Parameter Identification of Stochastic Delay Differential Equations Using Differential Evolution

This paper aims to identify the model parameters in the stochastic delay differential equations (SDDE) using the differential evolution (DE) algorithm. The financial datasets of the International Business Machines Corporation (IBM), the Microsoft Corporation (MSFT), and the Standard and Poor's 500 (S&P 500) are used in this paper. All datasets are traded every five minutes on weekdays. The empirical results obtained from the DE algorithm indicate that the estimated average volatility of each stock has a similar pattern to the actual volatility. In addition, the performance of different delays is investigated. It can be concluded that the estimate becomes more accurate when the delay is increased.