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All other second order sensitivities of option prices to underlying price, volatility and time, seem to have a commonly accepted names: Gamma, Vanna, Charm, Vomma/Volga, Veta as documented here (Wikipedia)

But the second order derivative of option price with respect to time, or the sensitivity of Theta to time, doesn't seem to have a popular name.

My question is:

  1. Is there a conventional name that people in the industry use?
  2. Why is the name not commonly known? Can one infer from this the lack of importance of this measure to option traders? Or is there something else in the history of options theory that is to blame?
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  1. No
  2. Because the P&L it generates is in $O(dt^2)$. Ito's lemma tells you that you can ignore this P&L.

$$PnL = \frac{\partial^2 V}{\partial t^2}dt^2 = 0$$

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