I need an accurate reference price of an American put option under GBM dynamics ($r > 0$).
I can use many numerical methods, but it would take too long to get any more than 3 or 4 digits of accuracy.
I need a reference price that is more accurate, preferably exact, but 6 - 8 digits of accuracy would do. Is there such a known reference price in the literature? The model parameters don't matter, I just need one particular specification so I can test my own methods on it.