# Black Scholes Theta Finite difference

I am trying to obtain the Theta from Closed Formula by using Finite Difference methods and I observe some discrepancies. For instance, here with the following parameters:

Spot:50, Strike:50, Rate: 0.12 Time To maturity: 0.25, Volatility: 0.3

BS Closed Form: -8.528247797676

BS Forward FD: -5.8503941392455516

I applied a change of -1/365 in T to compute the BS Forward FD.

Please note that I am perfectly able to match Delta, Gamma and Vega. I don’t know what is wrong with Theta. Any idea?

First and foremost I do not agree with you Closed Form value. I get $\Theta=-8.963$. There are various of BS calculator you can use the check your results and in general you should do that. Here is one: https://goodcalculators.com/black-scholes-calculator/
Have in mind that maturity T is fixed then your forward FD problem should look like this: $$\Theta(T-t_0) \approx \frac{C(....,T-t_0+h)-C(....,T-t_0)}{h}$$ $C(...,T-t)$ denotes the BS call price for time To maturity $T-t$. Choose a small value of $h$ say $h=1/100000$ and let the other parameters be those your mentioned in your post then at time 0 and maturity $T=1/4$ your FD problem will return: $$\Theta(T-0)=\Theta(T) \approx \frac{C(....,T+h)-C(....,T)}{h}=-8.963$$ Even for a much bigger value of $h$ namely $h=1/365$ the result is $\Theta(T)=-8.946$