期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 23, 期 9, 页码 1603-1628出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202513500176
关键词
Cucker-Smale model; Heston model; flocking; stochastic volatility; option in currency forward
资金
- World Class University (WCU) project through the National Research Foundation of Korea (NRF)
- Korean Ministry of Education, Science and Technology (MEST) [R31-2009-000-20007-0]
- [NRF-2011-0015388]
- [NRF-2011-0011855]
- National Research Foundation of Korea [2011-0011855, R31-2012-000-20007-0] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
In this study, we present a new stochastic volatility model incorporating a flocking mechanism between individual volatilities of assets. Collective phenomena of asset pricing and volatilities in financial markets are often observed; these phenomena are more apparent when the market is in critical situations (market crashes). In the classical Heston model, the constant theoretical mean of the square of the volatility was employed, which can be assumed a priori. Our proposed model does not assume this mean value a priori, we instead use the flocking effect to continuously update the theoretical mean value using the local weighted average of individual volatility values. To perform this function, we use the Cucker-Smale flocking mechanism to calculate the local mean. For some classes of interaction weights such as all-to-all and symmetric coupling with a positive lower bound, we show that the fluctuations of the square process of volatility are uniformly bounded, such that the overall dynamics are mainly dictated by the averaged process. We also provide several numerical examples showing the dynamics of volatility.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据