T722 · Risk Measurement
v1.0

How much does this bond's price move when yields move?

One bond, declared once, measured three ways: modified duration (art-329), DV01 (art-330), and convexity (art-331). All three share the same even-period bullet-bond cash-flow schedule, so the three answers describe one bond.

This page is a calculation check, not investment advice and not a pricing service. It computes textbook bond risk measures from inputs you supply; it does not recommend buying, selling, or holding any bond, and it does not price any bond for trading. Verify every result against your own models and current market data before relying on it for any decision.
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Office cell: middle office, not lifecycle-bound (risk measurement).

Inputs

Risk measures

MeasureValue
Price at the stated yield-
Macaulay duration, years (art-329)-
Modified duration, years (art-329)-
DV01, per 1bp (art-330, central-difference full reprice)-
Convexity, annualised (art-331)-

DV01 here is computed by art-330, a central-difference full reprice at yield plus and minus 1bp. Kernel line, art-330 line 67: "via central-difference full reprice at y±1bp". Kernel line, art-330 line 92: const dv01 = (priceDown - priceUp) / 2; Kernel line, art-330 line 107: method: 'central_difference_full_reprice'. Modified duration times price times 0.0001 is only the linear approximation compared against DV01. art-330 computes DV01 by full reprice.

Combined view: price move for the declared shock

EstimatePrice changeNew price
Duration only--
Duration plus convexity--
Full reprice at the declared shock (page's own one-sided reprice)--

Expected order: the full reprice is the reference. Duration plus convexity is nearer to it than duration only, for a rise or a fall. Convexity always moves the estimate in the holder's favour: for a yield rise it softens the fall, for a yield fall it adds to the gain.

The full reprice line is the page's own one-sided reprice at the declared shock: it reprices the same schedule at the shocked yield. That is distinct from art-330's DV01, which is a separate 1 bp central difference at yield plus and minus 1 bp. Duration only: change equals negative modified duration times yield change times price. Duration plus convexity: change equals (negative modified duration times yield change plus 0.5 times convexity times yield change squared) times price.

Limits

  • Bullet bonds only, on an even-period schedule. No odd first coupon and no stub period.
  • Parallel shifts only. The shock moves the whole yield curve by one amount; twists and non-parallel moves are out of scope.
  • No embedded options. Callable, putable, or convertible bonds are out of scope; their price sensitivity is not duration plus convexity alone.
  • Modified duration times price times 0.0001 is an approximation to DV01, shown for comparison only. The reported DV01 is the art-330 full reprice, which is a separate 1 bp central difference. The combined view's one-sided reprice at the declared shock is a different calculation.
  • The day-count convention is echoed for receipt transparency; the schedule itself assumes even periods.

Policy Mandate export

Run the computation, then export a Tier 1 Policy Mandate (JSON plus Markdown transcript) carrying the inputs and the three measures for audit.

Sources

  • art-329-tvm-bond-duration: Macaulay and modified duration, textbook definition (Fabozzi, Bond Markets).
  • art-330-tvm-dv01: DV01 / price value of a basis point, central-difference full reprice (Fabozzi, Bond Markets). art-330's DV01 is a separate 1 bp central difference; the combined view's full reprice line is the page's own one-sided reprice at the declared shock.
  • art-331-tvm-convexity: closed-form convexity, annualised by periods per year squared (Fabozzi, Bond Markets, Ch.4).

The page reimplements the three kernels' schedules and formulas in browser JavaScript. Kernel workers use a custom power series for determinism; this page uses Math.pow, and the displayed values agree with the kernel outputs to the displayed rounding for ordinary inputs.