Index Price

Dederi Index Price

Dederi calculates the index price, including the BTC index and ETH index, by aggregating and verifying the latest spot prices from five exchanges: Bitstamp, Gemini, Bitfinex, Coinbase, and Binance. If any exchange data exhibits a delay exceeding 3 minutes, that exchange is excluded from the index calculation. The index price is updated every second using the following algorithm:

Step 1: Calculate Unverified Index Price

The latest mid-price $P$ from each exchange is used as the sample price:

$$P = \frac{Bid + Ask}{2}$$

Determine the median as $\text{BenchmarkPrice}$:

$$BenchmarkPrice = \text{median}(P_1, P_2, …, P_n)$$

Clamp all prices within the range of $\pm 0.5\%$ of $\text{BenchmarkPrice}$ to obtain the adjusted sample price $\tilde{P}_k$:

$$\tilde{P}_k = \text{clamp}(P_k, BenchmarkPrice \cdot 99.5\%, BenchmarkPrice \cdot 100.5\%)$$

Compute the equal-weighted average to derive the $\text{IndexPrice}$:

$$IndexPrice = \frac{1}{n} \sum_{k=1}^{n} \tilde{P}_k$$

Step 2: Calculate Dederi Index Price

Compare the $\text{IndexPrice}$ with the Chainlink and Uniswap index price to evaluate price discrepancies:

$$\min\left(\frac{|IndexPrice - ChainlinkPrice|}{IndexPrice}, \frac{|IndexPrice - UniswapPrice|}{IndexPrice}\right) \leq MaxIndexDiscrepancy$$

If at least one of the price discrepancies remains within the $\text{MaxIndexDiscrepancy}$, the calculated $\text{IndexPrice}$ is valid and adopted; otherwise, an anomaly is flagged, and the $\text{IndexPrice}$ is computed as follows:

$$IndexPrice = \begin{cases} \min(LastIndexPrice\cdot(1+MaxIndexDiscrepancy),MedianPrice), & LastIndexPrice < MedianPrice \\[5pt] \max(LastIndexPrice\cdot(1-MaxIndexDiscrepancy),MedianPrice), & LastIndexPrice > MedianPrice \end{cases}$$

Here, $\text{LastIndexPrice}$ refers to the previously published $\text{IndexPrice}$, and $\text{MedianPrice}$ is computed as follows:

$$MedianPrice = \text{median}\left\{IndexPrice,ChainlinkPrice,UniswapPrice\right\}$$

Example

At 3:22 PM on January 9, 2024, market data was collected from five exchanges. The Chainlink and Uniswap index prices were 46,725.12 and 46,334.29, respectively. The Dederi index price algorithm works as follows:

Price/Exchange	Bitstamp	Gemini	Bitfinex	Coinbase	Binance
$Ask$	46869.52	46873.84	46849	46862.39	46838.09
$Bid$	46869.21	46867.88	46848	46860.61	46838.08
$P$	46869.37	46870.86	46849	46861.50	46838.09
$BenchmarkPrice$	46861.50
$\tilde{P}_k$	46869.37	46870.86	46849	46861.50	46838.09
$IndexPrice$	46857.66
Price Verification	(IndexPrice - ChainlinkPrice) / IndexPrice = 0.28% (Within Range) (IndexPrice - UniswapPrice) / IndexPrice = 1.12% (Out of Range) Passes Verification, Adopted
$IndexPrice$	46858

Index TWAP

IndexTWAP is the time-weighted average price of the underlying index price used to compute the smooth mark price.

Step 1: Calculate the IndexTWAP

IndexTWAP is computed off-chain by sampling the underlying index price at 5-second intervals and calculating the arithmetic mean of the samples over the most recent 10-minute window.

Step 2: On-Chain Verification

Validate the computed IndexTWAP by comparing it with the corresponding 10-minute TWAP from Chainlink and Uniswap. An exception is triggered if at least one price discrepancy ratios exceed the $\text{MaxIndexDiscrepancy}$:

$$\max\left(\frac{|IndexTWAP - ChainlinkTWAP|}{IndexTWAP}, \frac{|IndexTWAP - UniswapTWAP|}{IndexTWAP}\right) > MaxIndexDiscrepancy$$

Settle TWAP

SettleTWAP is the time-weighted average price of the underlying index price used for the settlements of futures and options.

Step 1: Calculate the SettleTWAP

SettleTWAP is computed off-chain by sampling the underlying index price at 5-second intervals and calculating the arithmetic mean of the samples over the 30-minute window prior to contract expiration.

Step 2: On-Chain Verification

Validate the computed IndexTWAP by comparing it with the corresponding 30-minute TWAP from Chainlink and Uniswap. An exception is triggered if at least one price discrepancy ratios exceed the $\text{MaxIndexDiscrepancy}$:

$$\max\left(\frac{|SettleTWAP - ChainlinkTWAP|}{SettleTWAP}, \frac{|SettleTWAP - UniswapTWAP|}{SettleTWAP}\right) > MaxIndexDiscrepancy$$