Neural Network Application For Predicting Stock Index Volatility Using High Frequency Data Project No CFWin03-32 Presented by: Venkatesh Manian Professor : Dr Ruppa K Tulasiram Outline Introduction and Motivation Background Problem Statement Solution Strategy and Implementation Results Conclusion and Future Work 1 2 Introduction and Motivation Background Index is defined as a statistical measure of the changes in the portfolio of stocks representing a portion of the overall market [3]. Hol and Koopman [2] calculates volatility using high frequency intraday returns. The noise present in the daily squared series decreases as the sampling frequency of the returns increases. Pierre et.al[7] says that price change are correlated only over a short period of time whereas absolute value has the ability to show correlation on time up to many years. Predicting capability of neural networks. Schwert in [9] points out the importance of intraday data on stock prices to keep track of market trends. Market decline on October 13, 1987. Refenes in [8] explains about different problem available and its solution strategies. He says that neural networks is used in cases where the behavior of the system cannot be predicted. 3 4 1
Problem Statement Solution Strategy and Implementation The goal of this project is to predict the volatility of stock index using Radial Basis Function (RBF) Neural Networks The project focuses on the following aspects.! Using high frequency intraday returns so as to reduce the noise present in the input.! Using RBF networks which can calculate the number of hidden nodes needed for predicting volatility at runtime so as to reduce the problems involved in using more hidden nodes or less. Prediction of stock index volatility is also tested using multilayer feedforward network. In this case sigmoidal function is used as activation function. Collection of every five-minute value of stock index. Intraday returns are calculated by subtracting successive log prices. Overnight returns is calculated in the similar way as the intraday returns using the closing price of the index and the price of index with which the market starts on the following day. Calculation of the daily realized volatility by finding the cumulative squared intraday returns. Realized volatility is used as input of the neural network and future stock index value is predicted. 5 6 Algorithm Radial Basis Function Networks o H 1 H 2 H 3 H 4 I 1 I n 7 8 2
Calculated intraday value and its corresponding realized volatility Normalization is done using the following equation =((x-mean)/standard deviation) Normalized input value 9 V Input Data o l a t i l i t y Day 10 Prediction using RBF network Configuration of the network Number of input nodes is ten. Initially the number of hidden nodes is set to zero. Number of output nodes is set to one. Due to the high computational complexity of the system the size of the network has to be kept minimal. Number of input nodes cannot be increased more than 15. Because for each hidden node added into the network number of parameters to be updated in each equation of the Extended Kalman Filter is k(nx+ny+1)+ny. Where k is number of hidden nodes, nx is number of inputs and ny is one in this case i.e. number of output. Learning in RBF network Learning of this network involved assigning a larger centers and then fine tuning of these centers. Based out difference between expected value and output. Setting up window size to see whether the normalized output value of each hidden node for a particular duration is below a threshold value. If the normalized output value of a particular hidden node is below a threshold vale for a duration called the window size then the particular hidden node is pruned. The major problem due to the presence of noise in the input data is over fitting. This results in increase in the number of hidden nodes with increasing the number patterns. Root Mean Square value of the output error is calculated to overcome this over fitting problem. 11 12 3
ANN using Sigmoid Function Problems encountered. Initially I did not use normalized inputs but I reduced the size by dividing each input by 1000. This experiment gave me a kind of favorable results. The number of hidden nodes learned in case is four. The number of input patterns used in this case is 200. Number of input nodes used in this case is 10. Since normalizing is the way to reduce the range of the input value, each input data is normalized with respect to the mean and standard deviation of the data. After normalizing the network started to overfit the data. I tried to update the value of different parameters. But I was unable to control the effect of this problem. Hence I used different network for prediction. I used sigmoid function in this case as the activation function. o H 1 H 2 H 3 H 4 I 1 I n Algorithm In this case all connections are associated with weights. Weighted sum is given is given to each nodes of the next layer which calculates sigmoid function. On receiving the output from the output node, it is compared with the expected value and the output error is calculated. This value of error propagated back into network to adjust the weights. 13 14 Results Results using test data I trained the network so as to get a minimum error in the testing phase. MAPE (mean absolute percentage error) is used as the evaluation method in this case. 15 The above table gives the output of the network using test data. 16 4
Conclusion and Future Work References I used high frequency intraday data for predicting the value of volatility. The method used for prediction in this project is neural network. Since I did not get any favorable results in this case, I would take some help in solving the problem due to over fitting of data. I will also try to find a way to get better results using ANN, which uses sigmoid function. I would also make up a better algorithm which can overcome the memory problem involved in using large amount of data. 1. Andersen, T. and T. Bollerslev (1997). Intraday periodicity and volatility persistence in Financial markets. Journal of Empirical Finance 4, 115-158. 2. Eugene Hol and Siem Jan Koopman, Stock Index Volatility Forecasting with High Frequency Data No 02-068/4 in Tinbergen Institute Discussion Papers from Tinbergen Institute. 3. Investopedia.com http://www.investopedia.com/university/indexes/index1.asp 4. JingTao Yao and Chew Lim Tan. Guidelines for Financial Forecasting with Neural Networks. In Proceeding of International Conference on Neural Information Processing, Shangai, China, Pages 772-777, 2001. 5. Iebeling Kaastra and Milton S. Boyd. Forecasting Futures trading volume using Neural Networks. Journal of Futures Market, 15(8):953-970, December 1995. 6. P. Sarachandran, N. Sundarajan and Lu Ying Wei. Radial Basis Function Neural Networks with Sequential Learning. World Scientific Publication Co. Pt. Ltd, march 1999. 7. Pierre Cizeau, Yanhui Liu, Martin Meyer, C-K. Peng and H. Eugene Stanley. Volatility distribution in the S&P500 stock index. arxiv:condmat/97081431, August 1997. 17 18 Thank You 8. Apostolos-Paul Refenes. Neural Network In the Capital Market. John Wiley and Sons, LONDON, 1995. 9. G. Williams Schwert. Stock Market Volatility. Financial Analysts Journal, pages 23-34, May-June 1990. 10. Yahoo Finance. http://finance.yahoo.com/ 19 20 5
Network Training I have considered two types of network in this project. Radial Basis Function(RBF) network Artificial Neural Network Sigmoid function 6