Abstract
It is shown that time series about financial market variables are highly nonlinearly dependent on time. Fluctuations or volatility of returns on assets is one of them. Portfolio managers, option traders and market makers are all interested in volatility forecasting in order to get higher profits and less risky positions. The nonlinear dependence on time is very complex and parametric approaches, and linear models fail. Therefore as nonparametric tools artificial neural networks (ANNs) are candidates to deal with the volatility and/or return forecasting problems. On the other hand, based on the fact that volatility is time varying and that periods of high volatility tend to cluster, the most popular models in modeling volatility are GARCH type models because they can account excess kurtosis and asymmetric effects of financial time series. A standard GARCH(1,1) model usually indicates high persistence in the conditional variance, which may originate from structural changes. Hence it is natural that artificial neural networks (ANN) will be constructed to capture the nonlinear relationship between past return innovations and conditional variance which may be missed by linear regression models. First a usual feedforward, back propagation network is used. The structure of the return data makes FFANN difficult to converge. To overcome this difficulty a neural network with appropriate recurrent connections in the context of nonlinear ARMA models are used. These are the Jordan neural networks (JNN). Then Elman recurrent networks (ENN) and a mixture of the two (EJNN) are also used. The data set consists of returns of the S&P100 index daily closing prices obtained from the S&P100 website. The results indicate that the selected JNN(1,1,1) model has superior performances compared to the standard GARCH(1,1) model. The contribution of this paper can be seen in determining the appropriate NN that is comparable to the standard GARCH(1,1) model and its application in forecasting conditional variance of stock returns. Moreover, from the econometric perspective, NN models are used as a semi-parametric method that combines flexibility of nonparametric methods and the interpretability of parameters of parametric methods.
Highlights
For several decades market makers, portfolio managers, and option traders are all interested in forecasting return fluctuations in order to maximize their profits, and minimize their risks
The data set consists of returns of the S&P100 index daily closing prices obtained from the S&P100 index website in the period from September 6, 2005 until June 7, 2016
For the long term forecasting for the purpose of this research, the first 1000 trade days of the data is neglected, and the remaining data is divided into two parts: the in-the-sample part consists of 1000 observations in the period from August 26, 2009 until August 14, 2013 which is used for the training and the estimation of parameters in the generalized autoregressive conditional heteroskedasticity (GARCH)(p,q), Jordan neural networks (JNN)(p,q,r), Elman recurrent networks (ENN)(p,q,r) and the EJNN(p,q,r,s) models; and the out-ofthe-sample part which consists of the 500 observations in period from August 14, 2013 to August 10, 2015 which is used for the two years ahead forecasting purposes
Summary
For several decades market makers, portfolio managers, and option traders are all interested in forecasting return fluctuations in order to maximize their profits, and minimize their risks. Where N is the cumulative normal distribution, S is the price of the underlying security, K is the strike price, r is the prevailing risk-free interest rate, T is the time-to-maturity and σ is the volatility of the underlying asset This model is helpful when some assumptions are fulfilled, and equations (1) - (3) do contain neither preferences of individuals nor the preferences of the aggregate market (Hull, 1993). As in the case of prices, returns, and the volatility of the market, while underlying relationships between market parameters are unknown or hard to describe, ANNs learn from examples, capture inherent functional relationships in the data, and generalize these relationships to the untouched test data For this reason ANNs are well suited for problems whose solutions require analytic relations like Black-Scholes formulas. Zhang et al (1998), authors attempted to provide a more comprehensive review of the status of research in this area in their time
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