In a model of fixed payments, the first derivative of price gives linear sensitivity, while the second derivative refines it for a finite change in yield. Convexity refers to this curvature, not to a separate cash payment. FINRA explains duration as sensitivity and warns about other risks.[16](#source-cm-duration)
Model dependence
The figure depends on the price function, the accrual method and the cash-flow stream. For an instrument with an embedded right to change payments, conclusions from a simple fixed-payment model must not be used silently. The SEC describes the variety of corporate-debt terms.[14](#source-cm-corporate) A second-order adjustment is not exact for every rate movement and does not measure credit quality. [Duration and convexity sensitivity analysis](/guides/duration-convexity-sensitivity/) provides derivatives and a direct recalculation of its own example, not a forecast of a market price.
General concepts; terms of specific contracts and jurisdictions must be checked separately.
Source references and link retained: FINRA.[16](#source-cm-duration), SEC.[14](#source-cm-corporate), [Duration and convexity sensitivity analysis](/guides/duration-convexity-sensitivity/); first and second derivatives, finite yield change, fixed-payment model, accrual, cash-flow, embedded-payment rights, corporate-debt terms, second-order limits, credit quality and market-price forecast caveats preserved.
Educational material is not individual investment, legal or tax advice.
