The market making game: how it works and how to do well

Most trading firms end their process with a market making game. Optiver, IMC, Flow Traders, Jane Street, SIG and others all run a version of it, usually on the final day. You do not need trading experience. You need to know the language, keep your head, and do simple expected value sums quickly while someone is talking to you.

The set-up

You are given a product with an unknown final value. It might be a fictional share, the sum of some dice, or the answer to an estimation question. You make a two-sided market: a bid, an offer and a size.

"98 bid at 102 offered, five up" means you will buy up to 5 at 98 and sell up to 5 at 102.

The assessor, or another candidate, then trades against you:

• "Mine 3" means they buy 3 at your offer. You have sold 3 at 102.
• "Yours 2" means they sell 2 at your bid. You have bought 2 at 98.

The most common mistake on the day is getting this backwards. Every trade has a buyer and a seller. If someone takes your offer, you are the seller.

Fair value is an expected value

Your market should sit around your best estimate of what the product is worth. That estimate is an expected value, and it changes as information arrives.

Example. A share is worth 100. News: a takeover has a 40% chance of completing at 125. If it fails the share falls to 90.

Fair value = 0.4 × 125 + 0.6 × 90 = 104.

A reasonable market is now 103 bid at 105 offered. If you are still quoting 99 at 101, someone will say "Mine" for your full size, and they will be right.

Then the probability changes. Further news lifts the chance of completion to 60%.

Fair value = 0.6 × 125 + 0.4 × 90 = 111.

This is the whole game: recompute, move your market, and do it before the other side trades.

Conditional probabilities

Later rounds chain events together. "The deal needs two approvals. The first is granted 50% of the time and, if it is, the second 50% of the time."

The chance of both is 0.5 × 0.5 = 25%. When the first approval comes through, the chance jumps to 50%, and your fair value jumps with it. Write the tree down once so that each update is a single multiplication.

With dice it works the same way. The sum of three dice is worth 10.5. When the first die shows a 6, the sum is worth 6 + 7 = 13.

Options appear too

Some firms make the product an option: "This pays the sum of two dice minus 8, if that is positive." You price it by averaging the payoff over the outcomes. Of 36 rolls, the sums 9, 10, 11 and 12 pay 1, 2, 3 and 4, and occur 4, 3, 2 and 1 times. The value is (4 + 6 + 6 + 4) / 36 = 0.56. When a die is revealed, average over what is left.

Position and limits

You will be given a limit, often 5 or 10 contracts long or short. Three habits matter:

1. Write down every trade: side, size, price, running position.
2. Know your room. Long 8 with a limit of 10 means you can only show 2 on your bid.
3. Shade your market. If you are long, move both prices down a little. You become less likely to buy more and more likely to sell. This is called skewing.

Counting P&L

At the end you are asked for your profit and loss. Add the cash from every trade (sales positive, purchases negative), then value what you still hold at the final price.

Example. You sell 4 at 101, buy 4 at 99, then buy 2 at 100. The product settles at 103.

Cash: +404 − 396 − 200 = −192. Position: +2 at 103 = +206. P&L = +14.

A shortcut: the round trip earned 4 × 2 = 8, and the 2 you still hold gained 3 each.

What assessors look for

• Markets that are centred on a sensible fair value and not too wide.
• Fast, correct updates when information arrives.
• An accurate position and P&L, at any moment.
• Clear speech: say the bid, the offer and the size every time, and confirm trades.
• Calm when a trade goes against you. Everyone gets picked off at least once.

How to practise

Reading is not enough. Say markets out loud with a friend, or use a simulator that makes you track your own position. Ten to fifteen minutes a day for a week makes the mechanics automatic, which frees your attention for the expected value sums.