Neural Network Application For Predicting Stock Index Volatility Using High Frequency Data

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Neural Network Application For Predicting Stock
Index Volatility Using High Frequency Data
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• Project No CFWin03-32
• Presented by Venkatesh Manian
• Professor Dr Ruppa K Tulasiram

May, 30, 2003
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Outline
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• Introduction and Motivation
• Background
• Problem Statement
• Solution Strategy and Implementation
• Results
• Conclusion and Future Work

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Introduction and Motivation
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• Index is defined as a statistical measure of the
  changes in the portfolio of stocks representing a
  portion of the overall market3.
• 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.al7 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.

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Background
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• 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.

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Problem Statement
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• 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.

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Solution Strategy and Implementation
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• 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.

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Algorithm Radial Basis Function Networks
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Cont..
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Cont..
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• Calculated intraday value and its corresponding
  realized volatility
• Normalized input value

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Cont..
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• Normalization is done using the following
  equation
• ((x-mean)/standard deviation)
• Input Data

Volatility
Day
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Prediction using RBF network
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• 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(nxny1)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.

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Cont..
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• 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.

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Cont..
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• 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.

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ANN using Sigmoid Function
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• 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.

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Results
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• 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.

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Results using test data
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• The above table gives the output of the network
  using test data.

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Conclusion and Future Work
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• 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.

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References
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• Andersen, T. and T. Bollerslev (1997). Intraday
  periodicity and volatility persistence in
  Financial markets. Journal of Empirical Finance
  4, 115-158.
• 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.
• Investopedia.com
• http//www.investopedia.com/university/indexes/in
  dex1.asp
• 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.
• Iebeling Kaastra and Milton S. Boyd. Forecasting
  Futures trading volume using Neural Networks.
  Journal of Futures Market, 15(8)953-970,
  December 1995.
• P. Sarachandran, N. Sundarajan and Lu Ying Wei.
  Radial Basis Function Neural Networks with
  Sequential Learning. World Scientific
  Publication Co. Pt. Ltd, march 1999.
• Pierre Cizeau, Yanhui Liu, Martin Meyer, C-K.
  Peng and H. Eugene Stanley. Volatility
  distribution in the SP500 stock index.
  arXivcondmat/97081431, August 1997.

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1. Apostolos-Paul Refenes. Neural Network In the
   Capital Market. John Wiley and Sons, LONDON,
   1995.
2. G. Williams Schwert. Stock Market Volatility.
   Financial Analysts Journal, pages 23-34, May-June
   1990.
3. Yahoo Finance. http//finance.yahoo.com/

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Thank You
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Network Training
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• I have considered two types of network in this
  project.
• Radial Basis Function(RBF) network
• Artificial Neural Network
• Sigmoid function