Quoted Spread

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export type TradeSide = "buy" | "sell";

function numberValue(name: string, value: unknown, positive = false): number {
  if (typeof value !== "number" || !Number.isFinite(value)) {
    throw new Error(`${name} must be a finite number`);
  }
  if (positive && value <= 0) throw new Error(`${name} must be greater than zero`);
  return value;
}

function sideDirection(side: unknown): number {
  if (side === "buy") return 1;
  if (side === "sell") return -1;
  throw new Error("side must be 'buy' or 'sell'");
}

function quoteValues(bid: unknown, ask: unknown): [number, number, number] {
  const bidValue = numberValue("bid", bid, true);
  const askValue = numberValue("ask", ask, true);
  if (askValue < bidValue) throw new Error("ask must be greater than or equal to bid");
  return [bidValue, askValue, (bidValue + askValue) / 2];
}

export function quotedSpread(bid: unknown, ask: unknown) {
  const [bidValue, askValue, midpoint] = quoteValues(bid, ask);
  const spread = askValue - bidValue;
  const relative = spread / midpoint;
  return {
    model: "quoted-spread",
    bid: bidValue,
    ask: askValue,
    midpoint,
    quoted_spread: spread,
    quoted_spread_relative: relative,
    quoted_spread_bps: relative * 10_000,
    state: spread === 0 ? "locked" : "two-sided",
  };
}

export function effectiveSpread(
  bid: unknown,
  ask: unknown,
  tradePrice: unknown,
  side: TradeSide,
) {
  const quote = quotedSpread(bid, ask);
  const trade = numberValue("trade_price", tradePrice, true);
  const direction = sideDirection(side);
  const effective = 2 * direction * (trade - quote.midpoint);
  const relative = effective / quote.midpoint;
  const quoteSidePrice = direction === 1 ? quote.ask : quote.bid;
  const priceImprovementPerShare = direction * (quoteSidePrice - trade);
  const roundTripSpreadReduction = quote.quoted_spread - effective;
  const tolerance = 1e-12;
  let state = "outside-quote";
  if (effective < -tolerance) state = "through-midpoint-improvement";
  else if (roundTripSpreadReduction > tolerance) state = "inside-quote";
  else if (Math.abs(roundTripSpreadReduction) <= tolerance) state = "at-quote";
  return {
    ...quote,
    model: "effective-spread",
    trade_price: trade,
    side,
    direction,
    effective_spread: effective,
    effective_spread_relative: relative,
    effective_spread_bps: relative * 10_000,
    quote_side_price: quoteSidePrice,
    price_improvement_per_share: priceImprovementPerShare,
    round_trip_spread_reduction: roundTripSpreadReduction,
    state,
  };
}

export function realizedSpread(
  bidAtTrade: unknown,
  askAtTrade: unknown,
  tradePrice: unknown,
  side: TradeSide,
  bidAfter: unknown,
  askAfter: unknown,
  horizonSeconds: unknown = 300,
) {
  const initial = effectiveSpread(bidAtTrade, askAtTrade, tradePrice, side);
  const [futureBid, futureAsk, futureMidpoint] = quoteValues(bidAfter, askAfter);
  const horizon = numberValue("horizon_seconds", horizonSeconds, true);
  const realized = 2 * initial.direction * (initial.trade_price - futureMidpoint);
  const priceImpact = 2 * initial.direction * (futureMidpoint - initial.midpoint);
  const relative = realized / initial.midpoint;
  const impactRelative = priceImpact / initial.midpoint;
  return {
    model: "realized-spread",
    side,
    direction: initial.direction,
    trade_price: initial.trade_price,
    midpoint_at_trade: initial.midpoint,
    midpoint_after: futureMidpoint,
    bid_after: futureBid,
    ask_after: futureAsk,
    horizon_seconds: horizon,
    effective_spread: initial.effective_spread,
    realized_spread: realized,
    realized_spread_relative: relative,
    realized_spread_bps: relative * 10_000,
    price_impact: priceImpact,
    price_impact_relative: impactRelative,
    price_impact_bps: impactRelative * 10_000,
    decomposition_error: initial.effective_spread - realized - priceImpact,
    state: realized < 0 ? "negative-realized" : "nonnegative-realized",
  };
}

function finiteSeries(name: string, values: unknown, minimum: number): number[] {
  if (!Array.isArray(values)) throw new Error(`${name} must be an array`);
  const result = values.map((value, index) => numberValue(`${name}[${index}]`, value, true));
  if (result.length < minimum) throw new Error(`${name} must contain at least ${minimum} observations`);
  return result;
}

function mean(values: number[]): number {
  return values.reduce((total, value) => total + value, 0) / values.length;
}

export function rollSpread(prices: unknown) {
  const priceValues = finiteSeries("prices", prices, 4);
  const changes = priceValues.slice(1).map((value, index) => value - priceValues[index]);
  const lagged = changes.slice(0, -1);
  const current = changes.slice(1);
  if (current.length < 2) throw new Error("prices must create at least two covariance pairs");
  const laggedMean = mean(lagged);
  const currentMean = mean(current);
  const covariance = lagged.reduce(
    (total, value, index) => total + (value - laggedMean) * (current[index] - currentMean),
    0,
  ) / (current.length - 1);
  const meanPrice = mean(priceValues);
  const covarianceTolerance = 1e-15;
  const spread = covariance < -covarianceTolerance ? 2 * Math.sqrt(-covariance) : null;
  const relative = spread === null ? null : spread / meanPrice;
  return {
    model: "roll-spread",
    observation_count: priceValues.length,
    change_count: changes.length,
    covariance_pair_count: current.length,
    lag1_price_change_covariance: covariance,
    covariance_tolerance: covarianceTolerance,
    mean_price: meanPrice,
    spread_estimate: spread,
    spread_estimate_relative: relative,
    spread_estimate_bps: relative === null ? null : relative * 10_000,
    state: spread === null ? "not-identified" : "estimated",
  };
}

export function amihudIlliquidity(
  closes: unknown,
  dollarVolumes: unknown,
  scale: unknown = 1_000_000,
) {
  const closeValues = finiteSeries("closes", closes, 2);
  const volumeValues = finiteSeries("dollar_volumes", dollarVolumes, 2);
  if (closeValues.length !== volumeValues.length) {
    throw new Error("closes and dollar_volumes must have equal length");
  }
  const scaleValue = numberValue("scale", scale, true);
  const returns = closeValues.slice(1).map((value, index) => value / closeValues[index] - 1);
  const ratios = returns.map((value, index) => Math.abs(value) / volumeValues[index + 1]);
  const raw = mean(ratios);
  return {
    model: "amihud-illiquidity",
    observation_count: closeValues.length,
    return_count: returns.length,
    returns,
    daily_illiquidity: ratios,
    illiquidity_per_currency_unit: raw,
    scale: scaleValue,
    illiquidity_per_scaled_volume: raw * scaleValue,
    state: "estimated",
  };
}

export function corwinSchultzSpread(
  highDay1: unknown,
  lowDay1: unknown,
  highDay2: unknown,
  lowDay2: unknown,
  clipNegative = true,
) {
  const h1 = numberValue("high_day_1", highDay1, true);
  const l1 = numberValue("low_day_1", lowDay1, true);
  const h2 = numberValue("high_day_2", highDay2, true);
  const l2 = numberValue("low_day_2", lowDay2, true);
  if (h1 < l1 || h2 < l2) throw new Error("each daily high must be greater than or equal to its low");
  const beta = Math.log(h1 / l1) ** 2 + Math.log(h2 / l2) ** 2;
  const gamma = Math.log(Math.max(h1, h2) / Math.min(l1, l2)) ** 2;
  const denominator = 3 - 2 * Math.sqrt(2);
  const alphaRaw = (
    (Math.sqrt(2 * beta) - Math.sqrt(beta)) / denominator
    - Math.sqrt(gamma / denominator)
  );
  const alpha = clipNegative ? Math.max(0, alphaRaw) : alphaRaw;
  const expAlpha = Math.exp(alpha);
  const spread = 2 * (expAlpha - 1) / (1 + expAlpha);
  return {
    model: "corwin-schultz-spread",
    beta,
    gamma,
    alpha_raw: alphaRaw,
    alpha_used: alpha,
    spread_estimate_relative: spread,
    spread_estimate_bps: spread * 10_000,
    clip_negative: clipNegative,
    state: clipNegative && alphaRaw < 0 ? "clipped-to-zero" : "estimated",
  };
}

export function calculate(topicId: string, inputs: Record<string, any>) {
  if (topicId === "D11-F02-A01") return quotedSpread(inputs.bid, inputs.ask);
  if (topicId === "D11-F02-A02") return effectiveSpread(inputs.bid, inputs.ask, inputs.trade_price, inputs.side);
  if (topicId === "D11-F02-A03") return realizedSpread(
    inputs.bid_at_trade,
    inputs.ask_at_trade,
    inputs.trade_price,
    inputs.side,
    inputs.bid_after,
    inputs.ask_after,
    inputs.horizon_seconds ?? 300,
  );
  if (topicId === "D11-F02-A04") return rollSpread(inputs.prices);
  if (topicId === "D11-F02-A05") return amihudIlliquidity(
    inputs.closes,
    inputs.dollar_volumes,
    inputs.scale ?? 1_000_000,
  );
  if (topicId === "D11-F02-A06") return corwinSchultzSpread(
    inputs.high_day_1,
    inputs.low_day_1,
    inputs.high_day_2,
    inputs.low_day_2,
    inputs.clip_negative ?? true,
  );
  throw new Error(`unsupported topic_id: ${topicId}`);
}