Trading and quant
Market-making games: quote, update, stay consistent
The vocabulary, the five-step method and worked dice and coin markets, plus what interviewers mark you on when they trade against you.
الأدلة باللغة الإنجليزية، لغة المقابلات.
What happens
The interviewer asks you to "make a market" on something uncertain: the sum of dice, the number of heads, or a quantity you can only estimate. You give a price to buy and a price to sell. They may trade with you or reveal information, and you update.
- Bid: the price you'll buy at. Offer (or ask): the price you'll sell at.
- "6.5 at 7.5" means a bid of 6.5 and an offer of 7.5. The width is 1.
- Your position is what you hold after trades: long if you bought, short if you sold.
The method
- 1
Fair value
Work out the expected value. That's the middle of your market.
- 2
Width
Wide enough not to lose on every trade, tight enough to be useful. Widen when you're unsure or the other side may know more.
- 3
Quote
Say it cleanly: "6.5 at 7.5".
- 4
Update on information
When something is revealed, recompute the fair value and move both prices.
- 5
Update on trades
Ask what a trade tells you. A buyer at your offer may know the value is higher. Your position matters too: if you're short, raising your quotes attracts sellers and reduces your risk.
Worked examples
مثال محلول · Sum of two dice
تم التحقق برمجيًاMake me a market on the sum of two dice. Then: the first die shows 5.
اعرض خطوات الحل
- 1.Each die averages 3.5, so the sum averages 7. Quote 6.5 at 7.5.
- 2.With the first die at 5, the fair value is 5 + 3.5 = 8.5. Move to 8 at 9.
الإجابة6.5 at 7.5, then 8 at 9.
مثال محلول · Higher of two dice
تم التحقق برمجيًاMake me a market on the higher of two dice. Then: the first die shows 4.
اعرض خطوات الحل
- 1.P(max = k) = (2k − 1)/36, so the fair value is (1 + 6 + 15 + 28 + 45 + 66)/36 = 161/36 ≈ 4.47. Quote 4 at 5.
- 2.With a 4 showing, the other die only matters when it beats 4: (4 + 4 + 4 + 4 + 5 + 6)/6 = 4.5. Quote 4 at 5, or tighten to 4.25 at 4.75.
الإجابةAbout 4.47, then 4.5.
مثال محلول · Heads in ten flips
تم التحقق برمجيًاMake me a market on the number of heads in ten coin flips. Then: four of the first five were heads.
اعرض خطوات الحل
- 1.Each flip adds 0.5 on average: 10 × 0.5 = 5. Quote 4.5 at 5.5.
- 2.Four heads are banked and five flips remain: 4 + 2.5 = 6.5. Move to 6 at 7.
الإجابة4.5 at 5.5, then 6 at 7.
What interviewers mark
- Quick, sensible fair values.
- Consistency: your new market follows from your old one and the news.
- Thinking about why someone trades with you.
- Knowing your position and P&L when asked.
- Staying calm when you're picked off.
Common mistakes
أخطاء شائعة
- Huge widths to avoid losing: "1 at 13" on two dice is useless and is marked down.
- Not moving after being traded with several times in a row.
- Forgetting your position when asked what you've made or lost.
- Moving only one side of the market after news.
Trading and quant