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Volatility is one of the most important concepts to understand when trading options. In this blog post, we will discuss implied volatility and how you can use it to improve your trading results. Implied volatility is a measure of the expected price movement of an option over time. It is calculated using a variety of factors, including the underlying security’s price, strike price, time until expiration, and implied interest rates. By understanding implied volatility, you can make better decisions about which options to trade and when to trade them.

## What volatility to use in the Black-Scholes model?

Implied volatility (IV) should be used in the Black-Scholes model. Implied volatility is a measure of the expected price movement of an underlying security over time. It is calculated using a variety of factors, including the underlying security’s price, strike price, time until expiration, and implied interest rates.

The most important concept in the Black-Scholes model is the volatility of the underlying security. This is because the value of an option is directly related to the volatility of the underlying security. The higher the volatility, the higher the price of the option. This is because high volatility means that there is a greater chance that the underlying security will move enough to make the option profitable. Conversely, low volatility means that there is a lower chance of the underlying security moving enough to make the option profitable.

## Why does a volatility smile exist?

The volatility smile is the name given to the shape of the implied volatility curve. The curve shows how IV changes as you move from left to right on the strike price axis. The curve is called a “smile” because it typically has a U-shape. The smile exists because IV is higher for options with strike prices that are further from the current price of the underlying security. This is because there is a greater chance that the underlying security will move enough to make these options profitable. The volatility smile is an important concept for traders to understand because it can help you choose which options to trade.

## What is volatility skew and why does it exist?

Volatility skew is the name given to the shape of the implied volatility curve. The curve shows how IV changes as you move from left to right on the strike price axis. The curve is called a “skew” because it typically has a U-shape. The skew exists because IV is higher for options with strike prices that are further from the current price of the underlying security.

## Who invented the volatility index, i.e. VIX?

The volatility index, or VIX, was invented by the Chicago Board Options Exchange (CBOE) in 1993. The VIX is a measure of the expected volatility of the S&P 500 index over the next 30 days. The VIX is calculated using a variety of factors, including the underlying security’s price, strike price, time until expiration, and implied interest rates. The VIX is an important tool for traders because it can help you gauge the market’s expectations for future volatility.

## Why does volatility scale as the square root of time?

Volatility scales as the square root of time because it is a measure of the expected price movement of an underlying security over time. It is calculated using a variety of factors, including the underlying security’s price, strike price, time until expiration, and implied interest rates. The square root of time rule is derived from the stochastic differential equation for the Geometric Brownian Motion. The square root of time rule can be used to convert volatilities in different timeframes.

## How to convert daily volatility to monthly or yearly volatility?

To convert daily volatility to monthly or yearly volatility, you can use the following formula:

**Volatility = Square Root of ((Number of Days in a Month or Year) x (Daily Volatility^(Two)))**

For example, if the daily volatility of a security is 20%, the monthly volatility would be:

Volatility = Square Root of ((30 x (20%^(Two))))

= Square Root of ((30 x (0.04)))

= Square Root of (1.2)

= 1.09

This means that the monthly volatility of the security is 109%.

## The bottom line

When trading options, it is important to understand implied volatility. Implied volatility is a measure of the expected price movement of an option over time. It is calculated using a variety of factors, including the underlying security’s price, strike price, time until expiration, and implied interest rates. By understanding the implied volatility, the smile and skew, traders can make informed decisions about which options to trade.

## Further questions

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