I recently had a final interview with Options MM for quant trader role, and the market making question was as follows:
Make a market on number of prime number btw 1 and 1000, spread being 50(which I don't understand why, but just stick to it)
-> I divided 10 by 6 & 7, expecting average amount of prime number btw unit of 10 being around 1.5. According to this logic, the bid-ask should be 143-166, so I just gave 130 - 180.
The trader lifted me at 180. So I thought the actual number must be larger than my ask offer. So gave another offer for 180 at 230. Then he lifted me at 230 again. I felt quite strange but thought maybe the actual value would be a slightly more than 230, so if offer 230 at 280, we would find the expected value. Surprisingly he again lifted me at 280. Well after 2 more rounds I ended up being lifted at 380.
I never expected this kind of situation, where I was certain that trader acted irrationally.(The true value was 168, so its really irrational to have lifted me at much higher price, right?)
Was I thinking wrong about this situation? or would there have been some special meaning for this behavior?
Would really appreciate the feedback:)
Thanks in advance!
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