Conclusions

Looking at the results of our design, it is clear to see that pricing with the Black-Scholes-Merton model using the implied and empirical volatilities failed in a majority of the cases. However, as stated in our objective, we were not expecting it to work for all industries all of the time. Granted, we can now say that it does not even work for one industry in the period of time that we analyzed (mostly between September and October of 2015). The technology industry came the closest to having accurate results when pricing using the implied volatilities, but this still was only successful with three out of the five companies. While we firmly believe that the pricing models would have been more accurate using year long maturity contracts had the required data been available, we do not have the evidence to back up such a claim. That being said, our results were conclusive in determining that neither the implied or empirical volatility had normal distributions, an assumption of the BSM, in most companies analyzed.  Therefore, we effectively displayed a limitation of the BSM model due to volatility in a short-term scenario as well as the theoretical failure in the long-term scenario mentioned in Warren Buffett’s letter to his shareholders.

We expect that our analysis technique can be practically applied by individuals pricing with the Black-Scholes-Merton model, and we hope that others will use our design methods and code to expand on our findings, as this is just a jumping off point. We conclude that our design has implemented a unique approach to the effects of options pricing using implied and empirical volatilities and provided insight to rather undocumented results.