Evaluating The Black-Scholes Option Pricing Model And Possible Option Pricing Alternative Using Market Data

This project investigates the underlying properties of the Black-Scholes option pricing model and unveils some of its limitations. We investigate its characteristics by employing historical S&P500 data on a number of options transactions and evaluate its assumptions in the light of market data . Knowing the outlined limitations of Black-Scholes, we will then study the effects of using a trinomial tree to approximate the Black-Scholes model as well as counter the weakness by developing a method to price options under non-constant volatility conditions and develop predictor algorithms for estimating future volatility. Option prices will be generated out from the trinomial tree using the two predictive algorithms namely; least mean square (LMS) and generalised auto-regressive conditional heteroscedasticity (GARCH). We hope to compare this against the historical S&P 500 market result and conclude that this new method is actually more effective than the Black-Scholes model. So far, studies have been done on individual models but mostly are just theory. Therefore, it will be rewarding to see the effects of using historical market data and simulate it on these models and compare their performance appropriately