Today, we'll condense potentially an entire semester of financial engineering into a single podcast episode. This show is a little longer than usual, but I think the time spent walking through the foundational elements of implied volatility, and its impact on option pricing, are critical for anyone interested in generating long-term income as an option seller. I encourage you also to listen to this episode multiple times if needed. Enjoy!

Introduction

• Implied volatility can be a complicated topic on the surface, but once you peel back some of the layers, it is actually very easy to understand. 
• The core of what we do as options traders is use IV to our advantage, selling rich IV compared to historical standards and trying to profit from mispricing that occurs.

Why Does Implied Volatility Exist?

• Stocks are totally different than options.
• They are understandable and valued on a forward-looking basis.
• Stocks do not have to factor into the price the expiration that options go through.

With options, there are two things to consider:

1. A finite life — options contracts have a definitive date in which they expire and cease to exist. 
2. Strike prices — the idea that you can pinpoint the strike prices in which you trade contracts, which could be the same price as the stock or dramatically higher or lower than the stock price.

So, how do you price in these additional factors? How do we determine a value for something that can die in the future but potentially has value now? How is the value determined for something that has a significantly higher or lower strike price than the stock price?

1. Time Value 

• We give value to time.
• The further out expiration is, the more time value the contract has. 
• If it has a long life expectancy, there is the potential to have a better chance of moving into a profitable range. 

Example: If you are trading a stock that is at $100 and you trade an option contract that is 2 years out, there are 2 years for it to move into a profitable range. However, if you have an options contract that is 2 days out, after 2 days, the options contract no longer exists. Those 2 days become critically important — only 2 days for things to go either right or wrong. 

2. Volatility

• The understanding is that you have to assign value to some expected or future movement in the stock to the option contracts. 
• How far do you expect the stock to move in the future? 
• You have to factor in some expectation of volatility, which dictates the value of strike prices. 

Example: If the stock is trading at $100 and you expect the stock to move nowhere for the next year, zero implied volatility. Therefore, if you know for a fact that the stock will never be lower or higher than $100 all year, almost no value would be associated with any options contracts that have a strike price higher or lower than $100. If there is no expected volatility, there is no value that can be derived from option contracts at different strike prices beyond $100. 

How do you determine how far a stock might move in the future?

• This determination then leads to the value of the underlying contracts. 

Example: If the stock is trading at $100 and you expect huge movements up or down by 100% in the next year, options contracts become valuable. The trades being made depend on which way you think the stock will move. In either case, whether the stock goes up or down, a value is assigned to these options contracts because of the potential to profit. 

What is Implied Volatility at its core?

• Implied volatility represents, as a percentage, the annualized expected one standard deviation range for a stock. 
• IV captures the one standard deviation of a log-normal distribution, which is 68% of the probable outcomes.

Example: If you have a stock trading at $200 with an IV of 25%, then the expectation is the stock moves in a range, up or down, of $50 (25% of $200 is $50) between now and the end of the year. The IV number of 25% captures a 68% probable range.

IV does not capture all of the possible ranges — it can never capture 100% of the possible range.

A 2 standard deviation range would capture about 95% of the expected move. So if you double the IV to 50%, that is a move up or down of $100. So there is a 68% chance that the stock moves up or down by $50 and a 95% chance the stock moves up or down by $100. 

How do we get this IV number?

• When you look at how options are priced, most pricing models use the Black Scholes Model.
• The Black Scholes Model uses a variety of inputs to then determine the value of an options contract.
• Inputs include things like:
  - Where is the option strike price compared to the current stock price?
  - Does it have intrinsic value, or not?
  - How long is it until expiration?
  - Are interest rates low or high?
• The Black Scholes Model also includes, as a function of the options price, implied volatility.
• As a general rule, when implied volatility is higher, option prices are higher across the board (all other things being equal).
• When you expect the stock to have huge movements, option prices on both sides increase.
• Generally, when implied volatility is low, option prices are low (all other things being equal).
• IV is forward-looking, you have to use it as an input for the Black Scholes Model.

So how do you determine IV when just getting started?

• We determine IV based on at-the-money and near at-the-money pricing of options contracts. 
• This is a backward way of calculating IV.
• Market makers and computer systems look at what people are willing to pay for at-the-money and near at-the-money contracts.
• Based on their activity and their willingness to buy options contracts or not, that derives how far people expect the market to move. 
• IV is user-generated and discerned through the buying behaviors of market participants.

Example: A stock is trading at $100. Someone who is buying the $100 strike call option is willing to pay $5 for that option contract. Through their buying actions, they have shown that they expect the stock to at least move 5% before expiration. If you are only willing to pay $4, you show you expect a 4% IV in that option over the next year. Again, through buying behavior, you derive the expected movement of the stock in the future. 

If you are willing to pay $15 for the options contract, you know that you will not be profitable unless the stock is worth more than $115 in the future. So, therefore, you are expecting a 15% move in the stock. Again, your actions derive what people expect — the supply and demand concept. 

• IV calculations only use at or near at-the-money contracts, because those are the most liquid, the most heavily traded, so it gives the system as much information as possible to derive IV. 
• Once IV is determined based on how actively people are trading, IV can be used to discern volatility and project volatility values for out of the money contracts. 
• Out-of-the-money options contracts price volatility based on at-the-money contracts.
• As buying behavior changes, implied volatility goes up and down, moving and shifting to the market all the time. 
• If there is no expected movement in the stock in the future, then the value of options go down. 

How do we use IV to our advantage?

For example, if the stock is trading at $100 and you buy the $100 strike call option for $5, that does not definitively tell you whether or not the stock will move $5 in the future.  That is simply how much you are willing to pay — your best guess at predicting the future. 

As a long-term average, the implied volatility number that market participants have generated through their buying activities is over-stated by some margin every single month.

If you expect the stock to move $5 this month, you usually find that the stock only moves $3. If you expect the stock to move $15, you will find that that stock only moves $13. It is always over-stated long-term. 

Why is IV always over-stated long term?

1. We are bad at pinpointing future movements of stocks.
2. When we expect things to move, we are either too optimistic or too pessimistic. 
3. Black Swan events are unpredictable by nature.

• In normal markets, we have periods where people start to become better at predicting the future movement, or it starts to become a much more narrow edge. 
• This generally happens during low implied volatility markets, making it a lot easier to predict stock movements. 
• What inevitably happens is a Black Swan event comes along.
• Black Swan events are an integral part of what we are doing as option sellers.
• Without Black Swans, we would have no edge in option selling.

Example: Everything is running smoothly; we expect a 10% move and see a 10% move. Then, a Black Swan event comes along, and we either get a huge drop or a huge move up in the stock. In the next year, the stock rallies 50%, which is way more than expected. This sets the new foundation for where people expect the market to go.

When IV escalates like that in a Black Swan event and the stock goes up 50%, now people start expecting 30-40% moves or maybe 50% moves the next year. That's when they begin overpaying for options contracts by a huge margin. When this happens, we see a huge difference between what the actual value is at the end of the year and what people pay. 

In these scenarios, it is better to be an option seller than an option buyer. On average, IV is always higher by some margin compared to historical. This presents a huge edge as option sellers to derive our income from this theoretical "edge.”

If everyone knows that IV is always higher than historical volatility, why can't we perfectly price everything?

• Options contracts are perfectly priced at the time of execution. 
• The day that you buy or sell an option contract, it is perfectly priced based on all the parameters that the market has at that exact time, including the expectation of future movement. 
• The market is perfectly efficient in pricing at the time of execution, based on the available information.
• The inefficiency comes with patience, and the only time that the mispricing happens is after you get through the time period between order execution, order entry, and expiration. 
• Once you wait through that period, then the mispricing (the differential between implied and actual volatility) starts to materialize.
• On order execution, an option buyer who's assuming a 25% move has got to see a 25% move in that stock. 
• This does not mean that the pricing on order entry was inefficient — it was correctly priced based on what the market had at the time. 
• Once you get to expiration, you find out that reality is different from expectation. 
• The IV edge takes time to unfold and materialize.