 A reflection principle for a random walk with implications for volatility estimation using extreme values of asset pricesDilip Kumar and S. Maheswaran Economic Modelling, 2014, vol. 38, issue C, 33-44 Abstract: In this paper, we derive a reflection principle for a random walk with the symmetric double exponential distribution. This allows us to come up with the closed form solution for the joint probability of the running maximum and the terminal value of the random walk. Based on this new theoretical result, we propose an extreme value estimator for the variance of the random walk that is not just approximately unbiased but exactly so. In simulations, we find that this estimator continues to be unbiased even when intraday mean reversion is present, as captured by the Binomial Markov Random Walk model. On the empirical side, we find that this estimator works well in a variety of global stock indices, including the S&P 500 Index, in the sense of being unbiased relative to the “usual” estimator, i.e., the sample variance of the daily returns. Keywords: Volatility estimation; Bias correction; Random walk effect; Binomial Markov Random Walk (BMRW) model (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:ecmode:v:38:y:2014:i:c:p:33-44 DOI: 10.1016/j.econmod.2013.11.045 Access Statistics for this article Economic Modelling is currently edited by S. Hall and P. Pauly More articles in Economic Modelling from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.