A mathematical model for volatility flocking with a regime switching mechanism in a stock market-Reference-Cited by-同舟云学术

A mathematical model for volatility flocking with a regime switching mechanism in a stock market

Published:2015-04-14 Issue:07 Volume:25 Page:1299-1335
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Bae Hyeong-Ohk¹,Ha Seung-Yeal²,Kim Yongsik¹,Lee Sang-Hyeok¹,Lim Hyuncheul³,Yoo Jane¹

Affiliation:

1. Department of Financial Engineering, Ajou University, Suwon 443-749, Korea

2. Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea

3. The Trading Department, KB Bank, Yeongdeungpo-gu, Seoul, Korea

Abstract

We present a mathematical model for stock market volatility flocking. Our proposed model consists of geometric Brownian motions with time-varying volatilities coupled with Cucker–Smale (C–S) flocking and regime switching mechanisms. For all-to-all interactions, we assume that all assets' volatilities are coupled to each other with a constant interaction weight, and we show that the common volatility emerges asymptotically and discuss its financial applications. We also provide several numerical simulations and compare them to existing analytical results.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202515500335

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