The Black-Scholes (B-S) formula, a well-known model for pricing derivative securities, exhibits certain systematic biases from observed option prices in the market. In this study, an attempt is made to reduce the biases and improve the accuracy of option price estimation using Artificial Neural Networks (ANN). It is based on all Nifty call option prices quoted on National Stock Exchange for the period May 28, 2004 to June 30, 2005. It is found that the error between the quoted option prices and estimated option prices using the Black-Scholes formula reduces to a large extent, when the original formula is modified using an Artificial Neural Network model. The usefulness of ANN is also validated with out-of-sample data.
The
valuation of options has generated tremendous interest among academics and investors
alike, and a number of valuation models have been developed. The most popular
model to date is the Black-Scholes (B-S) model (1973) which is based on the assumption
that stocks continuously compounded rate of return follows a normal distribution.
The model however, exhibits systematic biases from observed option prices. Macbeth
and Merville (1979) find that the B-S model under prices in the money options
and overprices out of the money options.
A
number of academic studies have attempted to explain and correct the biases of
the model but none seems to be complete (Robinstein, 1985). The most often challenged
assumption is the normality of stock returns ignoring heteroscedasticity. As it
was difficult to obtain a closed form of parametric solution, several nonparametric
approaches were also tried, among which Artificial Neural Network (ANN) based
models have emerged as a promising alternative (Bennell and Suteliffe, 2003). |
