Modeling dynamic volatility under uncertain environment with fuzziness and randomness

Abstract

Predicting the dynamic volatility in financial market provides a promising method for risk prediction, asset pricing and market supervision. Barndorff-Nielsen and Shephard model (BN-S) model, used to capture the stochastic behavior of high-frequency time series, is an accepted stochastic volatility model with Lévy process. Although this model is attractive and successful in theory, it needs to be improved in application. We build a new generalized BN-S model suitable for uncertain environment with fuzziness and randomness. This new model considers the delay phenomenon between price fluctuation and volatility changes, solves the problem of the lack of long-range dependence of classic models. Calculation results show that new model outperforms the classic model in volatility forecasting. Experiments on Dow Jones Industrial Average futures price data are conducted to verify feasibility and practicability of our proposed approach. Numerical examples are provided to illustrate the theoretical result. Three machine learning algorithms are applied to estimate new model parameter. Compared with the classical model, our method effectively combines the uncertain environmental characteristics, which makes the prediction of dynamic volatility more flexible and has ideal performance.