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I think you have the wrong idea about what a derivative is. The article does a pretty good job at explaining what a financial derivative is and gives some example of common ones. Financial derivatives have no real relationship with mathematical derivatives.

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Financial derivatives have no real relationship with mathematical derivatives.

Indirectly they do. Option prices are derived from the underlying price as well as the implied volatility, time, and interest rates.

So when certain parameters change, the price changes. And that is a relationship with a mathematical derivative. The change in option price vs the change in the underlying (delta) is the first derivative, and then you've got gamma as the 2nd derivative. And so on.

damn. do you think I could get people to pay me for a seminar on it anyway?

probably

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