[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8},"actionData","errors","root",{"_102":103,"_104":105},"routes/embed.x.$handle.$name.$",{"_9":10,"_11":12,"_13":14,"_15":16,"_17":18,"_19":20,"_21":-5},"handle","jfkll","name","ivmodule","path","surface.ts","project",{"_22":45,"_11":12,"_33":46,"_47":-5,"_48":42,"_49":50,"_51":50,"_52":53,"_54":-5,"_55":56,"_57":58,"_59":32,"_60":-5,"_61":-5,"_62":63,"_64":65,"_66":-5,"_67":-5,"_68":-5,"_69":-5,"_70":71,"_72":71,"_73":74,"_75":74,"_76":74,"_77":71,"_78":71,"_79":80,"_81":82,"_83":84,"_85":42},"file",{"_22":23,"_11":14,"_24":25,"_26":-5,"_27":28,"_29":30,"_31":32,"_33":34,"_35":36,"_37":38,"_39":40,"_41":42,"_43":-5,"_13":44},"permalink","https://www.val.town/x/jfkll/ivmodule/code/surface.ts","extension","id","11970ade-c283-41e2-b474-3a8d0d8ddfa0","fileId","617831aa-9e72-11f1-b3ff-1607ee4eb77e","parentId","branchId","9501ca55-9d64-4f95-91aa-9fa7ca96c333","branchVersion",34,"latest",true,"createdAt",["D",1787435129713],"version",3,"fileType","script","content","/**\n * surface.ts — the implied volatility surface layer.\n *\n * This is the module that makes the tool use IV WALLS proper, not just gamma\n * walls. Three outputs, in increasing order of ambition:\n *\n * 1. A smooth arbitrage-checked smile -> clean per-strike IV for gamma\n * 2. Curvature residuals -> IV WALLS (the actual signal)\n * 3. Risk-neutral density + local vol -> the market's own distribution\n *\n * The key economic point: gamma walls are built from OPEN INTEREST, which is\n * positioning, which is backward-looking and updates after clearing. IV walls\n * are built from PRICES, which are forward-looking and update every quote.\n * When they disagree, that disagreement is information.\n *\n * Zero dependencies. Pure. Same replay guarantees as the rest of the engine.\n */\n\n// ---------------------------------------------------------------------------\n// SVI\n// ---------------------------------------------------------------------------\n\n/**\n * Raw SVI (Gatheral) in total implied variance:\n *\n * w(k) = a + b * ( rho*(k - m) + sqrt( (k-m)^2 + sig^2 ) )\n *\n * where w = iv^2 * tau and k = ln(K / F).\n */\nexport interface SviParams {\n a: number;\n b: number;\n rho: number;\n m: number;\n sig: number;\n tau: number;\n /** Root-mean-square fit error in vol points. */\n rmse: number;\n /** True if Gatheral's butterfly condition g(k) >= 0 holds across the fit. */\n arbFree: boolean;\n nPoints: number;\n}\n\nexport function sviTotalVar(p: SviParams, k: number): number {\n const km = k - p.m;\n return p.a + p.b * (p.rho * km + Math.sqrt(km * km + p.sig * p.sig));\n}\n\nexport function sviIv(p: SviParams, k: number): number {\n const w = sviTotalVar(p, k);\n return w > 0 && p.tau > 0 ? Math.sqrt(w / p.tau) : 0;\n}\n\n/** dw/dk */\nexport function sviDw(p: SviParams, k: number): number {\n const km = k - p.m;\n return p.b * (p.rho + km / Math.sqrt(km * km + p.sig * p.sig));\n}\n\n/** d2w/dk2 */\nexport function sviD2w(p: SviParams, k: number): number {\n const km = k - p.m;\n const r = Math.sqrt(km * km + p.sig * p.sig);\n return (p.b * p.sig * p.sig) / (r * r * r);\n}\n\nexport interface SmilePoint {\n /** log-moneyness ln(K/F) */\n k: number;\n /** market implied vol */\n iv: number;\n /** weight — use open interest or 1/spread. Down-weights junk quotes. */\n weight: number;\n strike: number;\n}\n\n/**\n * Fit raw SVI by exploiting the fact that for FIXED (m, sig) the model is\n * LINEAR in (a, b*rho, b):\n *\n * w = a + c1 * (k-m) + c2 * sqrt((k-m)^2 + sig^2), c1 = b*rho, c2 = b\n *\n * So we grid over the two nonlinear parameters and solve a weighted 3x3\n * normal-equation system at each node. Deterministic, no optimiser, no\n * random restarts — which matters because the whole engine must replay\n * identically on historical snapshots.\n */\nexport function fitSvi(points: SmilePoint[], tau: number): SviParams | null {\n const pts = points.filter(\n (p) => Number.isFinite(p.k) && p.iv > 0.001 && p.iv < 5 && p.weight > 0,\n );\n if (pts.length < 6 || tau <= 0) return null;\n\n const ks = pts.map((p) => p.k);\n const kMin = Math.min(...ks);\n const kMax = Math.max(...ks);\n const kRange = Math.max(1e-4, kMax - kMin);\n\n let best: SviParams | null = null;\n let bestSse = Infinity;\n\n const M_STEPS = 24;\n const S_STEPS = 18;\n\n for (let mi = 0; mi <= M_STEPS; mi++) {\n const m = kMin - 0.25 * kRange + (1.5 * kRange * mi) / M_STEPS;\n for (let si = 1; si <= S_STEPS; si++) {\n const sig = (kRange * si) / S_STEPS * 1.2;\n\n // Weighted normal equations for [a, c1, c2].\n const A = [[0, 0, 0], [0, 0, 0], [0, 0, 0]];\n const rhs = [0, 0, 0];\n\n for (const p of pts) {\n const km = p.k - m;\n const basis = [1, km, Math.sqrt(km * km + sig * sig)];\n const w = p.iv * p.iv * tau;\n const wt = p.weight;\n for (let i = 0; i < 3; i++) {\n for (let j = 0; j < 3; j++) A[i][j] += wt * basis[i] * basis[j];\n rhs[i] += wt * basis[i] * w;\n }\n }\n\n const sol = solve3x3(A, rhs);\n if (!sol) continue;\n const [a, c1, c2] = sol;\n\n const b = c2;\n if (!(b > 0)) continue;\n const rho = c1 / b;\n if (!(Math.abs(rho) < 0.999)) continue;\n // No-arbitrage necessary condition: a + b*sig*sqrt(1-rho^2) >= 0\n if (a + b * sig * Math.sqrt(1 - rho * rho) < 0) continue;\n\n const cand: SviParams = {\n a,\n b,\n rho,\n m,\n sig,\n tau,\n rmse: 0,\n arbFree: true,\n nPoints: pts.length,\n };\n\n let sse = 0;\n let wsum = 0;\n let ok = true;\n for (const p of pts) {\n const wModel = sviTotalVar(cand, p.k);\n if (wModel <= 0) {\n ok = false;\n break;\n }\n const ivModel = Math.sqrt(wModel / tau);\n const e = ivModel - p.iv;\n sse += p.weight * e * e;\n wsum += p.weight;\n }\n if (!ok || wsum <= 0) continue;\n\n if (sse / wsum < bestSse) {\n bestSse = sse / wsum;\n cand.rmse = Math.sqrt(sse / wsum);\n best = cand;\n }\n }\n }\n\n if (best) best.arbFree = checkButterfly(best, kMin, kMax);\n return best;\n}\n\nfunction solve3x3(A: number[][], b: number[]): [number, number, number] | null {\n const M = [\n [A[0][0], A[0][1], A[0][2], b[0]],\n [A[1][0], A[1][1], A[1][2], b[1]],\n [A[2][0], A[2][1], A[2][2], b[2]],\n ];\n for (let col = 0; col < 3; col++) {\n let piv = col;\n for (let r = col + 1; r < 3; r++) {\n if (Math.abs(M[r][col]) > Math.abs(M[piv][col])) piv = r;\n }\n if (Math.abs(M[piv][col]) < 1e-14) return null;\n [M[col], M[piv]] = [M[piv], M[col]];\n for (let r = 0; r < 3; r++) {\n if (r === col) continue;\n const f = M[r][col] / M[col][col];\n for (let c = col; c < 4; c++) M[r][c] -= f * M[col][c];\n }\n }\n return [M[0][3] / M[0][0], M[1][3] / M[1][1], M[2][3] / M[2][2]];\n}\n\n/**\n * Gatheral's g function. g(k) >= 0 for all k is equivalent to the absence of\n * butterfly arbitrage, i.e. a non-negative risk-neutral density.\n *\n * g(k) = (1 - k*w'/(2w))^2 - (w'^2/4)(1/w + 1/4) + w''/2\n */\nexport function gatheralG(p: SviParams, k: number): number {\n const w = sviTotalVar(p, k);\n if (w <= 0) return -1;\n const dw = sviDw(p, k);\n const d2w = sviD2w(p, k);\n const t1 = Math.pow(1 - (k * dw) / (2 * w), 2);\n const t2 = ((dw * dw) / 4) * (1 / w + 0.25);\n return t1 - t2 + d2w / 2;\n}\n\nfunction checkButterfly(p: SviParams, kMin: number, kMax: number): boolean {\n for (let i = 0; i <= 40; i++) {\n const k = kMin + ((kMax - kMin) * i) / 40;\n if (gatheralG(p, k) < -1e-6) return false;\n }\n return true;\n}\n\n// ---------------------------------------------------------------------------\n// IV WALLS — curvature residual detection\n// ---------------------------------------------------------------------------\n\nexport interface IvWall {\n strike: number;\n /** Log-moneyness. */\n k: number;\n /** market IV minus fitted IV, in vol points. */\n residual: number;\n /** Second difference of the residual across neighbouring strikes. */\n curvature: number;\n /** Robust z-score of curvature vs the rest of the smile. */\n z: number;\n /**\n * vol_premium = market pays UP for vol here vs the smooth smile.\n * It is pricing a discontinuity: barrier / breakout candidate.\n * vol_discount = market pays DOWN for vol here.\n * It is pricing suppression: pin / magnet candidate.\n */\n kind: \"vol_premium\" | \"vol_discount\";\n}\n\n/**\n * An IV wall is a LOCAL CONVEXITY ANOMALY in the smile — a strike where the\n * market's own price is paying for a discontinuity that the smooth model does\n * not explain.\n *\n * Why the RESIDUAL and not the raw smile: the raw smile is convex everywhere\n * (that is just skew). What carries information is convexity the fitted model\n * fails to reproduce. Detrending against SVI is what turns \"there is a smile\"\n * into \"there is something HERE\".\n *\n * TWO gates, both required:\n *\n * 1. Statistical — robust z-score of curvature (MAD-based, because a few\n * genuine walls would inflate a standard deviation and hide themselves).\n * 2. ECONOMIC — an absolute floor on |residual| in vol points.\n *\n * Gate 2 exists because gate 1 alone is scale-free and therefore dangerous.\n * On a clean smile the residuals are float noise, the MAD collapses toward\n * zero, and dividing by it manufactures z-scores in the thousands out of\n * rounding error. Measured: 10 false positives on a synthetic clean smile.\n * A detector that fires on clean data is a noise generator. The absolute\n * floor is what makes \"no walls today\" an output the engine can actually\n * produce — and being able to say nothing is the point.\n */\nexport function detectIvWalls(\n points: SmilePoint[],\n fit: SviParams,\n zThreshold = 2.0,\n /** Minimum |residual| in vol points to qualify. 0.0015 = 0.15 vol pts. */\n minResidual = 0.0015,\n): IvWall[] {\n const sorted = [...points]\n .filter((p) => p.iv > 0.001 && p.weight > 0)\n .sort((a, b) => a.k - b.k);\n if (sorted.length < 7) return [];\n\n const resid = sorted.map((p) => p.iv - sviIv(fit, p.k));\n\n // Second difference on a possibly non-uniform k grid.\n const curv: number[] = new Array(sorted.length).fill(0);\n for (let i = 1; i < sorted.length - 1; i++) {\n const hL = sorted[i].k - sorted[i - 1].k;\n const hR = sorted[i + 1].k - sorted[i].k;\n if (hL <= 0 || hR <= 0) continue;\n curv[i] =\n (2 * (hR * resid[i - 1] - (hL + hR) * resid[i] + hL * resid[i + 1])) /\n (hL * hR * (hL + hR));\n }\n\n const interior = curv.slice(1, -1).filter((c) =>\n Number.isFinite(c) && c !== 0\n );\n if (interior.length < 5) return [];\n\n const med = median(interior);\n const mad = median(interior.map((c) => Math.abs(c - med)));\n\n // Floor the scale at the curvature a minResidual-sized kink would produce\n // over typical strike spacing. Below this, z-scores are meaningless.\n const typicalH = (sorted[sorted.length - 1].k - sorted[0].k) /\n (sorted.length - 1);\n const curvFloor = minResidual / Math.max(1e-9, typicalH * typicalH);\n const scale = Math.max(1.4826 * mad, curvFloor * 0.15);\n\n const walls: IvWall[] = [];\n for (let i = 1; i < sorted.length - 1; i++) {\n if (!Number.isFinite(curv[i]) || curv[i] === 0) continue;\n // Gate 2: economic significance, checked first because it is cheap.\n if (Math.abs(resid[i]) < minResidual) continue;\n // Clamp for reporting sanity. On a very clean smile the MAD collapses and\n // the raw z runs to hundreds, which looks like a stronger signal than it\n // is. The RESIDUAL is the number with economic meaning; z is only a\n // relative-to-local-noise check, so a saturated z is capped rather than\n // shown. Results are sorted by residual for exactly this reason.\n const zRaw = (curv[i] - med) / scale;\n if (Math.abs(zRaw) < zThreshold) continue;\n const z = Math.max(-50, Math.min(50, zRaw));\n walls.push({\n strike: sorted[i].strike,\n k: sorted[i].k,\n residual: resid[i],\n curvature: curv[i],\n z,\n // Classified by residual SIGN, not curvature sign. A local IV spike is a\n // peak in the residual and therefore has NEGATIVE second difference —\n // labelling off curvature would invert the economic meaning.\n kind: resid[i] > 0 ? \"vol_premium\" : \"vol_discount\",\n });\n }\n return walls.sort((a, b) => Math.abs(b.residual) - Math.abs(a.residual));\n}\n\nfunction median(xs: number[]): number {\n if (!xs.length) return 0;\n const s = [...xs].sort((a, b) => a - b);\n const h = Math.floor(s.length / 2);\n return s.length % 2 ? s[h] : 0.5 * (s[h - 1] + s[h]);\n}\n\n// ---------------------------------------------------------------------------\n// Risk-neutral density (Breeden-Litzenberger, via SVI)\n// ---------------------------------------------------------------------------\n\n/**\n * The RND is the market's OWN probability distribution over terminal price.\n * The engine's PDE independently produces a terminal distribution. Comparing\n * them is free validation that costs no extra data.\n *\n * Under SVI the density in log-moneyness is:\n * p(k) = g(k) / sqrt(2*pi*w(k)) * exp( -d2(k)^2 / 2 )\n * d2 = -k/sqrt(w) - sqrt(w)/2\n */\nexport function riskNeutralDensity(\n p: SviParams,\n kGrid: number[],\n): { k: number; density: number }[] {\n return kGrid.map((k) => {\n const w = sviTotalVar(p, k);\n if (w <= 0) return { k, density: 0 };\n const d2 = -k / Math.sqrt(w) - Math.sqrt(w) / 2;\n const g = Math.max(0, gatheralG(p, k));\n return {\n k,\n density: (g / Math.sqrt(2 * Math.PI * w)) * Math.exp(-0.5 * d2 * d2),\n };\n });\n}\n\n// ---------------------------------------------------------------------------\n// Local volatility\n// ---------------------------------------------------------------------------\n\n/**\n * Dupire local vol from the SVI surface.\n *\n * sigma_loc^2 = (dw/dT) / [ 1 - (k/w) dw/dk + 0.25(-0.25 - 1/w + k^2/w^2)(dw/dk)^2 + 0.5 d2w/dk2 ]\n *\n * IMPORTANT LIMITATION, stated plainly: dw/dT requires at least TWO expiries.\n * With a single expiry it cannot be computed and this returns null. The caller\n * must then fall back to the smile proxy below.\n *\n * This matters for the engine design: if two expiries are available, sigma_eff\n * can be READ OFF THE SURFACE instead of being fitted, which removes\n * lambda_sigma as a free parameter entirely. Fewer knobs is less overfitting.\n */\nexport function dupireLocalVol(\n near: SviParams,\n far: SviParams,\n k: number,\n): number | null {\n if (far.tau <= near.tau) return null;\n const wNear = sviTotalVar(near, k);\n const wFar = sviTotalVar(far, k);\n const dwdT = (wFar - wNear) / (far.tau - near.tau);\n if (!(dwdT > 0)) return null; // calendar arbitrage; refuse rather than fabricate\n\n const w = wNear;\n if (w <= 0) return null;\n const dw = sviDw(near, k);\n const d2w = sviD2w(near, k);\n\n const denom = 1 -\n (k / w) * dw +\n 0.25 * (-0.25 - 1 / w + (k * k) / (w * w)) * dw * dw +\n 0.5 * d2w;\n\n if (!(denom > 1e-8)) return null;\n const v2 = dwdT / denom;\n return v2 > 0 ? 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