An Empirical Comparison: Two Special Cases of CEV Option Pricing Model and Black-Scholes Model on S&P Canada 60 Index Call Options

Given that the options market is now very large and significant part of the trade of financial instruments, the evaluation of pricing of these derivatives becomes very important for regulators as well as market participants. The value of an option can be estimated by using a variety of quantitative techniques based on the concept of risk neutral pricing. In the famous Black-Scholes pricing formula it is assumed that the underlying stock price returns follow a lognormal distribution. However, empirical studies have shown that this assumption does not perfectly hold. Rubinstein (1994) examines the S&P 500 index option market and finds that Black-Scholes implied volatilities have a “smile” pattern prior to October 1987 market crash and a “sneer” after the crash. Consequently, several kinds of modification of the variances have been tried.