> For the complete documentation index, see [llms.txt](https://docs.jaawle.xyz/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.jaawle.xyz/protocol/worked-examples.md).

# Worked examples

The rules of the [trading engine](/protocol/trading-engine.md), [liquidation](/risk/liquidation-and-insurance.md), [pools](/protocol/pools-and-nav.md) and [dividends](/protocol/dividends.md) applied to five cases, with the local parameters. Amounts are rounded to the cent at each step; prices to the cent; the Regular session unless stated. Every fee and borrow amount is split 10 % to the insurance vault, 10 % to the treasury, 80 % to the pool.

## A. Long AAPL, 5x

| step                           | computation                               | result                                          |
| ------------------------------ | ----------------------------------------- | ----------------------------------------------- |
| post collateral                |                                           | 1 000.00 USDC                                   |
| open $5 000 long at ask 316.40 | tokens = 5 000 / 316.40                   | 15.8028 shares                                  |
| open fee                       | 5 000 x 0.05 %                            | 2.50 (0.25 insurance, 0.25 treasury, 2.00 pool) |
| collateral after fee           | 1 000 − 2.50                              | 997.50                                          |
| leverage check                 | 5 000 <= 997.50 x 10                      | passes (5.01x)                                  |
| pool side                      | `reserveInventory(15.8028)`               | 15.8028 shares reserved from inventory          |
| liquidation mark, Regular      | (5 000 + 25.00 + 2.50 − 997.50) / 15.8028 | 255.02 (−19.4 %)                                |
| liquidation mark, Extended     | (5 000 + 37.50 + 2.50 − 997.50) / 15.8028 | 255.81                                          |

Seven days later the bid is 330.00. Utilisation averaged 20 % and longs were 60 % of the market's open interest (skew 0.2), so the long side paid funding.

| step                          | computation                     | result                                            |
| ----------------------------- | ------------------------------- | ------------------------------------------------- |
| P\&L at the bid               | 15.8028 x 330.00 − 5 000        | +214.92                                           |
| borrow                        | 5 000 x 87.6 % x 20 % x 7 / 365 | 16.80                                             |
| funding                       | 5 000 x 10 % x 0.2 x 7 / 365    | 1.92                                              |
| borrow leg (borrow + funding) | 16.80 + 1.92                    | 18.72 (1.87 insurance, 1.87 treasury, 14.98 pool) |
| close fee                     | 5 000 x 0.05 %                  | 2.50 (0.25 / 0.25 / 2.00)                         |
| payout                        | 997.50 + 214.92 − 18.72 − 2.50  | 1 191.20                                          |

A +4.30 % move in the stock returned +19.1 % on the collateral posted. The pool paid 214.92 of P\&L and kept 18.98 in fees and borrow (2.00 + 2.00 + 14.98); the insurance vault received 2.37 and the treasury 2.37.

## B. Short ETH, 10x on a synthetic pool

| step                              | computation                                | result                                   |
| --------------------------------- | ------------------------------------------ | ---------------------------------------- |
| post collateral                   |                                            | 500.00 USDC                              |
| open $5 000 short at bid 2 480.00 | tokens = 5 000 / 2 480                     | 2.016129 ETH                             |
| open fee, collateral after        | 2.50; 500 − 2.50                           | 497.50                                   |
| leverage check                    | 5 000 <= 497.50 x 20                       | passes (10.05x)                          |
| pool side                         | `increaseShortOi(5 000)`                   | needs room under 80 % of the pool's USDC |
| liquidation mark                  | (497.50 + 5 000 − 25.00 − 2.50) / 2.016129 | 2 713.12 (+9.4 %)                        |

Three days later the ask is 2 400.00. Utilisation averaged 15 % and shorts were the lighter side, so no funding was owed.

| step            | computation                     | result  |
| --------------- | ------------------------------- | ------- |
| P\&L at the ask | 5 000 − 2.016129 x 2 400.00     | +161.29 |
| borrow          | 5 000 x 87.6 % x 15 % x 3 / 365 | 5.40    |
| close fee       | 5 000 x 0.05 %                  | 2.50    |
| payout          | 497.50 + 161.29 − 5.40 − 2.50   | 650.89  |

No dividends and no session rules on a crypto pool; the position could have been opened or closed at any hour.

## C. The long in A is liquidated

The stock falls to a mid of 254.80 the same day (borrow and funding negligible).

| step                               | computation                                    | result                    |
| ---------------------------------- | ---------------------------------------------- | ------------------------- |
| unrealised P\&L at the mid         | 15.8028 x 254.80 − 5 000                       | −973.45                   |
| equity                             | 997.50 − 973.45 − 2.50                         | 21.55                     |
| maintenance                        | 5 000 x 0.50 %                                 | 25.00: liquidatable       |
| who                                | the keeper at once; anyone 30 s after a `flag` |                           |
| chunk                              | 5 000 < 50 000                                 | full liquidation          |
| close at bid 254.70                | 15.8028 x 254.70 − 5 000                       | −975.03                   |
| close fee                          | 5 000 x 0.05 %                                 | 2.50 (0.25 / 0.25 / 2.00) |
| collateral left                    | 997.50 − 975.03 − 2.50                         | 19.97                     |
| penalty                            | min(1.5 % x 5 000 = 75.00, 19.97)              | 19.97                     |
| liquidator / insurance             | 30 % / 70 % of 19.97                           | 5.99 / 13.98              |
| rest of the collateral to the pool | 19.97 − 19.97                                  | 0.00                      |
| pool receives                      | 975.03 loss + 2.00 fee                         | 977.03                    |
| trader receives                    |                                                | 0.00                      |

The insurance vault received 14.23 in total (0.25 from the fee, 13.98 from the penalty) and the treasury 0.25.

**A gap instead.** Suppose the stock closed at 316 on Friday and the position was healthy, then opened Monday with a bid of 240.00. Nothing can execute while the market is Closed; the first live print arrives in the Extended session at 04:00 ET, where the close fee is doubled.

| step                        | computation                                      | result                    |
| --------------------------- | ------------------------------------------------ | ------------------------- |
| P\&L at the bid             | 15.8028 x 240.00 − 5 000                         | −1 207.33                 |
| close fee, Extended         | 5 000 x 0.05 % x 2                               | 5.00 (0.50 / 0.50 / 4.00) |
| collateral after settlement | 997.50 − 1 207.33 − 5.00                         | −214.83: bad debt         |
| insurance cover             | min(214.83, $50 000 per tx, daily room, balance) | 214.83                    |
| pool receives               | 1 207.33 loss + 4.00 fee                         | 1 211.33                  |
| penalty                     | nothing remains                                  | 0.00                      |
| trader loses                | the collateral, nothing more                     | 997.50                    |

Had the vault been unable to pay, the uncovered part would have been booked in `badDebtUsd` as a loss of the pool.

## D. An LP deposit

AAPL pool: NAV $367 746, LP token price 1.2295, stock weight 59.7 % (target 60 %). An LP requests a 10 000 USDC deposit. For a USDC request the pool looks at the cash side, target 40 %:

| step               | computation                                          | result                   |
| ------------------ | ---------------------------------------------------- | ------------------------ |
| cash weight before | 100 % − 59.7 %                                       | 4 030 bps, drift 30 bps  |
| cash weight after  | (4 030 x 367 746 + 10 000 x 10 000) / 377 746        | 4 188 bps, drift 188 bps |
| direction          | 188 > 30                                             | away from target: taxed  |
| tax                | min(50, 50 x (30 + 188) / 2 / 4 000) = 5 450 / 4 000 | 1 bps (integer division) |
| fee                | 30 + 1 bps of 10 000                                 | 31.00                    |
| LP tokens minted   | (10 000 − 31.00) / 1.2295                            | 8 108.17                 |

The tokens are minted when the keeper executes the request (within minutes, or at the first live print if the market was closed; the request lives 3 days), at the NAV of that moment. The 31.00 stays in the pool for the other LPs.

**Staking into a fresh pool.** The same LP holds $10 000 of AAPL dShares and stakes them (`DepositStock`) into a pool that has just been seeded with USDC only, so its stock weight is 0 % against a 60 % target. The request moves the pool toward the target; the rebate is `50 x 6 000 / 6 000 = 50 bps`, which exceeds the 30 bps base, so the fee is 0. The shares are valued at the bid and the LP receives the full $10 000 in LP tokens at NAV. The request executes in the Regular session only.

## E. A dividend

AAPL pays $0.26 per share. The pool holds 694.17 shares and receives 180.48 in cash (694.17 x 0.26). At sweep time longs hold 15.8028 shares of exposure (the position in A) and shorts none.

| step                                      | computation          | result                              |
| ----------------------------------------- | -------------------- | ----------------------------------- |
| cash arrived                              | 694.17 x 0.26        | 180.48                              |
| pass-through owed                         | (15.8028 − 0) x 0.26 | 4.11                                |
| to the treasury                           | (180.48 − 4.11) x 0  | 0.00                                |
| booked into the pool's cash               |                      | 180.48                              |
| liability to the long, via `poolExposure` |                      | 4.11                                |
| net added to NAV by the sweep             | 180.48 − 4.11        | 176.38 (from the unrounded figures) |

The long's position now carries a dividend credit of 4.11, paid into its collateral when it closes; a short of the same size would carry a 4.11 debit. The shares the pool holds are already ex-dividend, so over the whole event the LPs' stock exposure lost 180.48 and their cash gained 180.48 less the 4.11 they pass to the long: they keep the dividend on the 678.37 shares that are not lent to longs. The platform receives nothing.


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