In my financial derivatives class, I am confused by the meaning of the d's in the following equation. Are they derivatives? What are they?

dLt = mdt + σdBt

Where L = log(St), log return

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    financial derivatives class I would assume you should have some background in mathematics, specifically in calculus. How come you don't recognize signs used in differential calculus ?
    – DumbCoder
    Mar 3 '20 at 9:07
  • Shouldn't this be migrated to Quantitative Finance SE?
    – user10763
    Mar 4 '20 at 7:33
  • @DumbCoder: Because in differential calculus, you don't have random d's like that. They always take the form df(x)/dx. (Or ∂f(x)/∂x for a partial derivative).
    – MSalters
    Mar 5 '20 at 13:46
  • @MSalters you don't have random d's like that No there aren't any in the equation in the post. They are in perfectly legitimate places.
    – DumbCoder
    Mar 5 '20 at 14:17
  • @DumbCoder: There's not an / in sight. In differential calculus, the notation for derivatives is visually similar to a division, but it is not a division and you can't "multiply both sides by dt". This kind of notation abuse is common in physics and other applied uses, but if you don't have such a background then you might expect the correct mathematical notation.
    – MSalters
    Mar 5 '20 at 14:33

People in probability and finance theory to use this notation to write integral equations describing the behavior of continuous time stochastic processes (L, in this case). It's an informal shorthand way of writing an equation that otherwise would have cumbersome (and scary looking) integral signs in front of everything.

In other words, to see what it really means, write an integral sign in front of everything.

Take a look at the wikipedia section I linked. Based on the way you asked the question, it sounds like you may need to read a primer on stochastic calculus before you will have a reasonable understanding of an equation like this.


It's a stochastic differential equation (SDE) and d's are notation used in differential calculus. The derivatives (Mathematics not the financial ones like IFRS 9). To understand SDE, first try to understand ordinary differential equations (ODE), Probability theory and number theory, Linear algebra, Real analysis etc

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