1. Neural Networks for Predicting Options Volatility Mary Malliaris and Linda Salchenberger Loyola University Chicago World Congress on Neural Networks San Diego 1994

2. Introduction Volatility is a measure of price movement used to measure risk Traders use two estimates of options volatility – Historical – Implied We will compare these with a neural network model for predicting options volatility

3. Historical and Implied Historical – The annualized standard deviation of n-1 rates of daily return Implied – The volatility calculated using the Black-Scholes model

4. Neural Network Backpropagation model Frequently applied to prediction problems in nonlinear cases Used to forecast volatility one day ahead

5. Data S&P 100 (OEX) Daily closing call and put prices and the associated exercise prices closest to at-the- money S&P 100 Index prices Call volume and put volume Call open interest and put open interest All of 1992

6. Volatilities Historical – Three estimates using Index price samples of sizes 30, 45, and 60 Implied – Black-Scholes model calculations for the closest at-the-money call for three contracts: those expiring in the current month, one month away, and two months away (nearby, middle, and distant)

7. Historical vs Implied Dates of ForecastMADMSECorrect Directions Jun 22 – Jul 19.0318.0012.421 Jul 20 – Aug 21.0292.0019.440 Aug 24 – Sep 18.0406.0018.667 Sep 21 – Oct 16.0479.0027.350 Oct 19 – Nov 20.0213.0008.560 Nov 23 – Dec 18.0334.0014.444 Dec 21 – Dec 30.0294.0009.333

8. Network vs Implied Dates of ForecastMADMSECorrect Directions Jun 22 – Jul 19.0148.0003.842 Jul 20 – Aug 21.0107.0002.640 Aug 24 – Sep 18.0056.0001.722 Sep 21 – Oct 16.0127.0003.950 Oct 19 – Nov 20.0059.0001.800 Nov 23 – Dec 18.0068.0001.833 Dec 21 – Dec 30.0039.0000.833

9. Discussion The neural network model uses both short term historical data and contemporaneous variables to forecast future implied volatility NN predictions can be made for a full trading cycle The network forecasts were more accurate estimates of volatility