Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

feat: simplify margin calculation (remove order book slippage) #2167

Merged
merged 4 commits into from
Feb 9, 2024
Merged

feat: simplify margin calculation (remove order book slippage) #2167

Changes from all commits
Commits
Show all changes
4 commits
Select commit Hold shift + click to select a range
0dac479
feat: update margin slippage in AMM
Jiajia-Cui Feb 8, 2024
c576784
chore: format
Jiajia-Cui Feb 8, 2024
e346205
feat: update margin formula
Jiajia-Cui Feb 9, 2024
59d5596
feat: update ACs
Jiajia-Cui Feb 9, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
104 changes: 26 additions & 78 deletions protocol/0019-MCAL-margin_calculator.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -8,16 +8,6 @@

- Zero position and zero orders results in all zero margin levels (<a name="0019-MCAL-003" href="#0019-MCAL-003">0019-MCAL-003</a>)

- If `riskiest long > 0` and there are no bids on the order book, the `exit price` is equal to infinity and hence the slippage cap is used as the slippage component of the margin calculation. (<a name="0019-MCAL-014" href="#0019-MCAL-014">0019-MCAL-014</a>)

- If `riskiest long > 0 && 0 < *sum of volume of order book bids* < riskiest long`, the `exit price` is equal to infinity. (<a name="0019-MCAL-015" href="#0019-MCAL-015">0019-MCAL-015</a>)

- If `riskiest short < 0 && 0 < *sum of absolute volume of order book offers* < abs(riskiest short)`, the `exit price` is equal to infinity. (<a name="0019-MCAL-016" href="#0019-MCAL-016">0019-MCAL-016</a>)

- If `riskiest long > 0 && riskiest long < *sum of volume of order book bids*`, the `exit price` is equal to the *volume weighted price of the order book bids* with cumulative volume equal to the riskiest long, starting from best bid. (<a name="0019-MCAL-017" href="#0019-MCAL-017">0019-MCAL-017</a>)

- If `riskiest short < 0 && 0 abs(riskiest short) == *sum of absolute volume of order book offers* <`, the `exit price` is equal to the *volume weighted price of the order book offers*. (<a name="0019-MCAL-018" href="#0019-MCAL-018">0019-MCAL-018</a>)

- A feature test that checks margin in case market PDP > 0 is created and passes. (<a name="0019-MCAL-008" href="#0019-MCAL-008">0019-MCAL-008</a>)

- For each market and each party which has either orders or positions on the market, the API provides the 4 margin levels. (<a name="0019-MCAL-009" href="#0019-MCAL-009">0019-MCAL-009</a>)
Expand All @@ -34,9 +24,9 @@
sell 10 @ 100 100
```

then the maintenance margin for the party is `min(1 x (100000-15900), 15900 x 0.25 x 1) + 0.1 x 1 x 15900 = 5565`. (<a name="0019-MCAL-024" href="#0019-MCAL-024">0019-MCAL-024</a>)
then the maintenance margin for the party is `15900 x 0.25 x 1 + 0.1 x 1 x 15900 = 5565`. (<a name="0019-MCAL-210" href="#0019-MCAL-210">0019-MCAL-210</a>)

- In the same situation as above, if `market.linearSlippageFactor = 100`, (i.e. 10 000%) instead, then the margin for the party is `min(1 x (100000-15900), 15900 x 100 x 1) + 0.1 x 1 x 15900 = 85690`. (<a name="0019-MCAL-025" href="#0019-MCAL-025">0019-MCAL-025</a>)
- In the same situation as above, if `market.linearSlippageFactor = 100`, (i.e. 10 000%) instead, then the margin for the party is `15900 x 100 x 1 + 0.1 x 1 x 15900 = 85690`. (<a name="0019-MCAL-211" href="#0019-MCAL-211">0019-MCAL-211</a>)

- If the `market.linearSlippageFactor` is updated via governance then it will be used at the next margin evaluation i.e. at the first mark price update following the parameter update. (<a name="0019-MCAL-013" href="#0019-MCAL-013">0019-MCAL-013</a>)

Expand All @@ -51,7 +41,7 @@
sell 10 @ 100 100
```

then the dated future maintenance margin component for the party is `min(1 x (100000-15900), 15900 x 0.25 x 1) + 0.1 x 1 x 15900 = 5565`. The current accrued funding payment for the perpetual component is calculated using
then the dated future maintenance margin component for the party is `15900 x 0.25 x 1 + 0.1 x 1 x 15900 = 5565`. The current accrued funding payment for the perpetual component is calculated using

```book
delta_t = funding_period_end - max(funding_period_start, internal_data_points[0].t)
Expand Down Expand Up @@ -256,11 +246,7 @@ There should be an additional amount `limit price x size x margin factor = 15910
sell 10 @ 100 100
```

the maintenance margin for the party is `min(1 x (100 000-159 00), 159 00 x 0.25 x 1) + 0.1 x 1 x 159 00 = 5565`

for this market the party switches to isolated margin with `margin factor=0.9` then the party will have margin account balance of
`average entry price x current position x new margin factor = 57 500 x 1 x 0.9 = 6325`
the difference topped up from the party’s general account(<a name="0019-MCAL-233" href="#0019-MCAL-233">0019-MCAL-233</a>)
the maintenance margin for the party is `159 00 x 0.25 x 1 + 0.1 x 1 x 159 00 = 5565` for this market the party switches to isolated margin with `margin factor=0.9` then the party will have margin account balance of `average entry price x current position x new margin factor = 57 500 x 1 x 0.9 = 6325` the difference topped up from the party’s general account(<a name="0019-MCAL-233" href="#0019-MCAL-233">0019-MCAL-233</a>)

- In isolated margin mode, a party `short 1@15 900`, `margin factor=0.9` and order book is

Expand All @@ -274,7 +260,7 @@ There should be an additional amount `limit price x size x margin factor = 15910

the margin account will hold `average entry price x current position x new margin factor = 57 500 x 1 x 0.9 = 6325`

for this market the party switches to cross margin and the market has `market.linearSlippageFactor = 0.25`, `RF short = 0.1` then the maintenance margin for the party is `min(1 x (100 000-159 00), 159 00 x 0.25 x 1) + 0.1 x 1 x 159 00 = 5565`
for this market the party switches to cross margin and the market has `market.linearSlippageFactor = 0.25`, `RF short = 0.1` then the maintenance margin for the party is `159 00 x 0.25 x 1 + 0.1 x 1 x 159 00 = 5565`
but if `5565 < collatoral release level` the maintenance margin will remain unchanged at `6325`

the difference topped up from the party’s general account(<a name="0019-MCAL-232" href="#0019-MCAL-232">0019-MCAL-232</a>)
Expand Down Expand Up @@ -337,7 +323,6 @@ There should be an additional amount `limit price x size x margin factor = 15910

- When the party has position -1 and order -3, and new long orders with size 3 will be offset(<a name="0019-MCAL-231" href="#0019-MCAL-231">0019-MCAL-231</a>)


**Check decimals:**

- A feature test that checks margin in case market PDP > 0 is created and passes. (<a name="0019-MCAL-090" href="#0019-MCAL-090">0019-MCAL-090</a>)
Expand Down Expand Up @@ -367,7 +352,7 @@ There should be an additional amount `limit price x size x margin factor = 15910
sell 10 @ 100 100
```

then the dated future maintenance margin component for the party is `min(1 x (100000-15900), 15900 x 0.25 x 1) + 0.1 x 1 x 15900 = 5565`. The current accrued funding payment for the perpetual component is calculated using
then the dated future maintenance margin component for the party is `15900 x 0.25 x 1 + 0.1 x 1 x 15900 = 5565`. The current accrued funding payment for the perpetual component is calculated using

```book
delta_t = funding_period_end - max(funding_period_start, internal_data_points[0].t)
Expand Down Expand Up @@ -602,36 +587,16 @@ with

```formula
maintenance_margin_long
= max(min(riskiest_long * slippage_per_unit, product.value(market_observable) * (riskiest_long * market.linearSlippageFactor)), 0)
+ max(open_volume, 0) * [ quantitative_model.risk_factors_long ] . [ Product.value(market_observable) ] + buy_orders * [ quantitative_model.risk_factors_long ] . [ Product.value(market_observable) ]`,
= max(product.value(market_observable) * riskiest_long * market.linearSlippageFactor, 0)
+ max(open_volume, 0) * [quantitative_model.risk_factors_long] * [Product.value(market_observable)] + buy_orders * [ quantitative_model.risk_factors_long ] * [ Product.value(market_observable)]`,
```

where

`slippage_volume = max( open_volume, 0 )`,

and

if `open_volume > 0` then

`slippage_per_unit = max(0, Product.value(market_observable) - Product.value(exit_price))`,

else `slippage_per_unit = 0`.

where

`market_observable` = `settlement_mark_price` if in continuous trading, refer to [auction subsection](#margin-calculation-for-auctions) for details of the auction behaviour.

`settlement_mark_price` refers to the mark price most recently utilised in [mark to market settlement](./0003-MTMK-mark_to_market_settlement.md). If no previous mark to market settlement has occurred, the initial mark price, as defined by a market parameter, should be used.

`exit_price` is the price that would be achieved on the order book if the trader's position size on market were exited. Specifically:

- **Long positions** are exited by the system considering what the volume weighted price of **selling** the size of the open long position (not riskiest long position) on the order book (i.e. by selling to the bids on the order book). If there is no open long position, the slippage per unit is zero.

- **Short positions** are exited by the system considering what the volume weighted price of **buying** the size of the open short position (not riskiest short position) on the order book (i.e. by buying from the offers (asks) on the order book). If there is no open short position, the slippage per unit is zero.

If there is zero or insufficient order book volume on the relevant side of the order book to calculate the `exit_price`, then take `slippage_per_unit = +Infinity` which means that `min(slippage_volume * slippage_per_unit, mark_price * (slippage_volume * market.linearSlippageFactor)) = mark_price * (slippage_volume * market.linearSlippageFactor)` above.

### **Step 2**

If `riskiest short == 0` then `maintenance_margin_short = 0`.
Expand All @@ -640,36 +605,28 @@ Else

```formula
maintenance_margin_short
= max(min(abs(riskiest short) * slippage_per_unit, mark_price * (abs(riskiest short) * market.linearSlippageFactor), 0)
+ abs(min( open_volume, 0 )) * [ quantitative_model.risk_factors_short ] . [ Product.value(market_observable) ] + abs(sell_orders) * [ quantitative_model.risk_factors_short ] . [ Product.value(market_observable) ]`
= max(product.value(market_observable) * abs(riskiest short) * market.linearSlippageFactor, 0)
+ abs(min(open_volume, 0)) * [quantitative_model.risk_factors_short] * [Product.value(market_observable)] + abs
(sell_orders) * [quantitative_model.risk_factors_short] * [Product.value(market_observable)]`
```

where meanings of terms in Step 1 apply except for:

`slippage_per_unit = max(0, Product.value(exit_price)-Product.value(market_observable))`
where meanings of terms in Step 1 apply

### **Step 3**

If `open_volume > 0`:

`maintenance_margin = max(min(open_volume * slippage_per_unit, product.value(market_observable) * (open_volume * market.maxSlippageFraction[1] + open_volume^2 * market.maxSlippageFraction[2])), 0)
+ open_volume * [ quantitative_model.risk_factors_long ] . [ Product.value(market_observable) ]`
where

`slippage_per_unit = max(0, Product.value(market_observable) - Product.value(exit_price))`
`maintenance_margin = max(product.value(market_observable) * (open_volume * market.linearSlippageFactor), 0)
+ open_volume * [quantitative_model.risk_factors_long] * [Product.value(market_observable) ]`

If `open_volume < 0`:

```formula
maintenance_margin
= max(min(abs(open_volume) * slippage_per_unit, mark_price * (abs(open_volume) * market.maxSlippageFraction[1] + abs(slippage_volume)^2 * market.maxSlippageFraction[2])), 0)
+ abs(open_volume) * [ quantitative_model.risk_factors_short ] . [ Product.value(market_observable) ]`
= max(product.value(market_observable) * (abs(open_volume) * market.linearSlippageFactor), 0)
+ abs(open_volume) * [quantitative_model.risk_factors_short] * [Product.value(market_observable) ]`
```

where

`slippage_per_unit = max(0, Product.value(market_observable) - Product.value(exit_price))`

If `open_volume == 0`:

`maintenance_margin = 0`
Expand All @@ -692,8 +649,6 @@ Use the same calculation as above with the following re-defined:

- For the orders part of the margin: use `market_observable` = volume weighted average price of the party's long / short orders.

Note that because the order book is empty during auctions we will always end up with the slippage value implied by the the slippage cap.

## Scaling other margin levels

### **Step 5**
Expand Down Expand Up @@ -751,16 +706,9 @@ riskiest_short = min( open_volume + sell_orders, 0 ) = min( 10 - 8, 0 ) = 0

# Step 1

## exit price considers what selling the open position (10) on the order book would achieve.

slippage_per_unit = max(0, Product.value(previous_mark_price) - Product.value(exit_price)) = max(0, Product.value($144) - Product.value((1*120 + 4*110 + 5*108)/10)) = max(0, 144 - 110) = 34


maintenance_margin_long =max(min(riskiest_long * slippage_per_unit, product.value(market_observable) * (riskiest_long * market.linearSlippageFactor)), 0)
+ max(open_volume, 0 ) * [ quantitative_model.risk_factors_long ] . [ Product.value(market_observable) ] + buy_orders * [ quantitative_model.risk_factors_long ] . [ Product.value(market_observable) ]


= max(min(14 * 34, 144*(14 * 0.25), 0) + 10 * 0.1 * 144 + 4 * 0.1 * 144 = max(min(476, 532.224), 0) + 10 * 0.1 * 144 + 4 * 0.1 * 144 = 677.6
maintenance_margin_long =max(product.value(market_observable) * (riskiest_long * market.linearSlippageFactor), 0)
+ max(open_volume, 0 ) * [quantitative_model.risk_factors_long] . [Product.value(market_observable)] + buy_orders * [ quantitative_model.risk_factors_long ] . [ Product.value(market_observable) ]
= max(144*(14 * 0.25), 0) + 10 * 0.1 * 144 + 4 * 0.1 * 144 = 705.6

# Step 2

Expand All @@ -770,20 +718,20 @@ Since riskiest short == 0 then maintenance_margin_short = 0

Since open_volume == 10

maintenance_margin = max(min(open_volume * slippage_per_unit, product.value(market_observable) * (open_volume * market.maxSlippageFraction[1] + open_volume^2 * market.maxSlippageFraction[2])), 0)
maintenance_margin = max(product.value(market_observable) * (open_volume * market.maxSlippageFraction[1]), 0)
+ open_volume * [ quantitative_model.risk_factors_long ] . [ Product.value(market_observable) ]
= max(min(14 * 34, 144*(14 * 0.25 + 14 * 14 * 0.001), 0) + 10 * 0.1 * 144 = max(min(476, 532.224), 0) + 10 * 0.1 * 144 = 620
= max(144*(14 * 0.25), 0) + 10 * 0.1 * 144 = 648

# Step 4

maintenance_margin_with_orders = max ( 677.6, 0) = 677.6
order_margin = 677.6 - 620 = 57.6
maintenance_margin_with_orders = max (705.6, 0) = 677.6
order_margin = 705.6 - 648 = 47.6

# Step 5

collateral_release_level = 677.6 * collateral_release_scaling_factor = 677.6 * 1.1
initial_margin = 677.6 * initial_margin_scaling_factor = 677.6 * 1.2
search_level = 677.6 * search_level_scaling_factor = 677.6 * 1.3
collateral_release_level = 705.6 * collateral_release_scaling_factor = 705.6 * 1.1
initial_margin = 705.6 * initial_margin_scaling_factor = 705.6 * 1.2
search_level = 705.6 * search_level_scaling_factor = 705.6 * 1.3

```

Expand Down
Loading