Fill Price and Price Impact Calculation

Fill Price is the execution price of a trade that accounts for the trade's impact on the market (price impact).

Fill Price Formula

$\text{fillPrice} = \text{indexPrice} \times \left(1 + \frac{\text{skew} + \text{signedTradeSize}/2}{\text{SKEW\_SCALE}}\right)$

where:

• $\text{signedTradeSize} = \text{tradeSize}$ for long positions
• $\text{signedTradeSize} = -\text{tradeSize}$ for short positions

Parameters

Parameter	Description
indexPrice	Current Index Price
skew	Position imbalance: Long OI - Short OI
tradeSize	Trade size in USD: amountUsd × leverage
SKEW_SCALE	10,000,000 USD (scaling coefficient)
direction	Trade direction: "long" or "short"

Price Impact Formula

Price Impact shows how much the execution price differs from the Index Price:

$\text{priceImpact} = \frac{\text{fillPrice} - \text{indexPrice}}{\text{indexPrice}}$

Explanation

Average Price

Fill Price represents the average price between:

• Price before trade: $\text{indexPrice} \times \left(1 + \frac{\text{skew}}{\text{SKEW\_SCALE}}\right)$
• Price after trade: $\text{indexPrice} \times \left(1 + \frac{\text{skew} + \text{signedTradeSize}}{\text{SKEW\_SCALE}}\right)$

Simplified formula:

$\text{fillPrice} = \text{indexPrice} \times \left(1 + \frac{\text{skew} + \text{signedTradeSize}/2}{\text{SKEW\_SCALE}}\right)$

Direction Impact

• Long position: signedTradeSize > 0 → increases skew → raises price
• Short position: signedTradeSize < 0 → decreases skew → lowers price

Calculation Examples

Example 1: Opening a long position

Conditions:

• Index Price = $300,000
• Long OI = $5,000,000
• Short OI = $3,000,000
• Trade Size = $100,000 (long)

Calculation:

skew = $5,000,000 - $3,000,000 = $2,000,000
signedTradeSize = $100,000
fillPrice = $300,000 × (1 + ($2,000,000 + $100,000/2) / $10,000,000)
         = $300,000 × (1 + $2,050,000 / $10,000,000)
         = $300,000 × (1 + 0.205)
         = $300,000 × 1.205
         = $361,500

Price Impact:

priceImpact = ($361,500 - $300,000) / $300,000 = 0.205 (20.5%)

Example 2: Opening a short position

Conditions:

• Index Price = $300,000
• Long OI = $5,000,000
• Short OI = $3,000,000
• Trade Size = $100,000 (short)

Calculation:

skew = $5,000,000 - $3,000,000 = $2,000,000
signedTradeSize = -$100,000
fillPrice = $300,000 × (1 + ($2,000,000 - $100,000/2) / $10,000,000)
         = $300,000 × (1 + $1,950,000 / $10,000,000)
         = $300,000 × (1 + 0.195)
         = $300,000 × 1.195
         = $358,500

Price Impact:

priceImpact = ($358,500 - $300,000) / $300,000 = 0.195 (19.5%)

Example 3: Small trade on a balanced market

Conditions:

• Index Price = $300,000
• Long OI = $5,000,000
• Short OI = $5,000,000
• Trade Size = $10,000 (long)

Calculation:

skew = $5,000,000 - $5,000,000 = $0
signedTradeSize = $10,000
fillPrice = $300,000 × (1 + ($0 + $10,000/2) / $10,000,000)
         = $300,000 × (1 + $5,000 / $10,000,000)
         = $300,000 × (1 + 0.0005)
         = $300,000 × 1.0005
         = $300,150

Price Impact:

priceImpact = ($300,150 - $300,000) / $300,000 = 0.0005 (0.05%)

Important Notes

1. Small trades: For small trade sizes, price impact is minimal thanks to the large SKEW_SCALE value.

2. Large trades: For large trade sizes, price impact can be significant, reflecting the real market impact.

3. Balancing: Short positions on a market dominated by long positions will execute at a more favorable price, encouraging market balancing.