Stochastic Volatility in a Continuous-Time Random Walk Model of Financial Markets

Abstract

We develop a generalized continuous-time random walk (CTRW) formalism to describe asset price dynamics by coupling the classical Montroll-Weiss framework with stochastic volatility (SV) models, through Markovian volatility transitions. The study focuses on three primary features: (i) the derivation of a volatility-dependent Montroll-Weiss equation, (ii) the analysis of the distribution tails behaviour across time frames ranging from intraday horizons to a full trading year, and under variations of the SV parameters; and (iii) the determination of the diffusive behaviour of the price distribution through the assessment of its second-order moment.