CRIX - VCRIX




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

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Methodology

Methodology

CRIX: 

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

 
with Pit the price of the crypto i at time point t and Qi0 the amount of crypto i at time point 0. Pi0 is the price at time point 0. The CRIX is a slight modification 

where MVit 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.
 
Divisort-1 is the Divisor before the change in the amount of coins and Divisort directly afterwards.

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:

  1. 0.25 percentile of ADTV 

where ADTV0.25 is the 0.25 percentile of the ADTV distribution of all cryptos in the last period and ADTVi is the ADTV of a single crypto.

  1. 0.25 percentile of Average Daily Traded Coins (ADTC) 

where ADTC0.25 is the 0.25 percentile of the ADTCs of all cryptos in the last period and ADTCi is the ADTC of a single crypto. If a crypto fulfills at least one of the two rules, it is eligible for the CRIX set of constituents.

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

  1. 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.

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