Optional trading pricing with a new analytic method for the Black Scholes equation

The Black-Scholes pricing theory is one of the most important ways of valuating transaction options. This equation is used to pricing a variety of European options. In this paper, a new and different method was developed to prove and improve the Black-Scholes equation by focusing on the Black-Scholes main Schrödinger equation and solving this equation using the Nikkeuro-Ovaryov method. In the following, while investigating the possibility of improving the Black-Scholes equation with this method, a new equation for the pricing of transaction options was presented and tested. Increasing the accuracy of pricing arbitrary deals by using the equation provided, especially for high-value trades, checking logical solution in a new way, comparing output with numerical solution and innovating. Final formula. Option based on Lagrange polynomial functions, the goals of doing research are present. The results showed a different positive probability for the Black-Scholes equation by solving the differential equation by the method Nikkirovo-Ovaryov is feasible and at 95% confidence level, there is no significant difference between the price of the two main black-hole groups and the new model. In order to compare the output of the new model with the Black Sholes main model, information from the 50 Coin Deal options in Iran's Overseas Branch was limited to the 1394 to 1397 period and the Mann-Whitney independent nonparametric group was used to compare.