TWAP Execution

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/* Deterministic reference algorithms for D13-F01 Schedule-Based Execution. */

type Inputs = Record<string, any>;

function integer(name: string, value: unknown, positive = false, nonnegative = false): number {
  if (typeof value !== "number" || !Number.isInteger(value)) throw new Error(`${name} must be an integer`);
  if (positive && value <= 0) throw new Error(`${name} must be positive`);
  if (nonnegative && value < 0) throw new Error(`${name} must be nonnegative`);
  return value;
}

function weights(name: string, values: unknown): number[] {
  if (!Array.isArray(values) || !values.length) throw new Error(`${name} must be a nonempty array`);
  const parsed = values.map((value, index) => integer(`${name}[${index}]`, value, false, true));
  if (parsed.reduce((a, b) => a + b, 0) <= 0) throw new Error(`${name} must contain positive total weight`);
  return parsed;
}

function validateParent(totalQuantity: unknown, lotSize: unknown): [number, number] {
  const total = integer("total_quantity", totalQuantity, true);
  const lot = integer("lot_size", lotSize, true);
  if (total % lot !== 0) throw new Error("total_quantity must be divisible by lot_size");
  return [total, lot];
}

function allocateLots(totalQuantity: number, weightValues: number[], lotSize: number): number[] {
  const totalLots = totalQuantity / lotSize;
  const weightSum = weightValues.reduce((a, b) => a + b, 0);
  const bases: number[] = [], remainders: Array<[number, number]> = [];
  weightValues.forEach((weight, index) => {
    const numerator = totalLots * weight;
    bases.push(Math.floor(numerator / weightSum));
    remainders.push([numerator % weightSum, index]);
  });
  let residual = totalLots - bases.reduce((a, b) => a + b, 0);
  remainders.sort((a, b) => b[0] - a[0] || a[1] - b[1]);
  for (let i = 0; i < residual; i += 1) bases[remainders[i][1]] += 1;
  return bases.map((lots) => lots * lotSize);
}

export function twapExecution(
  total_quantity: unknown, start_time_ms: unknown, end_time_ms: unknown,
  bucket_count: unknown, lot_size: unknown,
): Record<string, unknown> {
  const [total, lot] = validateParent(total_quantity, lot_size);
  const start = integer("start_time_ms", start_time_ms, false, true);
  const end = integer("end_time_ms", end_time_ms, true);
  const buckets = integer("bucket_count", bucket_count, true);
  if (end <= start) throw new Error("end_time_ms must be greater than start_time_ms");
  if (total / lot < buckets) throw new Error("bucket_count cannot exceed available lots");
  const allocations = allocateLots(total, Array(buckets).fill(1), lot);
  const duration = end - start;
  let cumulative = 0;
  const schedule = allocations.map((quantity, index) => {
    cumulative += quantity;
    return {
      bucket: index + 1,
      start_time_ms: start + Math.floor(duration * index / buckets),
      end_time_ms: start + Math.floor(duration * (index + 1) / buckets),
      target_quantity: quantity,
      target_cumulative_quantity: cumulative,
    };
  });
  return {
    total_quantity: total, lot_size: lot, bucket_count: buckets,
    scheduled_quantity: cumulative, remaining_quantity: total - cumulative,
    schedule, state: "complete-schedule",
  };
}

export function historicalVwapExecution(
  total_quantity: unknown, historical_bucket_volumes: unknown,
  lot_size: unknown, profile_id: unknown,
): Record<string, unknown> {
  const [total, lot] = validateParent(total_quantity, lot_size);
  const volumes = weights("historical_bucket_volumes", historical_bucket_volumes);
  if (typeof profile_id !== "string" || !profile_id.trim()) throw new Error("profile_id must be a nonempty string");
  const allocations = allocateLots(total, volumes, lot);
  const volumeSum = volumes.reduce((a, b) => a + b, 0);
  let cumulative = 0;
  const schedule = volumes.map((volume, index) => {
    const quantity = allocations[index]; cumulative += quantity;
    return {
      bucket: index + 1, historical_volume: volume,
      historical_weight: Math.round((volume / volumeSum) * 1e12) / 1e12,
      target_quantity: quantity, target_cumulative_quantity: cumulative,
    };
  });
  return {
    profile_id: profile_id.trim(), total_quantity: total, lot_size: lot,
    bucket_count: volumes.length, historical_volume_total: volumeSum,
    scheduled_quantity: cumulative, remaining_quantity: total - cumulative,
    schedule, state: "complete-schedule",
  };
}

export function adaptiveVwapExecution(
  total_quantity: unknown, realized_market_volumes: unknown,
  remaining_forecast_volumes: unknown, executed_quantity: unknown,
  lot_size: unknown, forecast_version: unknown,
): Record<string, unknown> {
  const [total, lot] = validateParent(total_quantity, lot_size);
  const realized = weights("realized_market_volumes", realized_market_volumes);
  const forecast = weights("remaining_forecast_volumes", remaining_forecast_volumes);
  const executed = integer("executed_quantity", executed_quantity, false, true);
  if (executed > total || executed % lot !== 0) throw new Error("executed_quantity must be a lot-aligned value not exceeding total_quantity");
  if (typeof forecast_version !== "string" || !forecast_version.trim()) throw new Error("forecast_version must be a nonempty string");
  const realizedTotal = realized.reduce((a, b) => a + b, 0);
  const forecastTotal = forecast.reduce((a, b) => a + b, 0);
  const projectedMarketTotal = realizedTotal + forecastTotal;
  const targetCompleted = Math.floor(Math.floor(total * realizedTotal / projectedMarketTotal) / lot) * lot;
  const pacingError = executed - targetCompleted;
  const remainingParent = total - executed;
  const immediateCatchUp = Math.floor(Math.min(remainingParent, Math.max(0, -pacingError)) / lot) * lot;
  const postCatchUp = remainingParent - immediateCatchUp;
  const allocations = postCatchUp ? allocateLots(postCatchUp, forecast, lot) : Array(forecast.length).fill(0);
  if (allocations.length) allocations[0] += immediateCatchUp;
  let cumulative = executed;
  const schedule = forecast.map((volume, index) => {
    const quantity = allocations[index]; cumulative += quantity;
    return {
      future_bucket: index + 1, forecast_market_volume: volume,
      target_quantity: quantity, target_cumulative_quantity: cumulative,
      includes_catch_up_quantity: index === 0 ? immediateCatchUp : 0,
    };
  });
  const pacingState = pacingError < 0 ? "behind" : pacingError > 0 ? "ahead" : "on-schedule";
  return {
    forecast_version: forecast_version.trim(), total_quantity: total, executed_quantity: executed,
    remaining_quantity_before_schedule: remainingParent, realized_market_volume: realizedTotal,
    remaining_forecast_market_volume: forecastTotal, projected_market_volume: projectedMarketTotal,
    target_completed_quantity: targetCompleted, pacing_error_quantity: pacingError,
    pacing_state: pacingState, immediate_catch_up_quantity: immediateCatchUp,
    scheduled_future_quantity: allocations.reduce((a, b) => a + b, 0),
    schedule, state: "adaptive-schedule",
  };
}

export function percentageOfVolumeExecution(
  total_quantity: unknown, participation_rate_bps: unknown,
  market_volume_buckets: unknown, lot_size: unknown,
  max_child_quantity: unknown,
): Record<string, unknown> {
  const [total, lot] = validateParent(total_quantity, lot_size);
  const rate = integer("participation_rate_bps", participation_rate_bps, true);
  if (rate > 10000) throw new Error("participation_rate_bps cannot exceed 10000");
  const volumes = weights("market_volume_buckets", market_volume_buckets);
  let maxChild = integer("max_child_quantity", max_child_quantity, true);
  if (maxChild < lot) throw new Error("max_child_quantity must be at least one lot");
  maxChild = Math.floor(maxChild / lot) * lot;
  let cumulativeMarket = 0, released = 0;
  const schedule = volumes.map((volume, index) => {
    cumulativeMarket += volume;
    const rawTarget = Math.min(total, Math.floor(cumulativeMarket * rate / 10000));
    const target = Math.floor(rawTarget / lot) * lot;
    const desired = Math.max(0, target - released);
    let child = Math.min(desired, maxChild, total - released);
    child = Math.floor(child / lot) * lot;
    released += child;
    const achieved = Math.round((released * 10000 / cumulativeMarket) * 1e6) / 1e6;
    return {
      bucket: index + 1, market_volume: volume, cumulative_market_volume: cumulativeMarket,
      target_cumulative_quantity: target, child_quantity: child,
      released_cumulative_quantity: released, remaining_quantity: total - released,
      achieved_participation_bps: achieved,
    };
  });
  return {
    total_quantity: total, participation_rate_bps: rate, lot_size: lot,
    max_child_quantity: maxChild, observed_market_volume: cumulativeMarket,
    released_quantity: released, remaining_quantity: total - released,
    achieved_participation_bps: Math.round((released * 10000 / cumulativeMarket) * 1e6) / 1e6,
    schedule, state: released === total ? "parent-complete" : "participating",
  };
}

export function calculate(topicId: string, inputs: Inputs): Record<string, unknown> {
  if (!inputs || typeof inputs !== "object" || Array.isArray(inputs)) throw new Error("inputs must be an object");
  if (topicId === "D13-F01-A01") return twapExecution(inputs.total_quantity, inputs.start_time_ms, inputs.end_time_ms, inputs.bucket_count, inputs.lot_size);
  if (topicId === "D13-F01-A02") return historicalVwapExecution(inputs.total_quantity, inputs.historical_bucket_volumes, inputs.lot_size, inputs.profile_id);
  if (topicId === "D13-F01-A03") return adaptiveVwapExecution(inputs.total_quantity, inputs.realized_market_volumes, inputs.remaining_forecast_volumes, inputs.executed_quantity, inputs.lot_size, inputs.forecast_version);
  if (topicId === "D13-F01-A04") return percentageOfVolumeExecution(inputs.total_quantity, inputs.participation_rate_bps, inputs.market_volume_buckets, inputs.lot_size, inputs.max_child_quantity);
  throw new Error(`unsupported topic_id: ${topicId}`);
}