The platform's Index Price is derived from the estimated index price (Symbol: .EXXX, XXX is represented by the respective coin's abbreviations such as BTC, ETH, XRP, or EOS) and can be obtained from the basic data page for inverse contract and USDT contract respectively. For the purpose of writing this article, we will be using .EBTC (BTC inverse perpetual's index price) as an example.
To arrive at the final index price, 3 variables are required, namely Current Quote, Original Weight and Real-time Weight.
Current Quote
These figures represent the current real-live price quotes directly from the respective spot exchanges for the underlying coin asset.
Original weight
.EBTC is the sum of the weighted BTC spot trading prices from 5 major global spot exchanges, namely Bitstamp, Coinbase Pro, Kraken, Gemini and Bittrex. An original weight (Trade_WtO), as derived by each platform's respective monthly trade volume, is assigned to their respective current quote prices to determine its weighted influence on the overall calculation of .EBTC. To aid traders in understanding this concept, platforms A, B, and C will be used in the illustrations below.
$$ \text{Trade WtO_A} = {{ \text{Monthly Trade Vol. (A)}} \over {{\text{Monthly Trade Vol. (A)}} + { \text{Monthly Trade Vol. (B)} }+ { \text{Monthly Trade Vol. (C)}}}} $$
$$\text{.EBTC} = {\text{Trade WtO_A } \times \text{Spot Price_A} + \text{Trade WtO_B } \times \text{Spot Price_B} + \text{Trade WtO_C } \times \text{Spot Price_C}}$$
Real-time weight
Likewise, should any one of the 5 exchange’s spot price deviate significantly from the other 4, it may potentially cause an inaccurate representation of .EBTC on the Bybit platform. Hence, to mitigate such effects, Bybit will also factor in the price spread between each exchange and .EBTC to calculate the final Index Price based on their real-time weight (Trade_WtR). What this means is that the exchange with the largest price spread from .EBTC will, as a result, hold the least significant weightage on the final Index Price. Again using platforms A, B and C, please refer to the formula below.
$$\text{Price Spread} = {\text{|Exchange's Spot Price} - .EBTC|}$$
An inverse square of an exchange’s price spread shall be used as the real-time weight of the exchange.
$$ \text{Trade WtR_A} = {{1 \over \text{Price Spread(A)}^2} \over {{1 \over \text{Price Spread(A)}^2} + {1 \over \text{Price Spread(B)}^2 }+ {1 \over \text{Price Spread(C)}^2}}} $$
Last but not least, the Index Price shall then be derived from the sum of the Spot Price for each exchange multiplied by the respective real-time weight of Exchange. $$\text{Index Price} = ({\text{Spot Price_A}\times\text{Trade_WtR_A)}}) + ({\text{Spot Price_B} \times\text{Trade_WtR_B}}) + ({\text{Spot Price_C}\times\text{Trade_WtR_C}})$$
Additional notes:
Note: Bybit will only temporarily exclude an exchange from the index calculation when the following conditions are triggered:
1. The latest spot price obtained from an exchange has not changed for more than a minute. This is to remove the exchanges that are suffering from liquidity issues or are experiencing a service disruption.
2. The spot price obtained from an exchange deviates from the average price of the spot prices of the other 4 exchanges by more than 3%. This is to eliminate the occurrence of any price abnormality.
Example 1: When Exchange's BTC prices are relatively close and has equal monthly trade volume
$$\text{Exchange A Spot: } = {$10,048.00}$$$$\text{Exchange B Spot: } = {$10,046.00}$$$$\text{Exchange C Spot: } = {$10,056.00}$$ $$\text{.EBTC} = {1\over3} \times {$10,048.00} + {1\over3} \times {$10,046.00} + {1\over3} \times {$10,056.00} = {$10,050.00}$$$$\text{Price Spread of A} = {|{$10,048.00} - {$10,050.00}|} = $2.00 $$$$\text{Price Spread of B} = {|{$10,046.00} - {$10,050.00}|} = $4.00 $$$$\text{Price Spread of C} = {|{$10,056.00} - {$10,050.00}|} = $6.00 $$
$$ \text{Calculated A Weightage} = {{1 \over {$2.00}^2} \over {{1 \over {$2.00}^2} + {1 \over {$4.00}^2 }+ {1 \over {$6.00}^2}}} = 0.7346938775510203 $$$$ \text{Calculated B Weightage} = {{1 \over {$4.00}^2} \over {{1 \over {$2.00}^2} + {1 \over {$4.00}^2 }+ {1 \over {$6.00}^2}}} = 0.18367346938775508 $$$$ \text{Calculated C Weightage} = {{1 \over {$6.00}^2} \over {{1 \over {$2.00}^2} + {1 \over {$4.00}^2 }+ {1 \over {$6.00}^2}}} = 0.08163265306122448 $$
Hence, .BTCUSD final Index Price will be the following:
$$\text{Index Price} = \text{Calc A Weightage} \times {$10,048.00} + \text{Calc B Weightage} \times {$10,046.00} + \text{Calc C Weightage} \times {$10,056.00} \approx {$10,048.29}$$
In summary, in Example 1, since all 3 exchanges have equal mothly trade volume and have similar current quote prices, all 3 platform's quoted prices share similar weightages inside the calculation of the final index price.
Example 2: When one Exchange's BTC price differs from the other two Exchange but all 3 has equal monthly trade volume:
$$\text{Exchange A Spot: } = {$10,060.00}$$$$\text{Exchange B Spot: } = {$10,040.00}$$$$\text{Exchange C Spot: } = {$10,500.00}$$ $$\text{.EBTC} = {1\over3} \times {$10,060.00} + {1\over3} \times {$10,040.00} + {1\over3} \times {$10,500.00} = {$10,200.00}$$$$\text{Price Spread of A} = {|{$10,060.00} - {$10,200.00}|} = $140.00 $$$$\text{Price Spread of B} = {|{$10,040.00} - {$10,200.00}|} = $160.00 $$$$\text{Price Spread of C} = {|{$10,500.00} - {$10,200.00}|} = $300.00 $$
$$ \text{Calculated A Weightage} = {{1 \over {$140.00}^2} \over {{1 \over {$140.00}^2} + {1 \over {$160.00}^2 }+ {1 \over {$300.00}^2}}} = 0.5041840271699171 $$$$ \text{Calculated B Weightage} = {{1 \over {$160.00}^2} \over {{1 \over {$140.00}^2} + {1 \over {$160.00}^2 }+ {1 \over {$300.00}^2}}} = 0.3860158958019677 $$$$ \text{Calculated C Weightage} = {{1 \over {$300.00}^2} \over {{1 \over {$140.00}^2} + {1 \over {$160.00}^2 }+ {1 \over {$300.00}^2}}} = 0.10980007702811527 $$
Hence, .BTCUSD Index Price will be the following:
$$\text{Index Price} = \text{Calc A Weightage} \times {$10,060.00} + \text{Calc B Weightage} \times {$10,040.00} + \text{Calc C Weightage} \times {$10,500.00} \approx {$10,100.59}$$
In summary, unlike Example 1, when Exchange C's current quote price is much higher relative to the .EBTC in Example 2, the influence that Exchange C has on the final Index Price is also relatively reduced in weightage to reflect its price variance.