# 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?

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

Although I don't think that this is a question that fits in here, I will give you a reference.

You might want to have a look at the so called greeks, you find a first overview here:

http://en.wikipedia.org/wiki/Greeks_(finance)

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I'm sorry but this question has nothing to do with options. It's about mathematical derivatives of price. – thwd May 17 '13 at 16:41
@Tom: Price of what? Derivatives are called that way for a reason. – vonjd May 17 '13 at 17:17
Options are derivatives because their price is not a free variable but depends on the price of 1 or more other instruments. My question is about any instrument whose price is (presumed to be) a free variable e.g. equity, fx, commodities. – thwd May 17 '13 at 17:31
I'm not sure a physics approach is helpful. Maybe you could pick up a book on stochastic calculus. – John May 17 '13 at 18:34

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.

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