BTC VIX Trade Analysis

• Samneet Chepal

Note: This piece is only for educational purposes and does not constitute investment advice. Views are my own and do not express the opinions of LedgerPrime or T3.

During this past month, LedgerPrime made markets for the first-ever BTC VIX trade using T3’s BitVol index. In this article, we’ll go over the basics of reconstructing this index and highlight how the trade was structured.

In traditional financial markets, the VIX is used to gauge where the market expects volatility to be over the next 30 days. The VIX is also commonly referred to as the “fear index” as high volatility in the market often coincides with higher VIX values. Many market participants use VIX futures and options to speculate on volatility while others try to hedge their portfolio from market turbulence (ie: hedging a position with VIX futures before a FOMC meeting).

T3’s BitVol index is similar to the CBOE’s VIX methodology and uses many of the same principles of variance swap pricing to construct the index. In our analysis, we’ll first start by constructing the BTC VIX index from scratch using Deribit options data and compare whether our theoretical values match up to the actual index value. Note — in this analysis there were a few deviations from the original T3 BitVol white-paper to expedite the modelling process. The overall results are still close and should suffice for our purposes here.

1. For each daily observation we have to find two option maturities which are closest to 30 days to expiry. In other words, we have to find options expiring just under 30 days and options expiring just above 30 days. We need to use two maturities because in the final step we will linearly interpolate the volatilities between the two maturities to approximate the 30 day volatility.
2. From here we want to remove all options with bid and ask prices less than $10 to reduce the impact of noisy data. This is a simplifying assumption from T3’s approach but still does a good job at getting us an approximation for the index.
3. Similar to the calculation of the VIX in traditional markets, we now have to filter the options between the two maturities so we’re only looking at ATM and OTM options. At this point, we’re done pre-processing the data and are ready to apply the BTC VIX formula to the actual data.
4. The formula below is an approximation for variance swap pricing which is similar to the VIX calculation in traditional markets. It has the following parameters below:

• ∆K: Average distance between the option strike to nearest two option strikes
• p: Price of the option
• F: Forward price of BTC
• T: Time to maturity (years)
• K_ATM: ATM strike

To make the calculations easier to understand, let’s take a look at the following table below which explains the red box in the formula. This highlighted section of the formula describes the overall contribution of each option to the VIX index. As an example, if we look at the $3250 put option, the average strike distance for this option is [($3250 — $3000) + ($3500-$3250)] / 2 = $250. Following the formula above, we multiply $250 by the option’s price to get its contribution to the overall VIX index. We can see a majority of the index contribution comes from ATM strikes near the current price of BTC (near the $4000 strike).

For options at the beginning and end of the table (ie: $5500 and $3000 strikes), we can simply take the difference between the closest strike rather than calculating the average distance. From here we simply apply the rest of the formula to calculate the variance for each maturity.

Once we have variances for both maturities we use the final formula below to linearly interpolate the variance and retrieve the VIX index value (which is in terms of volatility given the square root). For more details on the index construction methodology check out the BitVol white paper here: https://t3index.com/wp-content/uploads/2020/07/BitVol-Process_Guide_08-July-2020.pdf

From here we can repeat this step for each day to get the theoretical price history of the BTC VIX index and compare it to the actual index value. Across most metrics, we did a decent job replicating the index as can be seen in the plots below. It is surprising however to see the rolling correlation between the theoretical vs actual VIX to be lower than expected — this is perhaps due to the simplifying assumptions made earlier. Nevertheless, we can see that BTC spot and BTC VIX rolling 30 day returns exhibit some positive convexity which is what we’d expect (larger percentage moves on either side are usually associated with higher volatility).

Trade Recap:

The counterparty who initiated this trade is a sophisticated player and wanted to bet on the BTC VIX while limiting their upfront cost. As a result, both parties found it mutually beneficial to trade a 1x2 call spread rather than a forward on the index. Below we can see the PNL profile for both the buyer and seller.

There are three outcomes in this case:

1. BTC VIX < 135 = neutral outcome (zero cost premium)
2. BTC VIX between 135 to 165: buyer makes money
3. BTC VIX > 165 = seller makes money

With volatility dampening over the past few months during this bull run, it’ll be interesting to see how this trade plays out. I think scenario A is most likely given there are no foreseeable events which could cause volatility to spike up to all time highs. In my opinion, anything in the realm of scenario C with volatility at such high levels would be due to extremely bearish news (ie: G7 nations collectively banning crypto).

Overall, it was exciting to witness the first BTC VIX trade and I look forward to seeing the market for cryptocurrency volatility products to grow as new participants enter this space!