Neural Networks for Predicting Options Volatility

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

• SP 100 (OEX)
• Daily closing call and put prices and the
  associated exercise prices closest to
  at-the-money
• SP 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 Forecast MAD MSE Correct 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 Forecast MAD MSE Correct 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
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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