Forecasting Stochastic Volatility Characteristics for the Financial Fossil Oil Market Densities

This paper builds and implements multifactor stochastic volatility models for the international oil/energy markets (Brent oil and WTI oil) for the period 2011–2021. The main objective is to make step ahead volatility predictions for the front month contracts followed by an implication discussion for the market (differences) and observed data dependence important for market participants, implying predictability. The paper estimates multifactor stochastic volatility models for both contracts giving access to a long-simulated realization of the state vector with associated contract movements. The realization establishes a functional form of the conditional distributions, which are evaluated on observed data giving the conditional mean function for the volatility factors at the data points (nonlinear Kalman filter). For both Brent and WTI oil contracts, the first factor is a slow-moving persistent factor while the second factor is a fast-moving immediate mean reverting factor. The negative correlation between the mean and volatility suggests higher volatilities from negative price movements. The results indicate that holding volatility as an asset of its own is insurance against market crashes as well as being an excellent diversification instrument. Furthermore, the volatility data dependence is strong, indicating predictability. Hence, using the Kalman filter from a realization of an optimal multifactor SV model visualizes the latent step ahead volatility paths, and the data dependence gives access to accurate static forecasts. The results extend market transparency and make it easier to implement risk management including derivative trading (including swaps).

Nonlinear Kalman filter with self-organizing model

To improve the accuracy of the aircraft navigation system error correction in the output signal is used. The errors of the navigation complex are estimated by using a nonlinear Kalman filter. It is proposed to use a nonlinear model constructed by the method of self-organization as a model of the process being evaluated. The effectiveness of the self-organization algorithm in comparison with the genetic algorithm and the neural network is confirmed by the results of mathematical modeling. Keywords aircraft; inertial navigation system; error model; self-organization algorithm