Realized volatility is a statistical measure that quantifies the degree of variation in the price of a financial asset over a specific period. This metric provides insights into the past behavior of asset prices and can be valuable for derivative traders.

This chart shows Bitcoin's (BTC) realized volatility over the past year. The x-axis represents time, while the y-axis shows the annualized realized volatility percentage. Higher realized volatility zones indicate periods of increased market activity and price changes.

What is Realized Volatility?

Realized volatility is calculated based on historical price data and is mathematically defined as the standard deviation of past returns. It measures the historical price fluctuations of an asset, providing an indication of its actual volatility. Typically expressed as an annualized percentage, realized volatility offers a standardized method for comparing the volatility of different assets over various time periods.

There are multiple methods to calculate realized volatility. These parameters can be chosen by the user to adjust according to their needs.

Calculating Realized Volatility

$$\text{Realized Volatility} = \sqrt{\frac{A}{N} \sum_{i=1}^{N} (r_i - \bar{r})^2}$$

where:

• $N$ is the number of observations (days),
• $r_i$ is the daily return,
• $\bar{r}$ is the average daily return,
• $A$ is the annualization factor and corresponds to the number of trading days in a year. For digital assets, since they are traded continuously, it is natural to take this number equal to $365$.

Realized Volatility vs. Implied Volatility

Volatility is crucial for option traders as it affects option prices; higher volatility generally makes options more valuable. While realized volatility measures historical price movements, implied volatility represents the market's expectations of future volatility.

• Implied Volatility (IV): Derived from the prices of options, IV reflects the market's forecast of future price fluctuations. It is forward-looking and can change rapidly based on market conditions.

• Realized Volatility (RV): Based on historical data, RV measures past price fluctuations over a specific period, providing a backward-looking perspective.

The two quantities are often highly correlated. Implied volatility corresponds to the market's expectation and the price of the option, while realized volatility reflects the actual volatility observed in the underlying market.

A historical analysis of IV versus RV can provide traders with insights into periods when options are underpriced or overpriced, thus identifying potential trading opportunities. For example, in the equity market, realized volatility is typically below implied volatility.

A similar analysis for the crypto market, along with the reasons for such behavior, will be covered in another blog.

Importance of Realized Volatility in Digital Asset Markets

Realized volatility plays a significant role in digital asset markets for several reasons:

• Pricing Derivatives: The options market for major crypto assets such as BTC, ETH, DOGE, and MATIC is well-established. However, there is increasing demand for non-quoted options on smaller digital assets. Given the high correlation between RV and IV, the realized volatility of an asset can serve as a proxy for its implied volatility. Market makers can adjust this measure based on their holdings and their views on future volatility levels and risk premiums.

• Trading strategies: Understanding the historical volatility of an asset and its microstructure in comparison to implied volatility can help traders and market makers develop strategies to exploit market imbalances.

• Market Sentiment: Analyzing volatility trends can provide insights into market sentiment. High volatility periods might indicate market uncertainty or significant news events impacting the asset. This metric, alongside option market data, can help adjust trading strategies.

Realized Volatility in Digital Markets

Digital asset markets have unique characteristics that affect realized volatility:

• Higher Volatility: Digital assets are generally more volatile compared to traditional assets, resulting in higher realized volatility that reflects more significant price swings.
• 24/7 Trading: Unlike traditional markets, digital asset markets operate 24/7. This continuous trading leads to more pronounced volatility patterns, with potential spikes during traditionally "off-peak" hours.

Advanced Techniques for Measuring Realized Volatility

While the standard deviation of daily returns is a common method for calculating realized volatility, more advanced techniques can provide deeper insights:

• GARCH Models: Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models estimate volatility by considering past variances and returns. These models are particularly useful for capturing volatility clustering, where periods of high volatility are followed by high volatility, and low volatility periods follow low volatility.
• High-Frequency Data: Using high-frequency data, such as minute-by-minute prices, offers a more granular view of volatility. This approach is especially relevant for digital asset markets, which operate 24/7 and can experience rapid price changes. Users can assess RV with any granular frequency and loop-back period, providing additional microstructure insights.
• Realized Kernels: Realized kernels are advanced statistical tools that account for microstructure noise in high-frequency data. They provide more accurate volatility estimates by filtering out noise and focusing on genuine price movements.

Conclusion

Realized volatility is an important metric for understanding the past behavior of underlying assets. It serves multiple purposes in the digital asset space, such as aiding in the pricing of over-the-counter options or non-listed crypto options. A granular analysis of RV and IV can reveal trading opportunities and improve risk management strategies by providing deeper insights into market sentiments. In a future blog, we will explore this relationship further within the crypto space.