upProbability function

double upProbability(PricerInputs inputs, double strike)

P(settle > strike) — the UP digital, with the SVI skew correction. inputs.svi is the already-rolled surface (no roll-down applied here). strike shares units with inputs.forward. Returns a probability in [0, 1].

Implementation

double upProbability(PricerInputs inputs, double strike) {
  final forward = inputs.forward;
  final svi = inputs.svi;
  if (!(forward > 0)) return 0;
  if (strike <= 0) return 1; // neg-inf limit
  final k = math.log(strike / forward);
  final km = k - svi.m;
  final root = math.sqrt(km * km + svi.sigma * svi.sigma);
  final inner = svi.rho * km + root; // >= 0 for |rho| <= 1
  final w = svi.a + svi.b * inner; // total variance
  // The chain guarantees w > 0 at every strike
  // (assert_min_total_variance_positive at load time), so this branch is
  // unreachable in practice; return the variance→0 tail limit rather than
  // throw, so a UI never crashes on a degenerate snapshot.
  if (w <= 0) return k < 0 ? 1 : 0;
  final sq = math.sqrt(w);
  final d2 = _clampD2(-((k + w / 2) / sq));
  final nd2 = _normalCdf(d2);
  final wPrime = svi.b * (svi.rho + km / root); // SVI slope × b
  final price = nd2 - (_normalPdf(d2) * wPrime) / (2 * sq); // skew correction
  return price < 0
      ? 0
      : price > 1
          ? 1
          : price;
}