Financial Options: History, Computational Analysis, and Future Significance

This presentation is directed toward a mathematical audience and looks at options, or derivatives, from a computational standpoint using computer programming with Python. A history of two options pricing formulas is given: the binomial pricing model and Black-Scholes’ formula (Cox, Ross, & Rubinstein, 1979; Black & Scholes, 1973). The two formulas are compared against one another to see the benefits of each. The Black-Scholes model is by far the superior way of pricing options. The binomial pricing model has a limit of Black-Scholes formula. The Black-Scholes model is tested against real world data, but significant error is found. The error can give an implied volatility for the stock, which indicates current stock volatility rather than historic. Black-Scholes can also use the error to find arbitrage opportunities in the market. I created a new options trading strategy using Python that gives a list of ranked arbitrage opportunities for all options in an option chain. The program lets the user know the optimal strike price to buy and sell put and call options in order to benefit on the arbitrage opportunities at hand. The future for options trading and pricing has not lost its significance since finding the solution 45 years ago.