Implied vs Realized Volatility: What is the Difference?

Implied volatility (IV) is a widely used metric in the options market that reflects the market's expectations for the future volatility of an underlying asset, such as a stock or index. In essence, implied volatility indicates how much the market expects an asset to move—up or down—over a specific period.

Implied volatility is derived from an option’s price using models like the Black-Scholes pricing model. When demand for options increases—often due to expectations of heightened volatility—implied volatility typically rises, as buyers are willing to pay a premium in anticipation of large price movements in the underlying asset. Conversely, when the market becomes complacent, implied volatility usually falls, as demand for options decreases.

While implied volatility represents the collective expectation of future volatility, it’s not always an accurate predictor. Studies have shown that implied volatility often overestimates actual volatility (realized volatility). This overstatement occurs because the market tends to factor in a cushion for potential adverse movements, anticipating larger swings than what ultimately materialize.

As a result, this cushion often functions as an "insurance" premium, where investors are willing to pay more for options that provide protection against unexpected, high-magnitude price moves in the associated underlying asset.

Realized volatility, also known as actual volatility or historical volatility, refers to the actual movement of an asset's price over a specified period in the past. Unlike implied volatility, which is forward-looking and based on market expectations, realized volatility measures how much the asset actually moved—up or down—during the time frame in question. It is calculated by analyzing past price changes, typically using statistical measures like standard deviation or variance.

Realized volatility provides a concrete view of how volatile an asset moved in the past, helping traders and investors assess how it has behaved historically. While it reflects what has already happened, it can still offer valuable insights that may inform future expectations, even though those expectations may not always align with actual outcomes.

Historical volatility is another term for realized or actual volatility. It refers to the actual price fluctuations of an asset over a specific period in the past. Whether called realized, actual, or historical volatility, the concept remains the same: it measures the magnitude of an asset's price movements based on historical data. By calculating how much the asset's price has varied over time, historical volatility provides a snapshot of its past volatility, offering traders and investors insights into how volatile the asset has been. Although it focuses on past performance, it can still help inform future expectations, though those expectations might not always align with actual outcomes.

Future volatility refers to the market’s forecast of how much an asset’s price is expected to fluctuate over a given period. Unlike historical volatility, which measures past price movements, future volatility is speculative, based on the collective expectations of market participants. This metric is akin to the “holy grail” in the options world, because accurately predicting it can be highly profitable, which is why hedge funds, banks, and proprietary trading firms invest heavily in sophisticated models to estimate future price movements. However, forecasting future volatility is inherently complex and difficult, as the future is uncertain and subject to unforeseen events.

Instead of trying to predict future volatility, many options traders instead focus on the principle of mean reversion, which suggests that volatility tends to return to its historical average over time. Research has shown that implied volatility often follows this pattern, expanding during periods of market uncertainty and contracting when the market stabilizes. This understanding leads traders to favor strategies that capitalize on volatility’s natural ebb and flow, betting on the normalization of extreme swings rather than relying on uncertain forecasts of future movements.

The key difference between historical and future volatility lies in their focus: historical volatility measures past price movements, while future volatility is a forecast of how much an asset is expected to move in the future. Historical volatility is based on actual data and reflects how volatile an asset has been over a specified period. In contrast, future volatility is speculative, often estimated through models or market expectations, attempting to predict future price fluctuations. While historical volatility is measurable and concrete, future volatility is highly uncertain, leading many options traders to instead rely on strategies like mean reversion - the latter of which suggests that extremes in implied volatility will eventually revert toward their historical average.

Historical volatility is typically calculated using the standard deviation of an asset's returns over a specific period. Here's a basic overview of the process:

• Choose the time period: Select the period over which you want to calculate the historical volatility (e.g., daily, weekly, monthly).

• Collect price data: Gather the asset's price data for the chosen period. This could be closing prices for each day within that period.

• Calculate daily returns: Calculate the percentage change in price from one period to the next. For daily returns, this is done by taking the difference between each day's closing price and the previous day's closing price, divided by the previous day's closing price: Return𝑡 = (Price𝑡 − Price𝑡 −1)/(Price𝑡 −1)

• Find the average return: Compute the average of all the daily returns over the selected period.

• Calculate the variance: For each return, subtract the average return, square the result, and then find the average of those squared differences. That provides the variance.

• Calculate the standard deviation: Finally, take the square root of the variance. The standard deviation is the historical volatility, which represents the asset's price fluctuations over the chosen time period.

Implied volatility (IV) is typically derived from the price of an option using an options pricing model, such as the Black-Scholes model. Here's a basic overview of how this is done: 

• Obtain the option's market price: First, find the current market price of the option (the price at which it is being bought or sold).

• Gather the required inputs: To calculate implied volatility, you'll need the following information:

• The current price of the underlying asset (stock, index, etc.)

• The strike price of the option

• The time to expiration (how long until the option expires)

• The risk-free interest rate (usually based on government bonds)

• The option's market price (from step 1)

• Use an options pricing model: The Black-Scholes model or other pricing models are used to calculate the theoretical price of the option based on the above inputs.

• Solve for implied volatility: Implied volatility is the input in the pricing model that, when plugged into the model, gives the option's market price. Since the pricing model is a mathematical equation, finding the implied volatility involves solving for the volatility value that matches the market price of the option. This is typically done through iterative methods or numerical techniques, as there is no closed-form solution for implied volatility.

• Interpret the result: The implied volatility calculated represents the market's expectation of future volatility for the underlying asset, as implied by the price of the option.

In essence, implied volatility is a backward calculation based on the price of options. As such, it is not directly observable, but instead inferred from market data.