For information on CRIX-option settlement pricing, please view the
SVJC Option Pricing Quantlet

Methodology

**CRIX:**

The CRIX is a market index and follows the Laspeyres construction. The index of Laspeyres is defined
as

with *P*_{it} the price of the crypto *i* at time point *t* and *Q*_{i0} the amount of crypto i at time point *0*. *P*_{i0} is the price at time point *0*. The CRIX is a slight modification

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

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 only price changes cause changes in CRIX.

**Constituents:**

It may happen, that a crypto has a high market capitalization, but 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

**Number of Constituents:**

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

**Special Events**

If the current price for a crypto contained in CRIX is not available at the exchanges, the index is made insensitive to this particular crypto.

- If a crypto contained in CRIX vanished, then it is excluded from the index at the next reallocation date.

**VCRIX:**

At the core of VCRIX index lies the HAR model, that is built on the premise that traders conduct their activities according to the strategies based on different frequencies (high frequency trading, daily traders, weekly, monthly), which in turn affects the overall market volatility at certain points in time. As cryptocurrency market is young and presumably still dominated by non-expert sporadic traders, presenting an informed judgement at this stage is rendered impossible by the implicit anonymity of most cryptocurrencies and its users. We made two adjustments to the original HAR model: implementations of rolling volatility instead of realized volatility (it was selected as most representative to proxy VIX) and the change of 5 (weekly) and 21 (monthly) trading frequencies to 7 and 30 days respectively. This change was dictated by the nature of cryptocurrencies that are being traded without time limitations. The final version of VCRIX is forward-looking and offers a forecast of the mean annualized daily volatility for the next 30 days. The index is re-estimated daily based on the realized daily volatility. Define t+1 as the next day's volatility, while the notations of t-6 references the value of 6 days prior to today. The forecast - - is estimated with a regression given the daily (initially estimated with a 30-day rolling window), weekly and monthly volatilities that are recalculated daily.

The initial value of the VCRIX is set to 1000, following the convention set by CRIX. A Divisor is introduced in order to account for the jumps that might occur due to the change in the number of constituents every month. The Divisor is set to a certain value on the first day to transform the estimated volatility to 1000 points of VCRIX. Divisor remains the same over the month. Every month the constituents can change. In this case, the value of VCRIX from the last day of the month will be transferred to the first day of the next month, after that the Divisor will be reevaluated in order to reflect the value for transformation.