Source: https://guthlabs.ai/docs/instruments/bond-duration-convexity/implementation/

instrument implementation / implementation-contract

# Bond Duration & Convexity implementation

A source-bound implementation contract for Bond Duration & Convexity; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-041

**Effect**: Computation or source lookup only

## Input and validation requirements

The input y=-1 makes every discounting denominator vanish, so the instrument must reject it. A further convention hazard exists because untyped values such as 5 and 1 can be interpreted either as decimal rates or as percentages.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "face_value": 100,
    "cash_flows": {
      "t=1": 0,
      "t=2": 100
    },
    "yield": 0.05,
    "yield_change": 0.01,
    "coupon_frequency": 1
  },
  "expected_outputs": {
    "price": 90.702947846,
    "macaulay_duration_years": 2,
    "modified_duration_years": 1.904761905,
    "convexity_years_squared": 5.442176871,
    "estimated_price_change_for_plus_1_percent_yield": -1.702994
  },
  "working": "PV1 = 0/(1.05)^1 = 0. PV2 = 100/(1.05)^2 = 100/1.1025 = 90.702947846. Price = 0 + 90.702947846 = 90.702947846. Macaulay D = [1·0 + 2·90.702947846]/90.702947846 = 2 years. Modified D = 2/1.05 = 1.904761905 years. Convexity = [1·2·0 + 2·3·90.702947846]/[90.702947846·(1.05)^2] = 6/1.1025 = 5.442176871 years². Relative estimated change = -(1.904761905)(0.01) + 0.5(5.442176871)(0.01)^2 = -0.01904761905 + 0.0002721088436 = -0.01877551020. Price change = 90.702947846·(-0.01877551020) = -1.702994 approximately. This is an edge case: zero coupon cash flows before maturity."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/bond-duration-convexity/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/bond-duration-convexity/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/bond-duration-convexity/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`