Why Theta’s Sensitivity to Time Has No Common Greek Name

Summary

The document asks whether the second derivative of an option’s value with respect to time has a conventional Greek name and whether its lack of a familiar label signals that traders consider it unimportant. The accepted answer says there is no commonly used name and links the measure’s limited practical role to the order of the resulting time-related P&L over a small time increment.

The explanation invokes Ito’s lemma: the contribution from this second time derivative scales with the square of the time increment, so it is neglected in the usual first-order differential P&L treatment. This gives a concise reason for why the sensitivity is not commonly tracked alongside better-known Greeks. The answer is brief and does not develop a discrete-time approximation, discuss unusual horizons, or address settings where higher-order effects may matter, so it should be read as an explanation within the standard local P&L framework rather than a general statement about every options application.

Key ideas

• The document reports no conventional industry name for the second time derivative of option value.
• The sensitivity measures how Theta changes as time advances.
• Its contribution to P&L is described as proportional to the square of the time increment.
• The answer uses Ito’s lemma to explain why the term is omitted in the usual differential P&L treatment.
• The brief response does not discuss cases where higher-order time effects could matter.

Tags

# What is the name (Greek) for sensitivity of an option's Theta to the Time to maturity?


# What is the name (Greek) for sensitivity of an option's Theta to the Time to maturity?












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:

- Is there a conventional name that people in the industry use?

- 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?

## Answer by ryc (score 6, accepted)

https://quant.stackexchange.com/a/55746

- No

- Because the P&L it generates is in $O(dt^2)$. Ito's lemma tells you that you can ignore this P&L.

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.