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Time:

A Neural Network Forecasts
Options Volatility

Mary
Malliaris

and Linda
Salchenberger


10
th

IEEE Conference on Artificial
Intelligence for Applications

Overview


We compare existing methods of estimating
the volatility of daily S&P 100 Index options


Implied volatility (calculated using the Black
-
Scholes model)


Historical volatility


A neural network is used to predict volatility

Volatility


A measure of price movement


Often used to ascertain risk


Ability to forecast volatility gives a
trader a significant advantage in
determining options premiums

Calculating Volatility


There are two main approaches to estimating
and predicting the non
-
constant volatility


The historical approach


However this assumes that future volatility will
not change and that history will repeat itself


The implied volatility approach


One solves the Black
-
Scholes model for the
volatility that yields the observed call price

Neural Networks


Layers of interconnected nodes


Constructed in three layers


Sigmoid function applied to sum of weighted
inputs at each node


Connection weights are learned by the
network through a training process by looking
at training set examples

Neural Network Architecture:

Nodes, Connections, & Weights

Each node in the
hidden

&
output

layers applies a
function to the sum of the
weighted inputs.

w1

w2

w3

w16

w17

w18

w19

w20

w21

F(sum inputs*weights)=node output

F(sum inputs*weights)=output

Data


S&P 100 (OEX)


Daily closing call and put prices


Associated exercise prices closest to at
-
the
-
money


S&P 100 Index prices


Call and put volume


Call and put open interest


250 observations for six series of volatilities

Comparison of Historical and
Implied Volatility Estimates

Neural Network and Implied
Volatility Estimates

Results


Historical volatility is only backward looking


Implied volatility provides estimates which are
only valid at that current time


Neural network volatility uses both short
-
term
historical knowledge and contemporaneous
variables in the estimate


NN predictions can be made for a full trading
cycle and are more accurate