Nonlinear neural network forecasting model for stock index option price: Hybrid GJR–GARCH approach
Introduction
Neural network model is an emerging computational technology that provides a new avenue for exploring the dynamics of various economic and financial applications. Artificial neural networks are an information processing technology for modeling mathematical relationships between input variables and output variables. Based on the construction of the human brain, a set of processing elements or neurons (nodes) are interconnected and organized in layers (Malliaris & Salchenberger, 1996). Recently, related researches have used of ANNs on the economic applications is expanding rapidly (Meraviglia, 1996, Shachmurove, 2005, Zhang and Berardi, 2001). For example, some studies have empirically rated bonds (Dutta and Shekar, 1988, Heston, 1993), some studies have empirically forecasted macroeconomic variables such as inflation, interest rates and exchange rate (Binner et al., 2005, Plasmans et al., 1998, Qi and Wu, 2003, Saltoglu, 2003). Furthermore, studies provided evidences of ANNs that to focus evaluation and prediction of consumer loans, corporate failures and bankruptcy (Ahn et al., 2000, Altman et al., 1994, Mahlhotra and Malhotra, 2003, Tam and Kiang, 1992).
Most studies have focused on the estimation and forecast of financial data (Medeiros, Teräsvirta, & Rech, 2005). This approach is effective for input and output relationship modeling even for noisy data, and has been demonstrated to effectively model nonlinear relationships. Such as, related studies have empirically estimated and forecasted stock prices (Black and McMillan, 2004, Donaldson and Kamstra, 1996, Jasic and Wood, 2004, Kanas, 2001, Kanas and Yannopoulos1, 2001, Maasoumi and Racine, 2002, Qi, 1999, Rapach and Wohar, 2005, Shively, 2003) and stock volatilities (Dunis and Huang, 2002, Hamid and Iqbal, 2004). Moreover, major studies on derivative securities pricing using neural network have attracted researchers and practitioners, and they applied the neural network model and obtained better results than using the traditional option-pricing model (Amilon, 2003, Binner et al., 2005, Heston and Nandi, 2000, Hutchinson et al., 1994, Lin and Yeh, 2005, Malliaris and Salchenberger, 1996, Qi, 1999, Yao et al., 2000).
Therefore, given lessons learned from the existing literature, the purpose of our paper is twofold. Our first objective is to develop a new model for conditional stock returns volatility which can capture important asymmetric effects that existing models do not capture. To this end we develop a Grey-GJR–GARCH approach to reduce the stochastic and nonlinearity of the error term sequence and then to improve the predicted ability of option-pricing model further. Our second objective is to integrate Grey-GJR–GARCH volatility approach into Artificial Neural Networks (ANNs), that has the functional flexibility to capture the nonlinearities in financial data.
Firstly, we employ the forecasting property of GM(1, 1) model to continually modify the squared error terms sequence (Deng, 1982), and the traditional symmetric GARCH model and GM(1, 1) model are combined, Grey-GJR–GARCH, to construct the conditional volatility. Moreover, we use different estimated volatility approaches, GARCH volatility, GJR–GARCH volatility, and Grey-GJR–GARCH, to estimate volatilities which these estimated volatilities provide an input in backpropagation ANN-pricing model in order to compare the performance of option-pricing. The remainder of this paper is organized as follows. section 2 outlines the different approaches to estimate volatility and demonstrates how each is calculated. Next, Section 3 describes the neural network model as prediction model. Moreover, Section 4 presents the empirical results. Finally, section 5 presents the conclusions.
Section snippets
Option-pricing model
Black and Scholes (1973) provided the famous model, B-S option-pricing model, to estimate the price of derivatives. In this model, the reasonable price of an option is strongly dependent on the volatility of the pricing process of the underlying financial asset and assumed that stock prices follow the standard lognormal diffusion: dSt/St = μ dt + σdWt, where St denotes the current stock price, μ represents the constant drift,σ is the constant volatility, and Wt denotes a standard Brownian motion.
Backpropagation neural networks
Neural networks can be classified into feedforward and feedback networks. Feedback networks contain neurons that are connected to themselves, enabling a neuron to influence other neurons. Kohonen self-organizing network and Hopfield network are the type of feedforward network. Backpropagation neural network, take inputs only from the previous layer and send outputs only to the next layer (see Fig. 1).
This study employs a backpropagation neural network, the most widely used network in business
Basic statistics description
In December 24 2001, the Taiwan Futures Exchange (TAIFEX) introduced the Taiwan stock index options (TXO). The TXO market has since become one of the fastest growing markets in the world, with annual trading volume reached 3 million contracts in 2006. The data used in this study is transaction data of Taiwan stock index options (TXO) traded on the Taiwan Futures Exchange (TAIFEX). This study investigated a sample of 21,120 call option price data from January 3, 2005 through December 29, 2006.
Conclusions
This study applies the nonlinear neural network forecast models with different volatility approaches to investigate the predictability of Taiwan stock index option price. Overall, the in-the-money option is valuable to call option price and the empirical result exhibits that The empirical result has been demonstrated to the in-the-money option Grey-GJR–GARCH volatility approach has relatively good market forecasting ability for TXO. Moreover, the Grey-GJR–GARCH volatility approach achieves
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