Option Volatility Part 1

Unfortunately, for the sake of brevity, I will not be able to explain every single concept or term that I invoke within this blog. But... any questions you may have can surely be answered here: Option Volatility . In fact, I would HIGHLY recommend that anyone interested in Options read the link above.

Or... I have built a google search tool at the top right corner of the blog page that I have linked only to credible sources of information. You can type any financial term into that search bar and be confident that you will get a trustworthy answer to your question.

Continuing on, by the end of Part 3 of this series we will have a Python Program that takes in certain option inputs and calculates a fair value for the premium, which is very useful in terms of evaluating an option position. Today, I will go over some of the basic factors and inputs behind option pricing.

Before we begin, it is important to understand that the fair value of an option is using calculated using the Black-Scholes Model . Essentially, there are 5 inputs for option price calculation:

1. Stock Price
2. Strike Price
3. Historical Volatility
4. Days to Expiration
5. Risk-free Rate of Interest

The output is the FAIR value of an option, which conveniently is not always equal to the market value.

Lets start with Volatility. There are two aspects:

Historical/Statistical Volatility - this is a value we can physically calculate based on past price movements. It basically tells us how much a security might move in the present or near future based on the price changes it experienced in the past. Note that HV/SV does not tell us anything about the direction of movement.

How HV/SV is calculated? It is calculated by taking looking at the closing prices for a given period (usually 10, 20, or 30 day period), calculating the percentage change from day to day (close to close), and finally we calculate a standard deviation of the percentage price changes and annualize it by multiplying the standard deviation by the square root of 254 (number of trading days in a year). For a detailed example calculation, reference the link at the top of the page. This method is the most basic and popular method for calculating HV/SV.

Implied Volatility - this metric is very important in determining whether an option is currently over-valued or under-valued. It is very often ignored by traders, but IV is often the reason that option traders are baffled when the underlying increases and their option premium does not. The link at the top of the post gives a great example using a tech stock in which a trader speculated a big move, however, when the big move occurred his option did not gain in value. This is because the move was already priced into the Option, which the trader would have seen if they had looked at how high the IV was.

How do we get the value for IV? Almost all online brokerages provide you with an IV number. Essentially, if you refer to the five inputs listed earlier, IV is calculated by changing the Fair Value output to a "market price" input, and then solving for volatility. It is a very math-y calculation, so I will spare you from it for now.


Actionable Result: Ultimately, we need HV/SV and IV to be different from each other. In this sense we can figure out if an option is under-valued or over-valued.

When IV > HV/SV -- Options are thought to be Over-Valued
When IV < HV/SV -- Options are thought to be Under-Valued

It is useful to define a few more Option relevant terms:

Delta - Measure of the sensitivity of an option price to the changes in the underlying's price (stock price).

Vega - Measure of the sensitivity of an option price to changes in Volatility.

It is important to have a firm grasp on both of these concepts because they can move together or against each other.

The delta value is one of the more straight-forward metrics of an Option, if the delta value is +0.5 for an Option, then for every $1 dollar that the Stock (Underlying) price increases, the option premium will increase by $0.5 dollars or 50 cents. It is simply a ratio of option price movement divided by underlying price movement.

For the Vega value, you can think of it as either betting on rising volatility ("long" volatility) or falling volatility ("short" volatility). This is very similar to being long or short on a stock, if you are "long" volatility and volatility increases then you are profiting. Conversely, if you are "short" volatility and volatility declines then you are profiting. Technically, Vega is defined as the amount that an option price changes for a 1% change in Volatility. For instance, if the Vega value for an option is -96, then if volatility increases by 1% the option price will decrease by $96 dollars.

We now have a basic understanding of all the inputs in option pricing. In Part 2, we will start to set up the methodology for our program, and how all the inputs come together to form a "decision." In Part 3, we will look at the actual source code and an execution of a decision on a particular option.