### Use of Explicit GEM million for American put Option => Stock prices for optimal exercise Application of of lto's lam mo to Geometric Bro wnion...

#### Description

Hi, I have a problem with plotting the optimal exercise boundary for American put. I am considering American put with current stock price = 100, strike K = 100, vol=20%, r=10%, div=0%, and 1 year to maturity. I am using a finite difference scheme to approximate the value of the option, and the optimal exercise boundary. I have managed to obtain an explicit finite difference scheme of Put option prices and subsequently, I wanted to plot stock prices as sort of critical values for each point of time of option duration so as to determine if it is optimal to early exercise or not. Using GBM explicit solution I have managed to get stock prices for time interval, however, I can see that the plot does not show the optimal boundary exercise because I am missing something. I am not sure, if I should somehow include into plot my calculated explicit finite difference scheme of Put option prices but if so, I don't know how. So my problem refers to how to plot the optimal exercise boundary for American put basing on the explicit finite difference scheme of Put option prices that I have calculated.I will be grateful for help as I am really stacked. I am attaching 1)and 2) how I have constructed explicit finite difference scheme of Put option prices and 3) (wrong) Plot of optimal exercise boundary

#### Question

Use of Explicit GEM million for American put Option => Stock prices for optimal exercise Application of of lto's lam mo to Geometric Bro wnion...

- Written in: 17-Oct-2019
- Paper ID: 335941

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### About this Question

STATUSApproved

DATE ANSWEREDOct 17, 2019

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