Time-Delayed Stochastic Volatility Model

28 Pages Posted: 10 Mar 2020 Last revised: 10 Nov 2021

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: November 30, 2021

Abstract

We propose a multivariate stochastic volatility model with time-delayed interactions, and study its emergent dynamics. The proposed model takes the form of an agent-based model with the Cucker-Smale mechanism, time-delayed interactions and regime-switching. It exhibits a collective behavior ``flocking" emerging from the all-to-all coupling with time-delayed interactions induced by the finite propagation speed of communications. We assume that the realized volatility path switches randomly between two regimes. In this setting, we provide theoretical and numerical solutions of the proposed model and show that our proposed theoretical framework is sufficient for volatility's exponential convergence toward a constant asymptotic value. The longer time-delay makes a volatility converge faster with a lower variance, and we also fit system parameters in the model with the daily observations on stock return and volatility to show model's high prediction power in both in and out of sample tests.

Keywords: Aggregation, Cucker-Smale mechanism, flocking, regime-switching, 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-Delayed Stochastic Volatility Model (November 30, 2021). 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)

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