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VCRIX - A Volatility Index for Crypto-Currencies

Public interest, explosive returns, and diversification opportunities gave stimulus to the adoption of traditional financial tools to crypto-currencies. While the CRIX offered the first scientifically-backed proxy to the crypto-market (analogous to S&P 500), measuring the forward-oriented risk in the crypto-currency market posed a challenge of a different kind. Following the intuition of the "fear index" VIX for the American stock market, the VCRIX volatility index was created to capture the investor expectations about the crypto-currency ecosystem. VCRIX is built based on CRIX and offers a forecast based on the Heterogeneous Auto-Regressive (HAR) model. The HAR model was selected as the most suitable out of a horse race of volatility models, with two proxies for implied volatility, namely the 30 days mean annualized volatility and realized volatility. The model was further examined by the simulation of VIX (resulting in a correlation of 78% between the actual VIX and a "VIX" version estimated with the VCRIX technology). Trading strategies confirmed the predictive power of VCRIX and supported the selection of the 30 days means annualized volatility proxy. The best performing trading strategy with the use of VCRIX outperformed the benchmark strategy for 99.8% of the tested period and 164% additional returns. VCRIX provides forecasting functionality and serves as a proxy for the investors' expectations in the absence of a developed crypto derivatives market. These features provide enhanced decision making capacities for market monitoring, trading strategies, and potentially option pricing.


Introduction
Since the inception of Bitcoin (BTC) in 2008 the crypto-currency (CC) ecosystem has seen a market capitalization explosion that reached 2525 billion USD at its highest point on May 12, 2021(CoinMarketCap (2021). Apart from traditional hedge-funds and institutional investors who are interested in diversication, the CC ecosystem saw more than 400 crypto-funds launched during the years (next. autonomous.com/cryptofundlist). The rapid growth of BTC price led to persistent talks about "bubble-like" behavior and general skepticism of the market (Hafner (2020), Cheung et al. (2015)), exposing the need for a deeper understanding of the underlying processes driving the valuation of CCs. The interest in the underlying process led to the development of monetary equilibrium models (Schilling and Uhlig, 2019) and factor models for the pricing of CCs (Liu et al., 2019). Traditional market instruments (indices, ratings, investment portfolios) joined the ecosystem, including the early eorts such as CRIX by Trimborn and Härdle (2018) and exploration of the potential of CC as an investment tool (Petukhina et al. (2021)). Also the informative value from experts sentiment and discussion topics was investigated for their ability to explain market movements (Trimborn and Li, 2021).
Introduction of BTC futures by the CME and Chicago Board Options Exchange (Cboe) on December 18, 2017 reinforced the positions of CC as a new asset class.
The emergence of the derivatives market signaled the need for solid pricing strategies and a reliable (and stable) risk measure. The paper on pricing CCs by (Hou et al., 2020) addressed this issue by employing a Stochastic Volatility with a Correlated Jumps model (Due et al., 2000) and using insights on implied volatility dynamics (Fengler et al., 2003) in order to match non-stationarity and local heterogeneity phenomena of CRIX returns.
Industry demand and research revealed the necessity to explore the behavior of the CC volatility further, to provide the nal ingredient -a proxy for implied volatility. In traditional markets, implied volatility is measured by volatility indices which can be considered a traditional nancial tool. At the end of the 20th century, nancial markets of the USA and Europe aimed to capture the global measure of volatility in the respective market, which led to the introduction of VIX or VDAX.
The index providers settled on the model most appropriate for the specics of the behavior of the corresponding derivative. Given the absence of a developed derivatives market for CCs, we have to infer the characteristics of the implied volatility from the CC market behavior only. The specics of the latter (high volatility and low liquidity) triggered the development of new investment methods, see Trimborn et al. (2019), further justifying the need for a volatility index, that would capture the unique specics of CC as an asset class and provide a reliable indicator for the continuously unstable market.
This study aims to develop a measure and model to capture the expectations of the CC market and map them into an index referred to as VCRIX -a volatility index for CCs. VCRIX is especially designed for markets akin to the CC ecosystem, see Subsection 3.4, capable of accurately reecting the market risk. The goal of the proposed VCRIX is proper risk measurement for the CRIX components and delivery of market status information, analogous to implied volatility indices that capture investors expectations. The study is challenged by the absence of derivatives for most CCs (except Bitcoin), which impedes the direct application of the underlying methodologies of VIX or VDAX which measure the implied volatility from the derivatives and map them into an index. Therefore any study and therefore also the methodology for VCRIX rests on achieving the following milestones: 1. Identication and estimation of a valid implied volatility proxy 2. Identication of a model to facilitate consistent predictive performance for the implied volatility proxy 3. Construction of VCRIX based on the implied volatility proxy as a measure for market uncertainty To tackle these milestones, we develop volatility measures intended to proxy implied volatility, namely 30 day rolling historical volatility and realized volatility.
To account for the forward-looking behaviour of implied volatility, we implement volatility models to achieve an estimated measure catching future information. We compare the performance of a large variety of volatility models to identify the best performing model towards our goal: Development of a measure and model to capture the expectations of the CC market and construction of VCRIX. The model contestants comprise of univariate and multivariate GARCH-type model, the machine learning approach of Long-Short Term Model (LSTM) as well as the Heterogeneous AutoRegressive Model (HAR). The results indicate that the HAR model is the best prediction tool for the proxies. The outperformance of the HAR model rests on its structure which is designed to reect the behaviour of market participants and the resulting eect on the volatility. Corsi (2009) motivates the HAR model from the Heterogeneous Market Hypothesis which recognizes heterogeneity in market participants behaviour. Whereas the HAR model was not designed and motivated for the CC market, its outstanding performance in this study gives rise to believe that similar volatility structures exist in the CC market as in equity markets. To evaluate the appropriateness of the selected methodology for its ability to proxy a volatility index, we apply the methodology to the S&P500 and compare the Approximated VIX (AVIX) against the actual VIX (Cboe, 2019). We nd that AVIX has a high correlation and matching Mean Directional Accuracy with VIX.
Finally we study the ability of VCRIX as a risk measure by employing its signals into a long-cash and long-short trading strategy. The trading strategy based upon VCRIX achieves a higher cumulative return than an investment into CRIX which provides evidence for VCRIX suitability as a global CC vola measure. Lastly we discuss the economic insights which VCRIX provides and how its state relates to major events in the CC market.
The paper is structured as follows. Section 2 oers an overview of the used data sets for both traditional and CC markets. Section 3 provides a detailed explanation of the methodology used, whereas Subsection 3.1 contains the details on the implied volatility proxy estimation, followed by Subsection 3.2 that claries VCRIX model selection and the evaluation in Subsection 3.3. A brief revision of CRIX is provided in Subsection 3.4 which was selected as an equivalent for the S&P 500, a note on the existing implied volatility indices and VIX methodology in particular (Subsection 3.5). Methodological results, details of the VIX simulation conducted to test the selected methodology and nal time series are showcased in Section 4. The ability of the proposed volatility index to predict future risk is further explored in Section 5, which contains a long-short trading implementation of VCRIX as the signal to the trading strategy. Additional observations and a summary of the conducted research are provided in Sections 6 and 7.

Data
This research employs, crypto-currency price data, CRIX data and traditional nancial data, namely S&P 500 index values and VIX, which is the volatility index of Cboe based on the S&P 500. The daily historical closing values of CRIX for the period from 2014-11-28 -the emergence of CRIX -to 2021-06-01 (2498 observations, including weekends) were sourced from thecrix.de and converted to log-returns.
The CC data underlying the derivation of CRIX were obtained from the database for CRIX, kindly provided by CoinGecko. One should note that the intra-day data for CRIX and the CCs it is comprised of are only available from the 2016-06-30.
Therefore parts of the study consider data from this date forward, however this still includes the CC market peaks and the cool-down periods.
The daily historical closing prices of the S&P 500 and VIX from 03.01.2000 to 31.12.2018 (4780 observations) were sourced from finance.yahoo.com. It must be pointed out that SPY (ETF on S&P 500 index) has closer relations to VIX by design, as claried in Subsection 3.1, however, the log-returns of S&P 500 and SPY reveal no dierence and thus could be interchangeable for the conducted analysis.
The S&P 500 time series were converted to log-returns, VIX values remained as is.

Methodology
Implied volatility became a subject of academic research with the development of the derivatives market in the last quarter of the 20th century. The Black and Scholes (1976) model yields implied volatility as a volatility measure because, by denition, the implied volatility is the future volatility expected by the market. However, the market crash of October 1987 that bent the volatility surface of index options into a skewed "volatility smile", motivated an alternative solution that would provide a more accurate t to market conditions. Bakshi et al. (1997) provide an extensive overview of the further developments in this eld, including the stochastic interest rate option models of Merton et al. (1973), the jump -diusion/pure jump models of Bates (1991), the stochastic volatility models of Heston (1993) and others. While acknowledging the diversity of options pricing models, authors agree on the necessity of matching the selection of one to the goals at hand.
The goal of this study, developing a measure to capture the expectations of the CC market and mapping them into the index VCRIX, requires a methodology which overcomes the challenges posed by the CC market, in particular the absence of a developed derivatives market. The methodology is inspired by the construction of VIX. In simplied terms, VIX "predicts" the mean annualized volatility of the S&P 500 for the next 30 days in the future, that is in turn derived from the implied volatility extracted from the S&P 500 ETF swap prices. In this section we are describing the measures which will serve as proxies for the implied volatility. Since the actual implied volatility has intrinsic predictive power, we conduct a model comparison to nd the proper volatility model to predict the proxies. Mapping the forecasted values into VCRIX, results in a forward-looking property of the index.
Finally we validate the appropriateness of this methodology in a simulation study for the S&P500 market by approximating VIX with our methodology.

Implied volatility proxy
The CC market lacks a broad derivative market which challenges the measurement of implied volatility.
Though a volatility index akin to VIX relies on implied volatility. As such the challenge is to nd a viable proxy which leads then to VCRIX. Due to the lacking implied volatility, a model has to be identied, capable of capturing the predictive power of a traditional implied volatility index like VIX.
VIX is derived from derivatives on the S&P500. Therefore the underlying, S&P500, carries already part of the information which inuence the implied volatility. We investigate the dynamics of the underlying to proxy implied volatility, whereas for the CC market CRIX serves as the underlying. In particular we utilize 2 measures as a proxy for implied volatility for this study: 1. the annualized historical rolling volatility of the log-returns over 30 days 2. the realized volatility measured from the intra-day observations of the underlying.
The choice is motivated by the fact that VIX measures how much the market thinks the S&P 500 will uctuate in the 30 days from the time of each tick, according to Cboe (2019)). Realized volatility proved to carry important information about the movements of assets (Hansen and Lunde, 2005;Patton and Sheppard, 2015), as such we include it as a second candidate for the implied volatility proxy. Equation (1) displays the rolling volatility method (r t being a daily return of an asset on day t andμ an estimated mean daily return over the 30 day period): In case of historical volatility, the σ t would dene the volatility of the last day of the month, while for forward volatility the same calculation will account for the volatility of the rst day of the month. It should be pointed out that we are not using the notion of forward volatility as in Taleb (1997), namely, how implied volatility diers for related nancial instruments with dierent maturities. In this case, the "forward" part only bears the idea of adjusting the time span of the traditional rolling volatility measure to be forward-looking (results are displayed in Figure 3).
The second proxy, the annualized realized volatility is dened as the sum of the intraday log-returns:

Model selection
The two proxies (1) and (2) are by construction current and/or backward looking measures, whereas implied volatility includes future information over the investors believes about the future performance of the underlying. Therefore we have to forecast the proxies to achieve a proper underlying for forward oriented analysis.
We considered the following models: 1. GARCH family (tested by Hansen and Lunde (2005), French et al. (1987), Antoniou and Holmes (1995), see also Teräsvirta (2009) 3. neural network-based Long short-term memory cell (LSTM) models (Hochreiter and Schmidhuber (1997)) 4. Multivariate GARCH models (see Bauwens et al. (2006)) The models are calibrated based on the log-returns of the CRIX, the annualized daily volatility over a 30-day rolling window and realized volatility. Hereby the models in the univariate and multivariate GARCH family are derived from the logreturns only. This setting is conducted, since the HAR model has the GARCH model as a special case. Whereas the models considered here are not exact special cases of the HAR model, it clearly outperforms these models in the model evaluations.
The LSTM represents a comparatively new approach to volatility modeling.
Its architecture belongs to the Recurrent Neural Networks family and has been extensively used (together with Gated Recurrent Units) for the modeling of sequential data like text or time series. Its complex architecture provides interesting forecasting opportunities that have been explored and proven useful by Kong et al. (2017), Pichl andKaizoji (2017), Kim and Won (2018), Luo et al. (2018).
The EWMA is a special case of a GARCH with a pre-specied decay parameter λ: where σ 2 i,t+1 is the variance of CRIX log-returns (r i,t ) in the next period. In this study, the decay parameter λ was set to λ=0.96 since it showed the best performance under this setting in the model comparison.
The LSTM model in its most general form is dened as whereas fθ is a function f dependent onθ, which signies the complex set of parameters that are optimized during the training of the neural network. As for the other models in this study, 365 observations were used as the testing dataset.
The training data correspond to the earlier remaining observations in the dataset.
In this study, the best results were achieved with an LSTM which has 15 epochs The HAR model is constructed based on realized volatility. Since CCs are traded also on the weekend, we amend the HAR model such that the weekly and monthly realized volatility is derived on 7 and 30 days respectively, instead of 5 and 21 as it is common in traditional equity markets. The change of 5 (weekly) and 21 (monthly) trading frequencies to 7 and 30 days respectively is reected in the calculation of weekly and monthly volatilities (Equations (5) and (6)).
Then, the daily realized volatility is forecasted with For the market risk proxy of 30-days historical rolling volatility (annualized, as shown in Equation (8), the daily realized volatility, RV d t , is proxied as follows: Similarly to Equation (1), r t is a daily return of CRIX on day t andμ an estimated mean daily return over the past 30 days, meanwhile, the number of days for annualising the realized volatility was changed to 365 for the same reason. Further on we will refer to σ 2 t as daily realized volatility RV d t to maintain the usual HAR notation, even when derived from the 30 days historical rolling volatility. The weekly and monthly realized volatility can be derived based on RV d t as in equations (5) and (6).
The VCRIX is constructed as follows: Divisor , whereas RV d i,t+1 indicates the volatility forecast derived from the method i. The nal version of VCRIX is forward-looking and re-estimated daily based on the realized daily volatility and mean annualized daily volatility for the next 30 days respectively.

Model evaluation
The Table 1 compares the results of the model contestants over the time period 2016-06-30 to 2020-05-05 (some earlier data reduction was necessary to align with high-frequency data and to estimate rolling volatility). The initial models were estimated over the time period 2016-06-30 until 2019-05-05 and the prediction performance was derived over 2019-05-06 to 2020-05-05 (365 days). The remaining data will be excluded here and utilized in trading strategy evaluation for a out-ofsample analysis from the model evaluation. The models are constructed as described above. Due to the usage of the 30-days rolling volatility as a proxy for the implied volatility and therefore the market risk, the correlation of the estimated volatility is high for all models. Though EWMA, HAR and LSTM, which are constructed based on respective data, stand out. Also in terms of Mean Squared Error (MSE) and Mean Absolute Error (MAE), they clearly outperform the other models. For the univariate GARCH models, the MSE and MAE are not too dierent from each other, though they perform better than the multivariate ones. This is an interesting observation, since the DCC based models are based on the individual CC return series, which comprise the CRIX. Therefore this models carry more information, however the large dimensionality makes them also subject to convergence problems. The results allow for the interpretation, that for the 30-days rolling volatility measure, the multivariate GARCH models are not appropriate.
As for the three best performing models, EWMA, HAR and LSTM, the HAR model clearly outperforms the other ones. It is remarkable, that HAR even outperforms an LSTM model since deep learning models are designed to model complex underlying structures, which a linear model like HAR would miss. However it appears, that the market behavioural foundation of the HAR model gives it an edge in this study.
The   CRIX employs Akaike Information Criterion (AIC, Akaike (1987)) that determine the number of constituents quarterly according to the explanatory power each CC has over the market movements. CRIX was used as a proxy to the CC market before in research papers by Elendner et al. (2018), Klein et al. (2018), Mihoci et al. (2020), and was adopted as a benchmark by commercial projects like Smarter Than Crypto, Crypto20, F5 Crypto Index, and also used by the European Central Bank, Euro Area Statistics, as a market indicator in the report dedicated to understanding the "crypto-asset phenomenon" (Chimienti et al., 2019). These use cases conrm the applicability of CRIX as an appropriate basis for VCRIX.   (10) such that the last and rst value of CRIX before and after the re-adjustment do not dier. This is necessary, since the in-or exclusion of CCs may alter the value of CRIX whereas the index has to be invariant to such an operation, which is ensured by the Divisor. For more details on the precise construction of the Divisor, we refer to Trimborn and Härdle (2018).
The initial value of 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 rst 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 rst day of the next month, after that the Divisor will be reevaluated in order to reect the value for transformation.

Implied volatility indices
Consideration of the existing volatility indices would constitute a logical step towards the selection of the appropriate solution. As observed by Siriopoulos and Fassas (2009)  Most importantly, the goal of the VCRIX is to grasp the investors' expectations of the whole CC market. As Figure 2 shows, the weight of BTC in CRIX has been remaining below 0.6 most of the time, and thus BTC and its options cannot be considered suciently representative. Unfortunately the LXVX is no longer available, which leaves CC market participants without the means of a market risk measure akin to VIX. The development further drives the importance of the introduction of VCRIX.
The current VIX methodology was developed based on the pioneering research of Whaley (1993), Neuberger (1994), Madan et al. (1998), Demeter et al. (1999) and Britten-Jones and Neuberger (2000) where T is time to expiration, F is a forward index level from index option prices, K 0 is a rst strike price below F, K i is a strike price of the ith OTM option (on average the range of i is between 1 and 500, reecting the composition of the S&P 500) , Q(K i ) is the midpoint of the bid-ask spread for each option with strike K i , ∆K i is an interval between strike prices (half the dierence between the strike on either side of K i ) and R the risk-free interest rate to expiration.

Simulation and assessment
In model back-testing, the HAR model won the horse race; for the setup of the model competition and the evaluation of the results, see the previous sections 3.1 -3.3. The results are presented in Table 1 for the 30-days rolling volatility and Table 3 for the realized volatility. It should be specied that the original HAR model, Corsi practices.
In the absence of data on CC traders' behavior, we have made the assumption that the traditional practices could potentially be applied for the CC case. Recall that CCs are traded 7 days a week and not 5 days a week like equities. We made two adjustments for the length of a week and month (see equations (5) and (6)) to the original HAR model, such that we account for the 2 additional trading days of CCs per week.
Notably we use 2 kinds of measures as proxies for the implied volatility and market risk, the realized volatility and 30-days rolling historical volatility. Whereas realized volatility is a widely studied measure for market risk and proved to carry important information about the market state (Hansen and Lunde, 2005;Patton and Sheppard, 2015), the latter is not an established measure. As such it requires additional justication for the selection of this measure as a viable proxy for market risk. To perform this task, we construct a version of the VIX with the methodology described in this study, which we will refer to as Approximated VIX (AVIX). It comprises of the application of the selected HAR model to the log-returns of the S&P 500 instead of CRIX. From the S&P 500 log-returns, we derive the 30-days rolling historical volatility and derive the AVIX. Then, we compare the AVIX to the actual values of VIX, which allows for a justication of the suitability of the 30-days rolling historical volatility and HAR model as a proxy for a volatility index.
The time series (Figure 3) analysis shows the correlation of 0.89 between VIX and 30-days rolling historical volatility, which is already a strong sign for the applicability, while the correlation between VIX and the 30 days rolling volatility measured 30days in the future (forward-looking) was 0.78. These two measures indicate, that the 30-days rolling historical volatility is already a viable measure to approximate VIX (89% correlation is fairly high) and also shows that VIX predicts the volatility in 30 days (78% correlation). However the t is worse within crisis periods (as it can be seen for 2009, compare Figure 3) but improves again during market cool-down.  rising to 64% in case lag of 21 days is considered, as indicated in Table 5. Figure 4 and Figure 5 showcase the dierence between the estimated values and actual VIX.
The analysis unveils, that the VIX can be approximated with the 30-days rolling historical volatility, however there is room for improvement. This underlines on the one hand the strength of the methodology which was selected for this study, but also showcases the importance to measure implied volatility. These results led us to believe that the chosen methodology of the HAR model in combination with the 30 days rolling historical volatility does indeed provide a solid estimation of the implied volatility in the absence of the derivatives market. observe that the proposed model lags in catching the big spikes but performs well when market volatility is lower.

Trading implementation
As a nal validation between the 2 proxies for implied volatility and the resulting volatility indices, we test their ability to predict market movements and utilize the signal in two trading strategies. This will indicate if the proxies and the construction of VCRIX actually give a forward-oriented look on the CC market movements. Certainly, there is no perfect prediction tool, however it will provide an indication about its suitability. The implementation also shows how VCRIX can become increasingly employed in trading strategies as the CC market develops and new nancial instruments based on CC appear. As one of the examples, an inverse volatility ETF is a nancial product that allows investors to gain exposure to volatility, and thus hedge against portfolio risk, without having to buy options.
The trading strategy, which we employ here, is an inverse volatility strategy. In CCs, whereas the rst period includes this time period. Though it does include the 2021 peak and will provide insights on how the VCRIX signal evolves from a relatively longer calmer market period into one which is highly volatile.
Regardless of the absence of the above mentioned derivative instruments, volatilitybased trading strategies may still be employed and tested. Conventional shortterm reversal strategies have been explored and perfected by scholars and industry practitioners (Lehmann (1990), Jegadeesh (1990), Blitz et al. (2013)) over the years.
As an input, we employ VCRIX with either the 30 day historical volatility or realized  and Vola30day 7,3 (blue), which are generated by the relationships between the daily VCRIX value based on realized volatility as well as 30-days rolling historical volatility and its two MA curves (1 and 14 days, 3 and 7 days respectively). The lower graph for the subset shows RealizedVola 7,3 and Vola30day 7,3 , which is comprised of the daily VCRIX value based on the two proxies and its two MA curves (3 and 7 days). In further notation we indicate days with the subscripts, as in RealizedVola 14,1 whereas the subscript indicates that the 14-days MA curve was compared to the 1-days curve and taken as a trading signal. The respective trading strategy, see However we observe that from 2018 the dierence between the cumulative return of the CRIX ETF and the trading strategy becomes ever thinner, regardless of the choice of the long-cash/long-short strategy or the proxy. The portfolio driven by the trading strategy based on realized volatility even overtakes a CRIX ETF at some point. This is a clear indicator, that the signals from VCRIX worked well after the CC market peak. The second graph in Figures 6 and 7 shows the performance of the same trading strategies (but dierent MA signals involved) when initiated after the market peak in early 2018. Whereas the CRIX ETF diminishes in value and only returns to reect a gain in October 2020, the long-cash and long-short trading strategies with either proxy generate a substantial return for the trader long before and hold the portfolio value mostly in the positive domain. The best performing long-cash strategy based on the VCRIX signals generates a cumulative return of 174% and long-short of 256% versus 92% from the CRIX ETF, which clearly indicates the ability of VCRIX to predict future market movements. We construct the MA for the spans 1, 3, 7, 14 days, and compare the results with the following measures:  We observe in Tables 6, 7 that the visual analysis from Figure 6 gets supported, hence none of the strategies outperform a CRIX ETF over the entire time period.
Though we already stated that these results are due to the impressive gain in     (Yermack, 2015). While mechanics and potential implications of CC in nancial economics are being explored , there is still no established consensus over the evaluation methods. Also an investigation into CC experts sentiment, revealed that their sentiment does not predict the market (Trimborn and Li, 2021). Nowadays agents are often left with nothing but the information on the overall market "feeling" about the CC, which is communicated by the rise and fall of the price, in other words, its volatility.
VCRIX captures the volatility jumps that correspond to the development of the CC-ecosystem and can tell a story of the CC adoption ( Figure 9). Note that VCRIX is displayed back to November 2014, which is possible due to the availability of closing data for this time period. Realized volatility, which depends on intraday data, would only allow for an analysis from 2017 onwards. We observe spikes of interest in BTC in 2015, winter and summer of 2016 when BTC was slowly making its way to the attention of the general public. The large scale swings in price would not constitute a signicant shock in absolute values, but when something that was still considered a digital maverick rose in value from roughly 400 USD to 1000 USD within a year (Business Insider, 2016 ("Bitcoin is still storming higher")), investors noticed. VCRIX further captures the beginning of the rst massive growth wave (also captured well by the CRIX in Figure 8) and development of altcoins (ETH, LTH, and others). can be interpreted as daily volatility of 140%). These levels of uncertainty were largely caused by the major legislative shifts that were happening in countriesjuggernauts of CC movement: China, Korea, Japan, and the USA. Additionally, BTC was going through the heated debates on the SegWit (Segregated Witness) fork that was supposed to improve the speed and cost of BTC transactions. The fork was implemented in August, 2017 and led to the emergence of BTC Cash due to a certain number of big miners disagreeing with the implementation. These volatility spikes yet proved to be minor in comparison with the major market meltdown that happened at the beginning of 2018, when prices of most currencies on average suered an 80% drop (CoinMarketCap (2021)). 2018 was considered to be a stabilization period when governments and nancial corporations were getting onboard, however, the end of 2018 saw another volatility spike, majorly driven by the "holiday race" and uncertainty driven by "Constantinople fork" that was expected from Ethereum at the beginning of 2019. We have set the goal of capturing the expectations on the CC market (represented by CRIX) through the construction of an implied volatility proxy in the absence of the derivatives for the majority of CC. Following the intuition of the "fear index" VIX for the American stock market, the VCRIX volatility index was created to capture the investor expectations about the crypto-currency ecosystem. We dened 2 proxy candidates for the implied volatility due to the absence of a developed derivatives market in the CC market. Based upon the proxies, namely 30-days mean annualized historical rolling volatility and realized volatility, we performed a model comparison for the predictive power to ensure the proxies have a forwardlooking nature like VIX. The model comparison between univariate and multivariate GARCH-type models, EWMA, LSTM and HAR led to the selection of the HAR model. The model was further examined by simulating the VIX with the VCRIX technology (AVIX), which resulted in a correlation of 78% between VIX and AVIX.
The high correlation conrms the applicability of the model. We further investigate the volatility-predictive information value of VCRIX by creating trading strategies based upon VCRIX signals and investigate their performance on 2 time horizons against each other and a CRIX ETF. In the period after the December 2017 peak, the best performing trading strategy with the use of VCRIX outperformed the benchmark strategy even for 99.8% of the tested period and generated 164% additional cumulative return.
The study showed that VCRIX provides forecasting functionality and serves as a proxy for the investors' expectations in the absence of a developed crypto derivatives market. These features provide enhanced decision making capacities for market monitoring, trading strategies, and potentially option pricing. Authors intend to conduct further research to capture the observed excessive volatility that is captured by derivative-based indices like VIX and presumably stems from the behavioral component of option pricing.