A risk report asks how much a price changes when a rate or another input moves. A derivative measures that local sensitivity. This lesson starts with a limit, derives a simple derivative and applies the main rules to a discounted payment. It prepares you to measure sensitivities to several inputs with partial derivatives.
Learning objectives. By the end of this note you should be able to:
- interpret without confusing it with ;
- compute a derivative from the difference quotient in a simple case;
- apply power, product, quotient and chain rules;
- differentiate exponential and logarithmic functions;
- interpret the sign and units of a derivative in finance.
In this lesson
- Limits describe nearby behaviour
- The derivative is a local rate
- Sensitivity in a pricing formula
- Reading a derivative
- A tangent estimates a small rate change
Before you start
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