Comparative empirical study of binomial call-option pricing methods using S&P 500 index data

In this paper, several binomial models are tested empirically on S&P500 Index on the levels of tradability, proximity to market (RMS) prices and profitability, especially close to expiration day. These comparisons will be carried out for many different business environments, including different market trends and moneyness levels traded. Among the models under analysis we assess the quality of the SH model, developed by the authors in previous work, in relation to other models. The option price in the SH model is affected by the players' assessments about the behavior of the prices of the underlying asset up to the expiration day and by their "eagemess" levels (i.e., players' readiness to respond to a given bid proposed by their opponent). We found that for all models, the higher the moneyness, the greater the proximity of models prices to actual market prices and that, eagerness parameters have a decisive effect on tradability. We also found that there was no correlation between the degree of proximity of modeled prices to actual prices and the expected profit gained by players that act according to a given model and that the SH model traded relatively small number of options. The expected profit is highest for the SH model in the ITM and ATM for days that are far from the expiration day.