# Volatility

An introduction to volatility, an important concept for trading options .

### What is Volatility?

Volatility, in financial markets, refers to the degree of variation of a trading price series over time. It is often used as a measure of risk. The higher the volatility, the more the price of the asset moves.

In options trading, the volatility of an underlying asset is a critical factor. The reason for this is simple: the price of an option is highly dependent on the expected future price movement of the underlying asset. This is of course also true when trading NFTs.

Options prices are typically calculated using models like the Black-Scholes model, which uses volatility as a crucial input. The model assumes that stock prices follow a statistical phenomenon known as a log-normal distribution, and thus their movements can be described by geometric Brownian motion.

### Volatility in the Black-Scholes Model

The Black-Scholes model, used in options pricing, incorporates volatility in its calculations. It uses the standard deviation of the underlying asset’s returns, which represents the volatility, to calculate the price of an option.

If the volatility input increases, the Black-Scholes model will output a higher option price. This is because higher volatility suggests a greater likelihood that the option will move in-the-money before its expiration date.

### What is Realized or Statistical Volatility?

Realized or statistical volatility refers to the volatility observed in an asset over a given period in the past. It's calculated based on historical prices and provides a measure of actual asset price changes.

It's important to note that realized volatility only tells us about past price movements and doesn't provide any direct insights into future volatility. However, it can be used as a reference point or a benchmark to gauge the relative volatility of an asset.

### What is Implied Volatility?

Implied volatility, on the other hand, is a forward-looking measure that provides an estimate of the expected future volatility of an asset. It's derived from the prices of options on that asset. If options are trading at high premiums, it implies that traders expect higher future volatility, and thus, implied volatility is high.

### Why Do We Use Annualized Volatility?

Volatility is usually expressed on an annualized basis for the sake of standardization and ease of comparison across different securities and timeframes.

The process of annualizing allows traders and investors to make meaningful comparisons of volatility over different periods. For example, a daily volatility of 1% could appear small, but when annualized it becomes significantly larger.

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