# Volatility and options pricing

Lesson in Course: Derivatives and options (advanced, 5min)

I understand that the value of the options is dependent on the value of the underlying stock. How do changes in the stock affect the option value?

If we've ever been on a boat ride on a windy day, we know that waves will cause the boat to go up and go down. Sometimes the wind blows hard enough and the boat ends up going off-course. We can use this simple analogy to understand how the movements of the underlying stock affect the price of our options.

## What is the wind?

The wind in our example can be thought of as the current market movements of our underlying stock. The stronger the wind blows, we'll see more volatility in our stock price and it's more likely we'll go off course.

Put simply, it's what causes our boat (stock) to move up and down in the waves. Volatility is an important measurement in many calculations regarding the potential future value of a stock and is used by investors worldwide. However, in the context of options, volatility affects not just the future value of options but also the current value.

In previous lessons, we learned that a changing underlying stock price can result in our positions being in-the-money or out-of-the-money. Volatility makes the likelihood of an option expiring in-the-money a lot less predictable and changes the intrinsic value of the options. The change in intrinsic value directly increases or decreases option prices.

Does volatility affect extrinsic value? To answer that question, we will need to know if we are sailing into the storm or away from the storm.

## Sailing into a storm

Do we expect the winds to blow harder or will the weather calm down?

The forward-looking consideration allows us to start factoring in time into the equation. If we are sailing into the storm, we can expect that waters get choppier and that we'd end up further off-course. This anticipated outcome is called implied volatility (IV).

The key thing to remember is that implied volatility is only a forecast—it's the collection of every market participant's best guess. Since no two investors are the same, the guessed outcome will make up a range of predictions.

The collective range of prices is indicated by implied volatility. We can imagine that if we were sailing into the storm, the bell curve would be wider since the winds are more unpredictable. On the other hand, if we were headed into calmer waters the curve would be narrower.

### The relationship between IV (implied volatility) and price

• High IV results in high option prices
• Low IV results in low option prices

Another way to think about how IV affects the prices of options is the amount of insurance we would need to buy.

If a major storm is coming, it's likely everyone needs insurance for their portfolios. The insurance comes in the form of options contracts. In times of high IV, the demand for insurance is high and so are options premiums. In calmer times, fewer investors are inclined to buy insurance, and options premiums are low during times of low IV.

There are many advanced options strategies that involve the understanding and use of IV.  While we won't cover them in this lesson, it's important for us to start understanding the concept of IV.

## Actionable ideas

A simple way for us to use our knowledge of IV to our advantage is to know when to buy options. At times of high IV, we need to remind ourselves that we are paying extra for our options. As soon as the storm changes direction and IV drops, our options will lose value even when the underlying stock price doesn't change—this is known as IV crush. The storms in our case metaphorically represent news events such as elections, earnings reports, or even mergers and acquisitions.

A good question for us to ask ourselves when we are looking to buy options is, "Is the IV high? If so, why is it high?"