A Regression Model to Investigate the Performance of Black-Scholes using Macroeconomic Predictors

As it is well known an option is defined as the right to buy sell a certain asset, thus, one can look at the purchase of an option as a bet on the financial instrument under consideration. Now while the evaluation of options is a completely different mathematical topic than the prediction of future stock prices, there is some relationship between the two. It is worthy to note that henceforth we will only consider options that have a given fixed expiration time T, i.e., we restrict the discussion to the so called European options. Now, for a simple illustration of the relationship between true stock prices and options let us consider the following situation: if at the beginning of January the S&P index is valued at $1,277 and then at the end of December of the same year the price of the index became $1,400 then the fair price of the option to buy this in January would be $123, assuming T=1. This is a fair price because if the holder purchases the option for $122 or less then he or she gains while if the holder purchases the option for $124 or more then the bank wins while $123 is neutral for both parties. As one can see from this simple illustration predicting the fair price of an option is directly related to predicting the value of the stock price in a future time T