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FINANCE / CURVATURE

Bond Convexity Calculator

Calculate standard discrete convexity for a fixed-rate, option-free bond and compare it with modified duration.

  • 01 Calculated in this tab
  • 02 Values stay in this browser tab
  • 03 Use boundary

Conversion input

Known value

Filter by unit name, symbol, or code. Your current selections remain available.

Bond terms

Market assumption

Bond terms

Preparing the calculator...

METHOD / WORKED EXAMPLE

Add curvature to the duration estimate

Convexity measures the curvature that a straight-line duration estimate misses when yield changes.

WORKED DEFAULT

Check the calculation with the default inputs

For a $1,000 face bond with a 5% coupon, 6% yield, 10 years, and semiannual payments, the same cash flows produce about $925.61 price, 7.665 modified duration, and approximately 71.79 convexity.

  1. Discount fixed coupons and principalAbout $925.61 model price
  2. Apply t(t+1) cash-flow weightsConvexity numerator
  3. Normalize by price and frequency²About 71.79 convexity

READ THE RESULT

Interpret the output in context

Use duration and convexity for small parallel yield scenarios. The estimate is not a complete forecast of traded price.

ASSUMPTIONS AND LIMITS

Know where the model stops

  • Cash flows are fixed and option-free.
  • Yield changes are parallel and the pricing yield convention stays consistent.
  • Credit, liquidity, tax, and transaction effects are omitted.

This is positive convexity for an option-free fixed cash-flow bond; embedded options require an effective-convexity model.

CFA Institute: yield-based bond convexity

COMMON QUESTIONS

Bond Convexity Calculator FAQs

Why use convexity with duration?

Duration creates a straight-line estimate of price sensitivity. The price-yield relationship is curved, so convexity supplies a second-order adjustment that can improve small-change estimates.

Is higher convexity always better?

Higher positive convexity can improve price behavior for equal duration and yield assumptions, but bonds can differ in credit, liquidity, call features, return, and price. Convexity alone is not an investment decision.

Does this work for callable bonds?

No. A callable bond can develop negative or changing effective convexity because its expected cash flows change with rates. This page assumes contractual cash flows do not change.

Use boundary

Calculation path

The calculator discounts each cash flow and applies the standard period t times t plus one weighting, normalized by price and payment frequency squared.

Calculation path

Convexity = sum(CF_t x t x (t + 1) / (1 + y/m)^(t + 2)) / (price x m^2).