Realized Volatility

Realized Volatility is calculated by taking the standard deviation of an asset's logarithmic returns over a specific historical period (e.g., 7, 30, or 90 days). It uses actual, observed price data, making it an ex-post (after the fact) measure. Common calculation methods include:

• Daily Close-to-Close: Uses daily closing prices.
• Parkinson Estimator: Uses daily high and low prices for greater efficiency.
• Realized Kernel: A more advanced method that uses intraday data to filter out market microstructure noise.

While Realized Volatility (RV) looks at what did happen, Implied Volatility (IV) is the market's forecast of future volatility, derived from options prices. The difference between them, the Volatility Risk Premium (VRP), is a key trading signal. Typically, IV > RV, as options buyers pay a premium for uncertainty. Protocols like Opyn and Hegic use this relationship to structure products that allow users to earn yield by selling volatility.

RV is a foundational input for on-chain derivatives and structured products.

• Options Pricing: Protocols like Lyra and Dopex use RV models to help price options contracts.
• Volatility Indexes: Serves as the basis for on-chain volatility indices (similar to the VIX), which can be traded as assets.
• Risk Parameter: Used to adjust collateral factors, liquidation thresholds, and insurance premiums in lending protocols and vault strategies.

Accurate RV calculation requires reliable, manipulation-resistant price feeds. This is a primary challenge in DeFi. Solutions include:

• Decentralized Oracles: Services like Chainlink or Pyth provide volume-weighted average prices (VWAP) over time windows, which are essential for robust RV computation.
• On-Chain Data: Protocols may calculate RV directly from DEX price data (e.g., Uniswap v3 ticks), though this can be gas-intensive and susceptible to flash loan spikes.

RV enables the creation of structured financial products that allow users to take a direct view on future volatility.

• Volatility Vaults: Protocols like Ribbon Finance create vaults that automatically sell options, earning premium based on the expected spread between IV and RV.
• Volatility Tokens: Synthetic assets that track the realized volatility of an underlying asset, allowing for direct speculation or hedging against volatility itself.

While powerful, RV has inherent limitations:

• Backward-Looking: It measures past noise, not future risk.
• Period Sensitivity: The calculated value is highly dependent on the chosen lookback period.
• Data Quality: Susceptible to outliers (e.g., flash crashes) and requires clean, frequent price sampling to be accurate. In crypto, 24/7 markets mean RV calculations can be more frequent but also noisier than in traditional finance.

Realized Volatility is the annualized standard deviation of an asset's logarithmic returns over a defined lookback period (e.g., 7, 30, or 90 days). It's calculated from actual on-chain or market price data, not from option prices like implied volatility.

• Formula: Typically the square root of the sum of squared daily returns.
• Annualization: Daily volatility is scaled to an annual figure (e.g., multiply by √365).
• Key Distinction: RV measures what happened, while implied volatility (IV) measures what the market expects to happen.

RV is a foundational input for quantitative strategies and risk management frameworks.

• Options & Derivatives Pricing: Used to calibrate and back-test pricing models, and to calculate the volatility risk premium (IV - RV).
• Risk-Adjusted Returns: Metrics like the Sharpe Ratio use volatility (often RV) to evaluate performance.
• Portfolio Management: Informs position sizing and hedging strategies based on an asset's recent risk profile.
• Protocol Parameter Tuning: DeFi lending protocols may use RV to adjust collateral factors or liquidation thresholds dynamically.

This is the most critical comparison for traders. Realized Volatility (RV) is historical and objective, derived from past price movements. Implied Volatility (IV) is forward-looking and subjective, derived from the market price of options.

• Volatility Risk Premium: When IV > RV, option sellers are theoretically compensated for bearing risk.
• Trading Signal: A high IV/RV ratio can signal that options are expensive relative to recent actual movement.
• Data Source: RV uses spot price history; IV uses derivatives market prices from platforms like Deribit or Hegic.

Calculating precise RV for crypto assets involves unique data challenges.

• 24/7 Markets: Requires continuous time series analysis, unlike traditional market close prices.
• Price Oracle Data: Relies on accurate, manipulation-resistant oracle feeds (e.g., Chainlink) for on-chain calculations.
• Illiquid Assets: For long-tail assets, infrequent trades can distort return series and volatility estimates.
• Extreme Outliers: Crypto's "fat tails" mean a single day's massive return can disproportionately impact the period's RV.

Specialized instruments track and allow trading on crypto volatility.

• Volatility Indexes: Benchmarks like the BTC DVOL Index (by Deribit) track the 30-day implied volatility of Bitcoin options, providing a standard gauge of market fear/greed.
• Volatility Tokens/ETPs: Products like the Bitcoin Volatility Token (BVOL) or Volmex Finance indices let traders take direct long/short positions on future realized volatility.
• Structured Products: Vaults and strategies that automatically sell options (earning premium) when the IV/RV spread is favorable.

To calculate Bitcoin's 30-day realized volatility as of a given date:

1. Gather Data: Collect the closing price for BTC/USD for the past 30 days.
2. Compute Daily Log Returns: ln(P_t / P_{t-1}) for each day.
3. Calculate Standard Deviation: Find the standard deviation of these 30 daily returns.
4. Annualize: Multiply the daily standard deviation by √365.

Result: A single percentage figure (e.g., 65% annualized). This means, based on the last month's price action, BTC's price exhibited volatility consistent with a 65% annual move. This concrete number can then be compared to current implied volatility from options markets.

A broad term for any measure of past price fluctuations, typically calculated as the standard deviation of an asset's returns over a specific lookback period. Realized Volatility is a specific, high-frequency implementation of historical volatility that sums intra-period returns (e.g., daily squared returns) to provide a more accurate and efficient estimate than using simple close-to-close prices.

Patterns observed in the Implied Volatility of options across different strike prices. A smile shows higher IV for deep in-the-money and out-of-the-money options. A skew shows IV sloping downward for higher strike prices (common in equity markets). These patterns arise because the market's forecast of Realized Volatility differs from the log-normal distribution assumed by simple models, often due to crash risk or demand for protection.