Hi, I am struggling with making a plot for American put option and its optimal exercise boundary. In order to obtain option values I have first used Explicit finite difference method to price the American put option ( I have obtained the grid) and now I am not sure how to make the plot that would contain critical values of the stock prices for each point in time to determine the curve of optimal exercise boundary. In that way I want to see if early exercise is optimal or not. I am using the following data:
Current stock price (S0) = 100, Strike price (K ) = 100, interest rate (r) = 10%, volatility = 20%, time to maturity (T) = 1 year.
In the attached pictures you can see:
Pic1: Computation of unknown option values via Explicit finite difference method
Pic2: My result of Put Option prices on the grid by a finite difference approach,
Pic3 and Pic4: Here, I am trying to calculate Stock price for each point of time using Geometric Brownian Motion, and then plot the values, however, I have completely no idea if it is actually correct and how to implement optimal exercise boundary.
Please, could I ask for a hand on that?