Frontiers in Applied Mathematics and Statistics (May 2024)
Empirical examination of the Black–Scholes model: evidence from the United States stock market
Abstract
Option pricing is crucial in enabling investors to hedge against risks. The Black–Scholes option pricing model is widely used for this purpose. This paper investigates whether the Black–Scholes model is a good indicator of option pricing in the United States stock market. We examine the relevance of the Black–Scholes model to certain stocks using paired sample t-test and Corrado and Miller’s approximation for the implied volatility. Empirical tests are applied to determine the significance of the relationship between the actual market values and the Black–Scholes model values. Paired sample t-tests are applied to 582 call options and 579 put options. The empirical test results show that there is no significant difference between the actual market premium value and the Black–Scholes model premium value for seven out of nine stocks considered for call options, and four out of nine stocks considered for put options. Thus, we conclude that the Black–Scholes option pricing model can be used to price call options but is not suitable for pricing put options in the United States stock market.
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