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Aug 3 at 18:42 comment added Jan Stuller Log-normality is not required at all for risk-neutral pricing. Models such as Heston or Bachelier assume different dynamics than the simple log-normal dynamics in the Black-Scholes model and they give the correct option prices, whilst the underlying still has to compound at riskless drift due to no-arbitrage between the spot and the forward.
Aug 3 at 7:35 comment added Frido @Arshdeep 's answer is in essence correct. At risk of stating the obvious I'd like to add that the asset needs to be a tradable to use $r$ as drift. If it's not tradable you can't buy/sell it and hence you don't need to fund it and hence $r$ is not required.
Aug 3 at 3:17 answer added Arshdeep timeline score: 1
Aug 3 at 0:38 history asked Thomas Redding CC BY-SA 4.0