Millennium's Bid-Ask and Market-Making Question

Millennium pairs clean object design with trading intuition. This market-making question starts as a tidy value class, then asks you to quote around a market price, then to lean those quotes against your inventory. Here is the full question, Java for each part, and a detailed rubric.

The question

Part 1 · The bid-ask spread

A small value class with an enforced invariant. Guard the constructor, and watch the divide-by-zero in the percentage.

class BidAskSpread {
    final double bid, ask;

    BidAskSpread(double bid, double ask) {
        if (bid > ask) throw new IllegalArgumentException("bid cannot exceed ask");
        this.bid = bid; this.ask = ask;
    }

    double spread()    { return ask - bid; }
    double midPrice()  { return (bid + ask) / 2.0; }

    double spreadPercentage() {
        double mid = midPrice();
        return mid == 0 ? 0 : spread() / mid * 100;   // avoid divide-by-zero
    }
}

Part 2 · A symmetric market maker

Center a quote on the market price and place the bid and ask half the spread width on each side.

class MarketMaker {
    final double spreadWidth;
    MarketMaker(double spreadWidth) { this.spreadWidth = spreadWidth; }

    BidAskSpread quote(double marketPrice) {
        double half = spreadWidth / 2.0;
        return new BidAskSpread(marketPrice - half, marketPrice + half);
    }
}

Part 3 · Skew against inventory

A real maker does not quote symmetrically forever. When it is long, it shifts both quotes down to attract sells and discourage buys; when short, it shifts up. The skew is proportional to inventory, and the spread width is preserved.

class InventoryAwareMaker {
    final double spreadWidth, skewPerUnit;
    double inventory;            // positive = long, negative = short

    InventoryAwareMaker(double spreadWidth, double skewPerUnit) {
        this.spreadWidth = spreadWidth; this.skewPerUnit = skewPerUnit;
    }

    BidAskSpread quote(double marketPrice) {
        double half = spreadWidth / 2.0;
        double center = marketPrice - inventory * skewPerUnit;  // long -> quote lower
        return new BidAskSpread(center - half, center + half);
    }

    void onFill(double signedQty) { inventory += signedQty; }   // +buy, -sell
}

Skewing the center while holding the width constant is the key idea: you keep your edge per trade but bias which side gets hit, nudging inventory back toward flat. Quoting symmetrically regardless of position is the answer that misses the point of market making.

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