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### Q:American Put Option and Critical stock price

Posted: **January 21st, 2017, 11:51 pm**

by **MAYbe**

I am writing my thesis now and i was wondering if anyone knows or if there is a code for Equation (23) and Equation (29) in

"The American Put Option and Its Critical Stock Price" by David S. Bunch and Herb Johnson ?

### Re: Q:American Put Option and Critical stock price

Posted: **February 13th, 2017, 8:45 pm**

by **DavidJN**

I haven't read the Bunch and Johnson paper but the solution of critical stock prices in similar papers (the Whaley Barone-Adesi American option pricing model comes to mind) is typically done using a numerical search algorithm much like the way implied volatility is solved. So you might get useful implementation ideas from papers or books that deal with the Whaley model. The Collector's (Espen Haug) book might be useful?

### Re: Q:American Put Option and Critical stock price

Posted: **February 15th, 2017, 5:03 pm**

by **DavidJN**

If the expression that defines the critical stock price can be differentiated w.r.t. the underlying price (and that is likely) you could use the Newton Raphson algorithm to solve for it. Again, the idea is much like solving the implied vol on an option. There's tons of free code on the web for solving option implied vols that you could adapt for your purpose.