A Modified Black Scholes Merton Model Based on Student’s t-distribution and GARCH model

Black Scholes Merton model, originally proposed by the black fisher, Myron Scholes, and independently by Robert Merton back in the 1970s. Their model serves as a valuation tool that can estimate the price of options based on other investment parameters. This paper will assess the accuracy of the original Black Scholes Merton model using realworld option transaction data. This paper will further modify some of the assumptions of the BS model such as the stock price will instead follow the student’s $\boldsymbol{t}$-distribution in order to reduce prediction errors. The results indicate that a composite model that combines both the original BS model and the modified BS model can effectively reduce prediction errors.