Re close votes: I believe this is a fair kind of opinion-based question because it's like those ethics questions in academia se or workplace se or because it's pedagogical.
Context: I'm actually asking this in the context of this maths education se question I have.
I have a pedagogical question to ask.
Pricing when arbitrage is possible through Negative Probabilities or something else --> in a stochastic calculus exam I took for my master's in applied maths 7 years ago, we were expected to give a price to something when all our formulas for pricing assumes absence of arbitrage but yet the absence of arbitrage assumption is violated! (And we were not told anything like price is automatically zero if this assumption is violated, if it's even true.)
- I asked during exam (this part was in English, though the next part wasn't)
Me: Sir/Mme, are you sure we can do this (determine the price), if you are allowed to say?
Instructor: What do you mean?
Me: Well, sir/mme, I mean...what if we cannot determine it?
Instructor: If it cannot be determined, then it cannot be determined. If it can be determined, then determine it.
Me: (smiles to myself thinking that I've figured out the 'trick')
- when returning our exams, our stochastic calculus professor said (assuming I translated good enough from Tagalog/the Philippine language to English) 'Apparently, there is arbitrage. I was lenient in the checking here. But I have a feeling there is a way to price it.' Oh so it wasn't a trick. It was a mistake. Interesting.
Ok anyway in retrospect, I think it would've been pretty unfair if it were given really as a trick and people were penalised if they didn't realise there was arbitrage. I distinctly remember correction ink over 'not needed' for something that supposedly (dis/)proves there was arbitrage in the market. I recall it was the existence of a strictly positive state price vector or something. I don't really remember finance anymore. But I do remember that the proof that there isn't arbitrage in a given market is not needed in computing the price...assuming there isn't arbitrage.
Question 1: Would it have been fair to really give this in class as a trick with the answer supposedly as 'There exists arbitrage(, so the formula doesn't apply).' ?
Question 2: Does your answer to Question 1 depend on whether or not there were no such exercises or homeworks with questions like 'Determine which of the following markets don't/have arbitrage. For the ones that don't, determine the prices in each market.' (well in my case, I don't recall there were any...based on what happened above)