How to interpret a partial derivative where variable in numerator doesn't denote a function?

Asked Nov 24 '20 at 07:06

Active Nov 24 '20 at 07:16

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I encountered the following passage (Option Trading, Euan Sinclair, 2010, p.45):

Calls are increasing functions of the underlying.

$$ \frac{∂C}{∂S} > 0 $$

C denotes an American option and S denotes the stock.

My understanding of partial derivatives is that the variable on top denotes a function and not a variable.

How do you interpret this passage?

edited Nov 24 '20 at 07:16

asked Nov 24 '20 at 07:06

anon

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Nov 24 '20 at 07:11
Sometimes the line between a function and a variable is blurred. Here I imagine $C$ is both a variable and a function. It's a function in the sense that its value depends on other variables like the price of the stock. So you might see somewhere in your text something like $C=C(S,\ldots)$. meaning that $C$ is shorthand for a function. – Math Helper Nov 24 '20 at 07:13

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