The XBTVIX uses the same methodology as the CBOE White Paper [1], which relies on gathering bid and ask quotes for options expiring between 23 and 37 days from the current point in time and reversing out the volatility implied by the options prices with a structured weighting and blending methodology to settle on an 30-day forward looking implied volatility.

We use options on BTC from Deribit, using contracts that expire each Friday at 08:00 UTC, as these have the highest trade volume.

VIX is a *fear gauge* used to measure the market’s expected volatility implied by at-the-money option prices [1].

To calculate an implied volatility time series from Bitcoin options data, we utilise CBOE's VIX method, assuming a risk-free rate (\(R\)) of zero [1]. This index is labelled VXBT. The contribution of each expiry to the index is defined as such:

$$ \sigma^2 = \dfrac{2}{T}\sum_i \dfrac{\Delta K_i}{K^2_i}e^{RT} Q(K_i) - \dfrac{1}{T}\Big(\dfrac{F}{K_0}-1\Big)^2 $$

Where \(K_i\) is the strike price of the i-th out-of-the-money option, \(\Delta K_i\) is half the difference between the strike prices on either side of \(K_i\), \(F\) is the strike prices of the option with the minimum absolute difference between call and put prices with the sum of that call price minus that put price, \(Q(K_i)\) is the midpoint of the bid-ask spread for each option with strike \(K_i\), \(K_0\) is the strike price equal to or otherwise immediately below F and T is the time from the option to expiry in minutes.

Using this formula, we interpolate the XBTVIX with the near term options contribution \(\sigma^2_1\) with time to expiry \(T_1\) and the next term options contribution \(\sigma^2_2\) with time to expiry \(T_2\):

$$ \text{VXBT} = 100 \times \sqrt{\Big\{T_1 \sigma^2_1\Big[\dfrac{N_{T_2} - N_7}{N_{T_2} - N_{T_1}}\Big] - T_2 \sigma^2_2\Big[\dfrac{N_7 - N_{T_1}}{N_{T_2} - N_{T_1}}\Big]\Big\} \times \dfrac{N_{365}}{N_7}} $$

XBTVIX differs from VIX in that rather than taking options expiring between 23 and 37 days from now, the options expiring on the next two Fridays are considered, giving the index a maturity of 7 days as opposed to VIX's 30-day maturity.

The algorithm that we use to compute VIX can be found in code here : https://github.com/Globe-Research/bitfear/blob/master/vix-implementation/vxbt_calc/vxbt_corrected_calc.py

We also conducted a study on XBTVIX, detailed in this paper "Fear and Volatility in Digital Assets" [2], linked here : https://arxiv.org/abs/2010.15611. This shows Bitcoin implied volatility on a 5 minute time horizon is modestly predictable from price, volatility momentum and alternative data including sentiment and engagement. Lagged Bitcoin index price and volatility movements contribute to the model alongside Google Trends with markets responding often several hours later. The code and datasets used in this paper can be found at https://github.com/Globe-Research/bitfear.

References

- Chicago Board Options Exchange. “Vix white paper”. In: (2003).url: http://www.cboe.com/micro/vix/vixwhite.pdf
- "Fear and volatility in digital assets", 2020. In: (2020).url: https://arxiv.org/abs/2010.15611

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