Articles

The paper considers a specific type of such financial instrument as an option, namely an exotic barrier call option of the European type. Exotic options are gaining popularity among ordinary investors due to the development of information and telecommunication technologies, thanks to which such specific financial instruments as options have become readily available. We investigate the hedging problem for such options with some restrictions on the payment function and the availability of dividend payment on a risky asset in the classical Black-Scholes model. An analogue of the Black-Scholes formula for the mentioned variant of the exotic barrier is proved. In the future, it is planned to generalize the obtained results for put options and for more general payment functions.

Financial markets have become more and more complex, so has been the number of data sources. Stock price prediction has hence become a tough but important task. The time dependencies in stock price movements tend to escape from traditional models. In this work, a hybrid ARIMA-LSTM model is suggested to enhance accuracy of stock price forecasts. Based on time series indicators like adjusted closing prices of S&P 500 stocks over a decade (2010–2019), the ARIMA-LSTM model combines influences of both autoregressive time series forecasting with the substantial sequence learning property of LSTM. Data preprocessing in all aspects including missing values interpolation, outlier’s detection and data scaling – Min-Max guarantees data quality. The model is trained on 90/10 training/testing split and met with main performance metrics: MaE, MSE & RMSE. As indicated in the results, the proposed ARIMA-LSTM model gives a MAE value and MSE value of 0.248 and 0.101 respectively and RMSE of 0.319, a measure high accuracy on stock price prediction. Coupled comparative analysis with other Artificial Neural Networks (ANN) and BP Neural Networks (BPNN) are examples of machine learning reference models, further illustrates the suitability and superiority of ARIMA-LSTM approach as compared to the underlying models with the least MAE and strong predictive capability. This work demonstrates the efficiency of integrating the classical time series models with deep learning methods for financial forecasting.