The Binance Volatility Index (BVI), similar to other volatility indices like the VIX for traditional markets, measures the expected implied volatility over a 30-day horizon, derived from cryptocurrency option prices. Although the text indicates that it does not depend on a "specific model", its calculation follows standard principles used in volatility indices. Below, I explain the general process, as Binance does not publish an exact formula, but is based on common and transparent methodologies:
1. Input data: Option prices
The index uses the prices of cryptocurrency options listed on Binance (for example, Bitcoin or Ethereum options). Both call and put options are taken with different strike prices and expirations close to 30 days.
2. Option selection
- Options with expirations surrounding the 30-day period are chosen (e.g., options that expire just before and after the 30 days).
- "Out-of-the-money" options are selected: puts with strike prices lower than the current price of the asset and calls with strike prices higher. This captures the market's perception of future movements.
- To avoid noise, options with very low prices or low volume are excluded.
3. Interpolation for 30 days
Since there are not always options that expire exactly in 30 days, the data is interpolated:
- Two implied volatilities are calculated: one for the nearest expiration (e.g., 25 days) and another for the farthest expiration (e.g., 35 days).
- Then, it is linearly interpolated to obtain the exact 30-day implied volatility.
4. Calculation of implied variance
For each expiration, the implied variance is calculated using the option prices:
- A formula based on an options pricing model is used (although a specific model is not specified, it is usually a variant of the Black-Scholes model or a model-free approach).
- The contribution of each option to the index is weighted according to its price and its distance to the current strike price. This implies summing the contributions of all options, adjusted by a factor that reflects the time until expiration and the risk-neutral approach.
The general formula for implied variance is:
\[
\sigma^2 = \frac{2}{T} \sum_i \frac{\Delta K_i}{K_i^2} e^{RT} P(K_i)
\]
Where:
- \(T\): time until expiration (in years, 30 days = 30/365).
- \(K_i\): strike price of option \(i\).
- \(\Delta K_i\): interval between consecutive strike prices.
- \(P(K_i)\): price of the option (call or put) with strike price \(K_i\).
- \(R\): risk-free interest rate (generally low or assumed to be zero in crypto).
5. Conversion to volatility
Once the variance (\(\sigma^2\)) is calculated, the implied volatility (\(\sigma\)) is obtained by taking the square root and annualizing:
\[
\text{Volatility} = \sigma \times \sqrt{365} \times 100
\]
The result is expressed as a percentage (e.g., 47.7506%).
6. Adjustments and weighting
- The index incorporates "the entire spectrum of option executions", which means it uses real-time market data to capture sentiment.
- Options are weighted according to their liquidity and relevance to avoid distortions from options with low volume.
7. Interpretation of the value
A value of 47.7506 (as in the chart) indicates that the market expects the underlying cryptocurrency (for example, Bitcoin) to have an annualized volatility of 47.75% over the next 30 days. This means that the market anticipates that the price could move (up or down) approximately 47.75% annualized, or about 47.75% / √12 ≈ 13.8% in 30 days, with a 68% probability (assuming a normal distribution).
Note: The methodology is transparent because it is based on verifiable market data (option prices) and not on subjective assumptions. However, Binance does not publish the exact details of its formula, but follows a standard approach similar to that of the VIX, adapted to the cryptocurrency market.
$DOGE This is a screenshot of the options trading interface for Dogecoin (DOGE) on Binance, showing real-time data for options contracts expiring on May 25, 2025 (approximately 1 day and 5 hours from the current date, May 07, 2025). The table lists various options with their execution prices (0.1470, 0.1500, 0.1540, 0.1570, 0.1590), types (Call or Put), bid and ask prices, implied volatility (IV), mark price, last price, position, and open interest.
- Call options give the right to buy DOGE at the specified price, while Put options give the right to sell.
- Bid/IV and Mark/IV show the bid price and implied volatility (a measure of expected price fluctuation) for each option.
- Position and At indicate the number of open positions and the last traded price or activity level.
- The index price is 0.1745, reflecting the current market reference price for DOGE options.
The data suggests active trading with varying implied volatilities (e.g., 0.0% for some calls, up to 222.93% for a put at 0.1470), indicating market expectations of potential price movements.
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