Non-stationary volatility with highly anti-persistent increments: An alternative paradigm in volatility modeling?
Abstract
We introduce the alternative paradigm to volatility modeling. On the example of three stocks of highly capitalized companies, we show that volatility process is non-stationary and its logarithmic transformation together with the logarithmic increments are approximately normally distributed while the latter are strongly anti-persistent.
Together with the assertion that loga- rithmic returns are normally distributed, and uncorrelated with time-varying volatility, we propose the new returns-generating process, which is able to re- markably mimic the real-world series and the standard stylized facts - uncor- related returns with heavy tails, strongly autocorrelated absolute returns and volatility clustering. The proposed methodology opens a wholly new field in research of financial volatility.