Case 073Market making and trading scenariosWarm up
A market maker quotes a stock's 500 call at 12.00 bid, 12.40 offered, lot 100. Over the day it buys 600 contracts on the bid and sells 400 on the offer; the option's delta is 0.5. What spread did it earn, what inventory is left, and how does it hedge it?
1The situation
Kanheri Market Makers is a designated market maker in options on Tungi Chemicals, a stock trading near Rs 500. All day it shows a two-way quote in the 500 strike call: 12.00 bid, 12.40 offered, for a lot of 100 options per contract.
By the close, sellers have hit its bid for 600 contracts and buyers have lifted its offer for 400 contracts. The option's delta is 0.5. The operations analyst preparing the end-of-day report must state what the desk earned, what position it is carrying overnight, and what hedge the trader should have on.
2Your task
Work out the spread earned on the matched trades, the leftover position in contracts, options and shares of delta, and the hedge, and say what could still go wrong with the overnight position.
Quick check
Before working it: what does the market maker earn from the day's trading, if the option's price has not moved?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
The desk earned Rs 16,000 on 400 matched round trips, 0.40 on 100 options each, and is left long 200 contracts, 20,000 options, which is 10,000 shares of delta at 0.5. To be hedged it sells 10,000 shares of Tungi. At the 12.20 mid the leftover options also show Rs 4,000 of unrealised gain, but that is a mark, not cash. Overnight the desk still carries gamma, vega and the risk that sellers knew something.
Step 1How much spread did the desk actually earn?
A money changer at an airport buys dollars at one price and sells them at a higher one. He earns the gap only on dollars he has both bought and sold; dollars still in his drawer are stock, not profit. Kanheri earns 0.40 a option each time it buys a contract at 12.00 and sells one at 12.40, so 400 round trips of 100 options each make 400 times 100 times 0.40, Rs 16,000. The other 200 contracts bought on the bid are still in the drawer.
Step 2What position is left, and what hedge does it need?
Long 200 contracts is 20,000 call options. Each has a delta of 0.5, so together they behave like 10,000 shares of Tungi: a Rs 1 rise in the stock makes the desk about Rs 10,000. A market maker is paid for providing liquidity, not for taking a view on the stock, so it sells 10,000 shares, about Rs 50 lakh at Rs 500, and the overnight position is delta neutral. The same arithmetic in reverse applies when the desk ends a day short options: it buys stock.
| Item | Working | Result |
|---|---|---|
| Matched round trips | min(600, 400) | 400 contracts |
| Spread earned | 400 x 100 x (12.40 - 12.00) | Rs 16,000 |
| Leftover inventory | 600 - 400 contracts, x 100 | 20,000 options long |
| Delta of inventory | 20,000 x 0.5 | 10,000 shares |
| Hedge | sell stock | 10,000 shares |
Step 3What can still go wrong overnight?
Three things, and an analyst who names them shows they understand the business. The first is adverse selection: if the 600 contracts were sold to the desk by traders who expected the stock to fall, the 12.20 mid will not hold, and the Rs 4,000 unrealised gain on the leftover options can turn into a loss larger than the day's spread. The second is that the delta hedge is only first-order: being long options leaves the desk long gamma and long vega, so a fall in implied volatility overnight lowers the options' value even with the stock unchanged. The third is inventory itself: the desk would rather be flat, so tomorrow it may skew its quote, for example to 11.95 bid and 12.35 offered, to attract buyers and discourage more sellers, accepting a little less spread to shed the 200 contracts.
The numbers are small, which is the point of the exercise. A market maker's living is many small spreads, and the risk to that living is the occasional day when one side of the flow was better informed than the quote. Reporting the earned spread separately from the marked inventory, and the delta hedge alongside both, is what lets the desk see which of the two kinds of day it just had.
Where candidates lose it
Candidates multiply the spread by all 1,000 contracts traded and report Rs 40,000. A spread is earned per round trip; the 200 unmatched contracts are inventory with a mark, not earned spread.
The second miss is hedging in contracts instead of shares: 200 contracts are 20,000 options, and at a delta of 0.5 the hedge is 10,000 shares, not 100.
What the interviewer asks next
- Overnight the stock falls Rs 6 and implied volatility drops 1 point. Roughly what happens to the hedged position?
- Why would a market maker skew its quotes rather than simply widen them?
- How would the report change if the 600 contracts had been bought from one large seller in a single trade?
Asked at Susquehanna International Group, Operations, Bala Cynwyd, 2025 (Wall Street Oasis): Will most likely ask why the firm and what is a market maker. Also would recommend researching options trading beforehand.
Company names and figures are illustrative.