English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper we study the possible microscopic origin of heavy-tailedprobability density distributions for the price variation of financialinstruments. We extend the standard log-normal process to include anotherrandom component in the so-called stochastic volatility models. We study thesemodels under an assumption, akin to the Born-Oppenheimer approximation, inwhich the volatility has already relaxed to its equilibrium distribution andacts as a background to the evolution of the price process. In thisapproximation, we show that all models of stochastic volatility should exhibita scaling relation in the time lag of zero-drift modified log-returns. Weverify that the Dow-Jones Industrial Average index indeed follows this scaling.We then focus on two popular stochastic volatility models, the Heston andHull-White models. In particular, we show that in the Hull-White model theresulting probability distribution of log-returns in this approximationcorresponds to the Tsallis (t-Student) distribution. The Tsallis parameters aregiven in terms of the microscopic stochastic volatility model. Finally, we showthat the log-returns for 30 years Dow Jones index data is well fitted by aTsallis distribution, obtaining the relevant parameters.

Microscopic Origin of Non-Gaussian Distributions of Financial Returns