Methodology

**CRIX**

The CRIX is a market index and follows the Laspeyres derivation

with *P _{it}* the price of the crypto

where *MV*_{it} is the market capitalization of the crypto *i* at time point *t*. The *Divisor* ensures that the changes are stable. For CRIX, the *Divisor* is chosen such that

The starting value of
the CRIX is therefore *1000*. Whenever the amount of coins of a
crypto changes, the *Divisor* is adjusted. This ensures that solely price changes cause CRIX changes

**Constituents rule:** It may happen, that a crypto has a high market capitalization, but if it is not traded frequently. Two measures are applied which are modified versions of the liquidity
rules from the STOXX Japan 600 and the AEX Family. The applied rules are the following:

*0.25*percentile of*ADTV*

where *ADTV _{0.25}* is the

*0.25*percentile of Average Daily Traded Coins (*ADTC*)

where *ADTC _{0.25}* is the

If a crypto fulfills at least one of the two rules, it is eligible for the set of constituents of the CRIX.

**Number of Constituents**

A fixed number of constituents may be a good approach for relatively stable markets. For CRIX, AIC and BIC are employed. First by applying the CRIX formula an index for the total market is calculated. Next several indices with different numbers of constituents are computed. The number of constituents is then determined via AIC respectively BIC.

**Weights**

Each cryptos in CRIX is weighted with its market capitalization.

**Reallocation**

The reallocation period of the CRIX is 1 month. At this time point the liquidity will be checked again.

Every 3 month the number of constituents are rechecked.

**Special Events**

If the current price for a constituent of CRIX is not available at the corresponding exchanges the CRIX is made insensitive to this

If a constituent of CRIX vanished then it is excluded at the next reallocation date.

**VCRIX**

VCRIX (based on CRIX) is a volatility index, able to grasp the risk induced by the crypto-currency market, much like VIX for the S&P components. The crypto ‘fear index’ addresses the limitations constituted by the absence of developed derivative market for cryptos and offers an adequate measure for implied volatility, thus proved to be a proper basis for option pricing.