I am currently writing a small paper comparing the Black-Scholes formula to the Bachelier model. However I am wondering how exactly I should compare the two models?
Obviously I am comparing the prices given by the two models, but the whole point of implementing the Bachelier model (in a context of energy option specifically) is that it allows for negative prices on the underlying asset. The Black-Scholes model does not allow for negative prices (or strikes) as input and hence I cannot directly compare the prices of the options when the price of the underlying turns negative.
How can I meaningfully compare the two models? So far I am trying to model the squared difference between the two prices but I would like to do more.
Also, if anybody has a link to analytical formulas for the greeks of the Bachelier model I would greatly appreciate it.
Thanks a lot!