there's a standard explanation obtained by substituting the pay-off (S-K) at expiration into the PDE and looking at the sign of [$]\frac{\partial V}{\partial t}[$] at expiration [$]\frac{\partial V}{\partial t}=-\frac{S^{2}\sigma^{2}}{2}\frac{\partial^{2}V}{\partial S^{2}}-(r-D)S\frac{\partial V}{\...

According to Kim (1990, p.560) in "The Analytic Valuation of American Options". https://imgur.com/a/kua3M I understand the first minimum condition where K sets the lower bound of the optimal exercise boundary at expiry, but the second one is unclear to me,   Update: $\delta$ = divdend rate...

As mentioned, there is no 'simple' FDM for this IMO. And since this is a nonlinear problem then accuracy is first-order, all things being equal. Or use front-tracking. LIke this http://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=2287&context=cstech It's trickier than usual FDM but is doable...

It's highly accurate for most cases (I expect 6 digits here), but there are exstreme-ish parameter configurations where it blows up. I would still need to quantify that region before I would use it in production. It's the method described in this paper " High Performance American Option Pricin...

It's highly accurate for most cases (I expect 6 digits here), but there are exstreme-ish parameter configurations where it blows up. I would still need to quantify that region before I would use it in production. It's the method described in this paper " High Performance American Option Pricin...

is your method extremely accurate?. Just want to get a feel for your boundary compared to FDM or any other numerical method.

would it look different if You had used FDM to create it?

My value is very close "  8.94366"  Did you attain those values using FDM ?  Also, I maybe asking for a lot here but,  your plot is exactly what I want but I would like the dots to be more connected (a line between them maybe? ) so the boundary the depicted would be almost like a continuou...

Hi i been looking around the net for a Finite difference script/routine (For Matlab, c++, python) which specifically can depict the early exercise boundary for an American put with the following inputs: S = 100 K = 100 r = 0.08 volatility = 0.2 dividend = 0.04 T = 3.0 dt = 0.03 I want the routine to...

Can someone explain how they do get Bt values using this backward recursion ?

It is related to the uploaded picture..

I want to understand the logic for why this is: We have our model for the stock price behaviour: $$d{S_t} = \mu {S_t}dt + \sigma {S_t}d{\tilde W_t}$$ It describes the development of a stock price over time using the risk-adjusted expected return $\mu$ and the real uncertainty in the stochastic term....

Possible typo in first passage probability formula? The first passage probability given by Bunch and Johnson is given as $$Z = {1 \over \sigma }\left[ {\log {S \over {Sc}} + (r - {1 \over 2}{\sigma ^2})t} \right]$$ after reading some literature should it not be the case that the first passage probab...

I wonder if it is derived from $$Z = \exp \left\{ {\sigma X(t) + (\sigma r - {1 \over 2}{\sigma ^2})t} \right\}$$ where $$X(t) = \log S/Sc$$

can you write it more clearly?

In this article the authors present this first passage probability formula  $$Z = {1 \over \sigma }\left[ {\log S/{S_t} + (r - {1 \over 2}{\sigma ^2})t} \right]$$ ${{S_t}}$ value of the stock at time t , r ror on the stock, $\sigma $ standard deviation. The authors ref. Feller (1971) "An Introd...