{
  "annotation_id": "9bffd270-7696-4625-ae7c-be1d956910c2",
  "date_created": "2026-03-02T18:01:07.015000Z",
  "date_modified": "2026-03-02T18:01:07.015000Z",
  "file_hash": "c8ee841d6ae510da3dfaea5e5dffce7371c79c87e308d9415de83464855c93da",
  "private": false,
  "record": {
    "abstract": "In this short note, using our geometric method introduced in a previous paper\n\\cite{phl} and initiated by \\cite{ave}, we derive an asymptotic swaption\nimplied volatility at the first-order for a general stochastic volatility Libor\nMarket Model. This formula is useful to quickly calibrate a model to a full\nswaption matrix. We apply this formula to a specific model where the forward\nrates are assumed to follow a multi-dimensional CEV process correlated to a\nSABR process. For a caplet, this model degenerates to the classical SABR model\nand our asymptotic swaption implied volatility reduces naturally to the\nHagan-al formula \\cite{sab}. The geometry underlying this model is the\nhyperbolic manifold $\\HH^{n+1}$ with $n$ the number of Libor forward rates.",
    "arxiv_id": "physics/0602102",
    "authors": [
      "Pierre Henry-Labordere"
    ],
    "categories": [
      "physics.soc-ph",
      "cond-mat.other",
      "q-fin.CP"
    ],
    "title": "Unifying the BGM and SABR Models: A short Ride in Hyperbolic Geometry",
    "url": "https://arxiv.org/abs/physics/0602102"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c192909f-1f35-4e8f-8286-adda1f86077d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}