1 Financial Informatics –IX: Financial Neural Computing Khurshid Ahmad, Professor of Computer Science, Department of Computer Science Trinity College, Dublin-2, IRELAND November 17 th,

2 Financial Informatics: Neural Computing and Volatility Hamida, Shaikh A, and Zahid Iqbal (2004). Using neural networks for forecasting volatility of S&P 500 Index futures prices. Journal of Business Research Vol. 57, pp 1116– 1125 Financial time series models are used extensively in econometrics and in finance. However, pre-condition of the use of these models includes: (a)Model Identification: whether to choose autoregressive or moving average or a hybrid of the two; (b)The order of the model (c) The time series has minimal or noise.

3 Financial Informatics: Neural Computing and Volatility Hamida, Shaikh A, and Zahid Iqbal (2004). Using neural networks for forecasting volatility of S&P 500 Index futures prices. Journal of Business Research Vol. 57, pp 1116– 1125 Network Architecture: The number of neurons in the first layer—13—is equal to the number of explanatory variables. We specified two times that many neurons in the second layer.

4 Financial Informatics: Neural Computing and Volatility Hamida, Shaikh A, and Zahid Iqbal (2004). Using neural networks for forecasting volatility of S&P 500 Index futures prices. Journal of Business Research Vol. 57, pp 1116– 1125 Training and Testing Data: We want to predict the volatility of the S&P 500 Index futures prices. Our raw data series consists of closing settlement prices of 16 nearest futures contracts and 3 spot indexes. We take the futures contract series that will mature in the nearest maturity month. The maturity months are March, June, September, and December# Future Contracts. Seven of the 16 futures contracts are on commodities (silver, platinum, palladium, heating oil, copper, gold, crude oil), 3 are on Treasury obligations (Treasury notes, bonds, and bills), and 6 are on foreign currencies (Swiss frank, yen, mark, Canadian dollar, British pound, euro dollar). The three spot indexes are DJIA, NYSE Composite Index, and S&P 500 Index.We also use 1- day lagged S&P 500 futures prices as an additional explanatory variable for a total of 20 variables. We select these variables because of availability of 10 years of daily data on them—from February 1, 1984, to January 31, 1994—2531 observations per variable. The data set was obtained from Knight–Ridder Financial Publishing. Since neural networks need to be trained with a large data set, it fits well with our needs. From the raw data series, we calculate 20-day rolling historical standard deviations (HSDs). We calculate HSDs from daily percentage price changes of the 20 variables calculated as natural log relatives of the price or index series. The percentage change for Day 2 based on prices P1 and P2 will be given by: ln( P2/P1).We use 500 HSD observations to train the network and the rest for forecasting.

5 Financial Informatics: Neural Computing and Volatility Hamida, Shaikh A, and Zahid Iqbal (2004). Using neural networks for forecasting volatility of S&P 500 Index futures prices. Journal of Business Research Vol. 57, pp 1116– 1125 Future ContractsElaborationNumber CommoditiesSilver, platinum, palladium, heating oil, copper, gold, crude oil 7 Treasury obligationsTreasury notes, bonds, and bills3 Foreign CurrenciesSwiss frank, yen, mark, Canadian dollar, British pound, euro dollar 6 Spot IndexesDJIA, NYSE Composite Index, and S&P 500 Index 3 Future Prices1-Day lagged S&P futures data points were extracted from the 20 time series

6 Financial Informatics: Neural Computing and Volatility Hamida, Shaikh A, and Zahid Iqbal (2004). Using neural networks for forecasting volatility of S&P 500 Index futures prices. Journal of Business Research Vol. 57, pp 1116– 1125 Future Contracts ElaborationNum ber CommoditiesSilver, platinum, palladium, heating oil, copper, gold, crude oil 7 Treasury obligations Treasury notes, bonds, and bills3 Foreign Currencies Swiss frank, yen, mark, Canadian dollar, British pound, euro dollar 6 Spot IndexesDJIA, NYSE Composite Index, and S&P 500 Index3 Future Prices1-Day lagged S&P futures1 From the raw data series, we calculate 20-day rolling historical standard deviations (HSDs). We calculate HSDs from daily percentage price changes of the 20 variables calculated as natural log relatives of the price or index series. The percentage change for Day 2 based on prices P1 and P2 will be given by: ln( P2/P1).We use 500 HSD observations to train the network and the rest for forecasting.