Time Delay in Stochastic Volatility Model

Abstract

Time delay in communication(information) flow is often found in many network systems. Inspired by volatility spillovers and clustering explained by “flocking” mechanism, we study the effect of the time delay in our model system of heterogeneous stock returns’ volatilities. Our model is a stochastic multi-volatility model in which a volatility’s dynamics is conditional on its value relative to others. Due to the finite speed of propagation, the dynamics is updated by volatilities’ one-to-one relationship with a short time delay. Our theoretical framework is sufficient to show the exponential convergence of volatilities toward the constant asymptotic value. When time delay is considered, convergence happens faster with lower variance than that in the model without time delay.