and Derivatives, and the anonymous referee for helpful comments and suggestions. The financial support of the Social Sciences and Humanity Research Council of Canada is gratefully acknowledged.

Correspondence author, Finance Area, Finance Area, Schulich School of Business, York University, 4700 Keele Street, Toronto, ON, Canada M3J 1P3. Tel: 416-736-2100 ext. 77943


Under the efficient market hypothesis, option-implied forward variance forms a martingale and changes in forward variance follow a random walk. In this study, we extract forward variance from option prices following a model-free approach and empirically test the random walk hypothesis. Although results from standard orthogonality tests support the martingale restriction, further results from autoregressive regressions seem to reject the martingale restriction as daily changes in forward variance are found to exhibit negative autocorrelation. However, this anomalous pattern of negative correlation is fully explained by illiquidity effects. Overall, the findings support the random walk hypothesis and informational efficiency of the options market. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:505–535, 2012