Formula and worked example

This page defines the Kimp Index formula and walks through one computation from raw inputs to the published value.

Formula#

kimp     = (P_upbit_krw / USDKRW) / P_global_usd − 1kimp_bps = kimp × 10,000

USDT is quoted at par with USD. Source rules, including what happens when a venue is unavailable, are in Sources.

Worked example: BTC#

Assume the following inputs at one epoch.

Step 1: convert the Upbit price to USD#

P_upbit_usd = P_upbit_krw / USDKRW            = 148,500,000 / 1,380.00            = 107,608.70 USD

Step 2: divide by the global price#

ratio = P_upbit_usd / P_global_usd      = 107,608.70 / 105,000      = 1.024845

Step 3: subtract one#

kimp = 1.024845 − 1     = 0.024845

Step 4: convert to basis points#

kimp_bps = 0.024845 × 10,000         = 248.45         → +248 bps

The published value is +248 bps. Bitcoin trades 2.48% higher on Upbit than on global markets at this epoch.

Rounding#

Reporters compute the premium at full precision and round to the nearest whole basis point before signing, with halves rounded away from zero. The on-chain value is a signed integer. In the example, 248.45 bps rounds to +248 bps.

Intermediate rounding in the steps above is for display only. A reporter computes the ratio in one pass without rounding the USD-converted price.

Reverse premium#

The same formula produces negative values when Upbit trades below the global price. With the same USDKRW and global price, an Upbit price of 143,000,000 KRW gives:

P_upbit_usd = 143,000,000 / 1,380.00 = 103,623.19 USDkimp        = 103,623.19 / 105,000 − 1 = −0.013112kimp_bps    = −131.12 → −131 bps

A negative value is a reverse premium (역프). Contracts treat it like any other value on a signed scale.

Sensitivity#

The index moves when any input moves.

• A 1% rise in the Upbit KRW price, all else equal, raises the index by about 102 bps at this level.
• A 1% rise in USDKRW, all else equal, lowers the index by about 101 bps, because the same KRW price converts to fewer dollars.
• A 1% rise in the global price lowers the index by about 101 bps.

This is why the FX reference is treated with the same care as the price sources. An FX error is a premium error.

From one value to the on-chain index#

Each active reporter performs this computation independently for every asset, once per epoch. The contract takes the median of valid reports. See Sampling and median and Reporter set.