Option price forecasting using neural networks Jingtao Yao, Yili Li, Chew Lim Tan* School of Computing, National University of Singapore, Singapore 119260, Singapore Received 1 August 1998; accepted 1 September 1999 Abstract In this research, forecasting of the option prices of Nikkei 225 index futures is carried out using backpropagation neural networks. Dierent results in terms of accuracy are achieved by grouping the data dierently. The results suggest that for volatile markets a neural network option pricing model outperforms the traditional Black±Scholes model. However, the Black±Scholes model is still good for pricing at-the-money options. In using the neural network model, data partition according to moneyness should be applied. Those who prefer less risk and less returns may use the traditional Black±Scholes model results while those who prefer high risk and high return may choose to use the neural network model results. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Neural networks; Forecasting; Option pricing; Black±Scholes model 1. Introduction There has been a tremendous increase in the aware- ness and activities of derivative securities in recent years. Option markets are among the top most popular shares of ®nancial institutions. To explore the markets well and improve investment yields, pricing of options has attracted researchers' attention for years. Modeling or predicting option prices is very important for prac- titioners. Numerous pricing models have been created and studied. The Black±Scholes model [2,16] is the most widely used model which is based on certain assumptions such as geometric Brownian motion of stock price movements, that the option is exercised at the time of maturity (i.e. European option), constant interest rate, continuous trading without dividends and tax applied to the stocks, and that the market is fric- tionless. Although research results show that the Black±Scholes model does outperform other option pricing models except in the case of deep-in-the-money and deep-out-of-the-money, the fact that real data often violate most of the model's assumptions brings it under suspicion. Violations may be found in the fol- lowing situations: (1) instead of random walk descrip- tion, fractal may be a better hypothesis for the market movement [20]. Akgiray [1] has also rejected the assumption of constant variance of stocks. (2) In fact, American option dominates the real markets. People want more choices when the market changes, such as when it is near the time to pay dividends. (3) Divi- dends are common practice especially for stocks. There are many attempts to modify the Black± Scholes model with the view to avoiding the above vio- lations. The following are some examples of such attempts: pure jump model [5] and mixed diusion jump model [17] based on continuous constraints; square root constant elasticity of variance diusion model [5], displaced diusion model [25] and com- pound option diusion model [8] based on the con- Omega 28 (2000) 455±466 0305-0483/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S0305-0483(99)00066-3 www.elsevier.com/locate/dsw * Corresponding author. Tel.: +65-874-2900; fax: +65-779- 4580. E-mail address: tancl@comp.nus.edu.sg (C.L. Tan).