We provide two series of indexes calculated according to different methodologies: BVIX and ATM_IV. Bitcoin Volatility Indexes show implied volatility ratios for a certain time period. The tickers of both indexes contain the number of days that were used for calculation (after the _ sign). 

As a reference for the BVIX calculating approach we use CBOE VIX methodology. All metrics are calculated by analogy with the traditional VIX, but Bitcoin options are used. ATM_IV uses a slightly different method of calculating sigma, only the options closest to the center strike are taken into account. For calculations, we use full orderbooks of Deribit options. Indexes tick once a minute. You can choose an index suitable for your trading or scientific goals from different approach methodologies.

Calculation pipeline and assumptions

Some of the index calculations are very similar, so for ease of understanding, we will describe the general pipeline and branch off the different calculation descriptions where necessary.

1. Calculating the variables associated with the time horizon of the calculation

Target Time = Сurrent Time + Number Of Days To Calculate The Index [1, 2, 7, 14, 21, 28]

Next, Select 2 option series closest to the Target Time (one series before the Target Time and one after). For each option series calculate T (time till expiration in minutes) and annualized (annualized time till expiration in minutes)

2. For each index calculating sigma with different approaches.

BVIX

— Risk Free Rate (Rf) is equal to 0. According to the VIX formula, the Rf introduces negligible error into the final result, especially if you take into account the approximate differences of Rf in the traditional market and in the cryptocurrency market. 

— Find the Strike Prices for both series to calculate the forward price. In our case, it will be a strike with the minimum difference of the Q-value (bid price + ask price) / 2 between the call and the put. For further calculations, we take the Q-values of the options (Call Price and Put Price) on this Strike Price.

— Сalculating the forward index price for each of the two option series:


— Calculate K0 - the strike price equal to or otherwise immediately below the forward index level, F - for the near- and next term options.

— Select out-of-the-money put options with Strike Price <= K0. Stop calculation if two None values in a row. Repeat the procedure for  call options with Strike Price >= K0.

— For the selected options calculate ΔKi (half the difference between the strike prices on either side of Ki, where i is the Strike Price). At the upper and lower edges of any given strip of options, ΔKi is simply the difference between Ki and the adjacent strike price.

— Calculate the value Cumulative Value for both near and long term options:

— Calculate squared volatility for both near and next term options:


ATM_IV

— Calculating IV of the 1st ATM Call and 1st ATM Put options with Newton Method.

— Calculate squared volatility for both near and next term options:


3. The resulting index is a linear interpolation between the weighted variation of near and far options.

— NTnear  = number of minutes to settlement of the near-term options 

— NTnext = number of minutes to settlement of the next-term options 

— Ni = number of minutes in  i [1, 2, 7, 14, 21, 28] days (i x 1,440) 

— N365 = number of minutes in a 365-day year (365 x 1,440 = 525,600)