Assessing the Accuracy of Implied Volatility and Historical Volatility in the Black Scholes Merton Model

This paper demonstrates a comparative analysis of estimating option prices using the Black Scholes Merton model with implied volatility and volatility estimated by historical data. The call option prices were calculated using data from the company Electronic Arts (EA) collected from Yahoo Finance. The analysis suggests that using implied volatility in the Black Scholes model for pricing options yields more accurate estimation than using the volatility calculated from historical data, as attested by comparing the absolute error, error percentage, mean squared error, and financial profit or loss of the two methods.

From the results, using implied volatility in the model generate a set of option prices that are closer to the market prices, with an average error percentage of 9.17% and mean squared error of 0.1359, which has significantly lower deviation than using historical volatility in the model, with an average error percentage of 42.46% and mean squared error of 2.4574. A delta-neutral hedging strategy was proposed based on the more accurate method of estimation, utilizing the total delta to reduce the risk of the portfolio. The findings highlight the advantage of implied volatility for option pricing in the Black Scholes model.