A price can change because the stock price, volatility or interest rate changes. A partial derivative measures the effect of one input while the others stay fixed. This lesson extends single-variable differentiation to that controlled experiment. It then combines sensitivities in a vector to estimate the effect of several small changes.
Learning objectives. By the end of this note you should be able to:
- compute first partial derivatives by holding other variables fixed;
- interpret a partial derivative as a slice-slope and local sensitivity;
- compute simple second and mixed partial derivatives;
- form a gradient vector;
- distinguish a partial sensitivity from a total realised change.
In this lesson
- One variable moves, the others wait
- The gradient packages sensitivities
- Second partials and curvature
- Holding the other weight fixed
Before you start
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