{
  "slug": "convexity",
  "name": "Bond Convexity",
  "category": "Fixed Income",
  "description": "Second-order sensitivity of bond price to yield changes; corrects the duration approximation for large yield moves.",
  "formula": "ΔP/P ≈ -MD × Δy + ½ × Convexity × (Δy)²",
  "formula_latex": "\\dfrac{\\Delta P}{P} \\approx -\\text{MD}\\,\\Delta y + \\tfrac{1}{2}\\,\\text{Convexity}\\,(\\Delta y)^2",
  "parameters": [
    {
      "name": "Modified Duration",
      "symbol": "MD",
      "type": "number",
      "default": 7
    },
    {
      "name": "Convexity",
      "symbol": "Cx",
      "type": "number",
      "default": 60
    },
    {
      "name": "Yield change",
      "symbol": "Δy",
      "type": "percent",
      "default": 0.01
    }
  ],
  "outputs": [
    {
      "name": "Approx price change %",
      "symbol": "ΔP/P",
      "type": "percent"
    }
  ],
  "worked_example": {
    "inputs": {
      "MD": 7,
      "Cx": 60,
      "dy": 0.01
    },
    "expected_outputs": {
      "dpct": -0.067
    }
  },
  "related_terms": [
    "convexity",
    "duration",
    "key-rate-duration"
  ]
}