# What's the first time-integral of price called?

In general I'm wondering about the names of time-derivatives of price.

E.g. in physics the first few time-derivatives of position are:

• f(x) = displacement
• f'(x) = velocity
• f''(x) = acceleration

And the first integral (anti-derivative) of displacement is called absement.

What would the equivalent financial terms be?

• What your looking for is Stochastic Calculus – pyCthon May 23 '13 at 2:33

Well, if you divide a time integral by the length of the time interval, you'll get the average (in time) price: $$\frac{1}{t}\int_0^T x_t\mathrm dt$$ so at least on of the meanings of the integral itself is an average price time the length of the interval. In such a case, I think the normalized quantity (the integral divided by the length) is more meaningful. It is used e.g. in the exotic options whose payoff depends on the average price.