An option pricing model focus on spread based on the stock price of Apple and Tesla

Abstract

Option on a spread is typically valued by the difference between two stock prices. However, there may be several limitations for this form if the two prices differ enormously. We thus establish the option based on the difference of profits as opposed to pure stock prices and the option value is largely determined by the growth rate or potential profits. In the valuation process, we use the geometric Brownian motion model to estimate the stock price in 15 days and compute the rate of return as well as the investment profits. Consequently, the value of the option could be calculated if the strike price is given. To gain a more general conclusion we simulate the valuation process 1000 times and test the sensitivity of the option based on several input variables. Our work is to provide a new form of option on a spread that could be utilized in more general combinations of stocks.