This paper proposes an innovative semiparametric nonlinear fuzzy-EGARCH-ANN model to solve the problem of accurate modeling for forecasting stock market volatility. This model has been developed by a combination of the FIS, ANN, and EGARCH models. Because the proposed model is highly nonlinear and gradient-based parameter estimation methods might not give global optimal parameters for highly nonlinear models, the study has decided to use evolutionary algorithms instead. In particular, a differential evolution (DE) algorithm is suggested to solve the parameter estimation problem of the proposed model. After this, the semiparametric nonlinear fuzzy-EGARCH-ANN model has been developed mathematically from the three models mentioned before, and the study has simulated data by it. After the simulation, parameter estimation of the proposed model using a differential evolution algorithm on the simulated data is done. Finally, it is seen that the proposed model is good in capturing the volatility clustering and leverage effects of highly nonlinear and complicated financial time series data that were overlooked by the EGARCH model.
Precise recognition of a time series path is important to policy makers, statisticians, economists, traders, hedgers and speculators alike. The correct time series path is also a key ingredient in pricing models. This study uses daily futures prices of crude oil and other distillate fuels. This paper considers the statistical properties of energy futures and spot prices and investigates the trends that underlie the price dynamics in order to gain further insights into possible nuances of price discovery and energy market dynamics. The family of ARMA-GARCH models was explored. The trends depict time varying variability and persistence of oil price shocks. The return series conform to a constant mean model with GARCH variance.
The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an optimal stopping problem, which is the value function of a stochastic control problem given by a non-linear second order partial differential equation. The theory of viscosity solutions is applied to solve the stochastic control problem such that the value function is also the solution of the corresponding Bellman equation. Under some regularity assumptions, the existence and uniqueness of the solution of the pricing equation are derived by the application of the Perron method and Banach Fixed Point theorem.
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