I've been trying to create a black normal model and have used http://janroman.dhis.org/finance/Swaptions/normal%20swaptions.pdf as a guide.
I am trying to validate the theta formula in this paper - which is effectively (for puts):
θ = -r * option_price
where option_price : $$ e^{−r(T−t)}[(K−F)N(−d1)+\frac{σ\sqrt{T−t}}{\sqrt{2π}}e^{−d^2_1/2}]$$
however - I computed theta for an option where I fixed all parameters but varied the time to expiry (T) by a day. As you can see from the graph below: the theta from this model doesn't conform to typical time decay.
As you can see - theta seems to increase as T -> 0, which is incorrect.
Would anyone be able to provide some insight into where I might have interpreted the paper incorrectly - or provide some papers on how to compute theta for the black scholes normal model?
For reference - these are my parameters: S = 2, K = 2, r = 0.02, T = range from 365 -> 0