How Does One Use Sigma To Trade Options?

Sigma is the most neglected factor in amateur trading. It is a critical assumption during options trading, that price movement will not deviate from sigma at a certain percentage (e.g. 3 sigmas 99.7%, normal Gaussian distribution).

Sigma Normal Distribution

To note, other schools of thought is that the prices of a stock move more like Levy distribution, (which you can look up too) and also Taleb (who famously predicted 2008 stock market crash) distribution.

Sigma is the measure of statistical dispersion. It tells about how widely spread values are on the data set. When the data points are close to mean, then the sigma is close to zero. If the data points are far away from the mean, then sigma is far from zero.

Sigma is also further translated into “Implied Volatility (IV)". Implied volatility is used to calculate the price of the option from today to the expiration day.” In other words, you can say that it is a measure of volatility and data around the mean. 

Understanding Standard Deviation (Sigma)

Implied volatility is actually the estimation of price volatility without any underlying knowledge of the stock itself.

Investors use this metric to estimate future fluctuations. Traders calculate security prices based on certain predictive factors. It is denoted by a symbol σ. It is used to calculate percentages and standard deviation over a specified time horizon.

When the concept of sigma is applied to the stock market, remember that

  • Sigma is unidirectional, so it ignores Bearish or Bullish markets and generally increases when there are price movements. (e.g. investors believe that equity prices will decline over time).
  • Sigma or IV usually decreases during the time of the bullish market as the market is usually predicted to go up in the long term.
  • Bearish markets are riskier and considered to be undesirable by the majority of equity investors.
  • The biggest disadvantage of sigma is it doesn’t predict in which the price change will proceed. For example, a high standard deviation means there will be a large price swing. But this swing can be either very high upward or very low downward.  So, this value fluctuates between two directions. When the value of implied volatility is low, it means it wouldn’t make too much unpredictable and broad change. 

Sigma and Options

In the pricing of options, implied volatility or sigma plays a major role. When the buying options contract, it allows the holder to buy or sell an asset at a particular price during the pre-determined period. Sigma takes the future value of the option, and also the current value is also taken into consideration. Options that have high sigma value will have high premiums and vice versa. One thing that should be clear is that implied volatility is all about probability. It just provides the estimates of future prices instead of indication. However, investors take the standard deviation into account while making investment decisions. Sometimes it brings lots of useful benefits. 

As sigma provides the predicted pattern, and there is no guarantee that the option’s price will follow the pattern. However, when investors are interested in making investments, it helps them to consider those options that other investors are taking with the option. Sigma has a direct relation with the market opinion. So, it directly affects the option pricing. Implied volatility also affects interest rates. 

How Traders Use Sigma To Trade Options? 

In the world of options trading how tightly stock prices are bunched around the current price. Some stocks, such as KO, don’t show too much deviation from the current price. While on the other hand, AAPL can show a huge variation. Traders use sigma to calculate the potential percentage of a dollar by a specific date. Let’s take an example, for a $100 stock sigma is either $10 or 10%. 

Traders calculate the standard deviation (Sigma) based on the future date, index volatility, and the current index price. The interest rate is also incorporated in sigma but up to a lesser extent. Look at three key points.

  • The higher the volatility, the more will be the standard deviation.
  • Far the future dates, the bigger will be the sigma. 
  • The larger the index price, the more will be the standard deviation. 

You can use historical volatility as well. But in my opinion, IV can be a good estimate of future volatility. 

The Formula for Standard Deviation Calculation

You can calculate the standard deviation (Sigma) by the formula given below:

Standard Deviation = Stock Price * Volatility * Square root of days to expiration/365.

Factors That Affect Standard Deviation or Implied Volatility

Standard deviation is subject to unpredictable changes as with the whole market. Major determining factors for sigma are supply and demand.

The price will be high when the demand for an asset is high. The same will be the case with implied volatility, and the option price will be high.

When the supply is more than the market demand, the standard deviation falls, and the option price is decreased.

Another important factor is the time value of the option. In other words, you can say the amount of time until the option expires.

For a short-dated option, the standard deviation will below. While for the long-dated option, the implied volatility will be high. So the main difference lies in the amount of time left before the expiration of the contract. 

What Are The Pros And Cons Of The Implied Volatility?

Standard deviation helps to quantify market prices. Sigma calculates the size of the movement an asset may take. However, it does not indicate the direction of movement.

Investors look at the implied volatility when they choose an investment. When the volatility is high, they go for safer products or sectors. The implied volatility is solely based on the price and doesn’t take market assets into account. Natural disasters, adverse news, wars, or other events can impact the implied volatility. 

Pros Of Sigma

Cons Of Sigma

It is used to set option prices. 

Implied volatility is sensitive to news events and unexpected factors.

It can be helpful in determining the trading strategy.

It just predicts the movement of an asset but not the direction.

Sigma is used to quantify market uncertainty and sentiment.

It is just based on the prices and not take fundamentals into account. 


So, investors use sigma to calculate option pricing. It just predicts the patterns and doesn’t indicate the direction. However, it plays a crucial role, and most of the investors use this before investing in the stock exchange. 

Sky Hoon. Read Full Bio
Website Owner, Twitter-er
He has been trading since 2008. He started this blog to share the journey about option trading. He dabbled in stocks, bitcoin, ethereum (in Celsius Network), ETF (lazy Dollar Cost Averaging) and also built websites for fun. He used this as a platform to share my experiences and mistakes in trading, especially options which I just picked up.