Qual Quant (2009) 43:833–843
Using neural network to forecast stock index option
price: a new hybrid GARCH approach
Published online: 22 May 2008
© Springer Science+Business Media B.V. 2008
Abstract This study aims to apply a new hybrid approach to estimate volatility in neural
network option-pricing model. The analytical results also indicate that the new hybrid method
can be used to forecast the prices of derivative securities. Owing to combines the grey fore-
casting model with the GARCH to improve the estimated ability, the empirical evidence
shows that the new hybrid GARCH model outperforms the other approaches in the neural
network option-pricing model.
Keywords Option-pricing model · GARCH · Grey forecasting model · Volatility
Accurate measures and good forecasts of volatility are essential for option pricing theories.
Volatility is a measure of price movement that is frequently used to determine risk and signal
large movements in underlying markets. The predictability of market volatility is important
for options practitioners to forecast closing prices and determine expected market return.
Estimating stock market volatility has received considerable attention by both academics
and practitioners. Some studies have been speciﬁed the stochastic volatility of the underlying
asset as a deterministic function of time and the price of the underlying asset (Scott 1987;
Hull and White 1987; Heston 1993; Bates 1996; Watanabe 1999; Kim and Kim 2004), and
other related research compared the ability of various members of the GARCH family to
estimate market volatility (Duan 1995; Sabbatini and Linton 1998; Chung and Hung 2000;
Heston and Nandi 2000; Duan and Zhang 2001; Szakmary et al. 2003; McMillan and Speight
Although in the past, GARCH models have been used as estimates of market volatility,
there is a growing body of evidence that suggests that the use of volatility predicted from more
sophisticated models will lead to more accurate forecasting time-series models.
Y. -H . Wa n g (
Department of Finance, Yuanpei University, Hsin Chu 300, Taiwan, ROC