# Deriving Bachelier Greeks

I am working on the Bachelier Model with r not equal to 0 as described in the first and most upvoted answer in following link:

Bachelier model call option pricing formula

This is fairly easy to code and to derive delta, vega and gamma. I want to derive however other first order greeks, namely: rho and theta.

I found the following paper that derived these greeks for a Bachelier model with r = 0 and I am using it as support:

In their derivation of theta I do not understand equation A32 on page 16. They write:

Shouldn't it be ? If not, why ?:

On a side note, if anyone has a reference where these bachelier with r != 0 greeks are derived I'll take it

EDIT:

Here are theta and rho that I derived. Hope someone can tell me if it's correct or not.

• Yes, it's a typo ($\partial \sigma$ should be $\partial \tau$).
– ir7
Oct 4 at 16:23