Time Delay in Stochastic Volatility Model

26 Pages Posted: 10 Mar 2020

See all articles by Hyeong-Ohk Bae

Hyeong-Ohk Bae

Ajou University - Department of Financial Engineering

Seung-Yeal Ha

Seoul National University - Research Institute of Mathematics

Myeongju Kang

Seoul National University - Department of Mathematical Sciences

Yongsik Kim

Ajou University - Department of Financial Engineering

Hyuncheul Lim

KB Bank

Jane Yoo

Ajou University - School of Business

Date Written: February 18, 2020

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.

Keywords: Cucker–Smale model, geometric Brownian motion, flocking, regime switching, volatility, Wiener process, time delay

JEL Classification: C15, C61, G17

Suggested Citation

Bae, Hyeong-Ohk and Ha, Seung-Yeal and Kang, Myeongju and Kim, Yongsik and Lim, Hyuncheul and Yoo, Jane, Time Delay in Stochastic Volatility Model (February 18, 2020). Available at SSRN: https://ssrn.com/abstract=3540195 or http://dx.doi.org/10.2139/ssrn.3540195

Hyeong-Ohk Bae

Ajou University - Department of Financial Engineering ( email )

Suwon
Korea, Republic of (South Korea)

Seung-Yeal Ha

Seoul National University - Research Institute of Mathematics ( email )

Seoul
Korea, Republic of (South Korea)

Myeongju Kang

Seoul National University - Department of Mathematical Sciences ( email )

Seoul
Korea, Republic of (South Korea)

Yongsik Kim

Ajou University - Department of Financial Engineering ( email )

Suwon
Korea, Republic of (South Korea)

Hyuncheul Lim

KB Bank ( email )

Seoul, Yeongdeungpo-gu
Korea, Republic of (South Korea)

Jane Yoo (Contact Author)

Ajou University - School of Business ( email )

206 Worldcup-ro
Yeongtong-gu
Suwon
Korea, Republic of (South Korea)

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
31
Abstract Views
164
PlumX Metrics