inconsistency

[aupilot]

Hi Davis,

First, thanks for the great piece of code!

It seems that there is some inconsistency in BS and American models. Specifically, if you calculate put option prices with two methods, the both prices look good, but the American model spits out flipped sign for delta and rho. I believe that BS model values are correct. Here is an example:

Black Scholes
value delta gamma theta vega rho
1.21 -0.64 0.20 -7.02 2.36 -0.90
American
value delta gamma theta vega rho
1.22 0.67 0.19 -7.18 2.35 0.85

Code used:

fs = 30.17; x = 31; t=16/365; r=0.051; v=0.3; q=0.01;
value, delta, gamma, theta, vega, rho = black_scholes("p", fs=fs, x=x, t=t, r=r, v=v)
value, delta, gamma, theta, vega, rho = american("p", fs=fs, x=x, t=t, r=r, q=q, v=v)