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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:

https://www.nottingham.ac.uk/business/who-we-are/centres-and-institutes/gcbfi/documents/cris-reports/cris-paper-2007-7.pdf

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

enter image description here

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

enter image description here

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.

Theta

Rho

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

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