Volatility and Vega

Different Ways to Look at Volatility

We have already learned what volatility means and how it can be calculated.

Now we need to understand an important distinction:

Not all volatility numbers represent the same thing.

For option trading, three ideas are particularly useful:

• Historical Volatility
• Expected Future Volatility
• Implied Volatility

Understanding the difference between them helps explain why option premiums can change even when the underlying price has not moved significantly.

Historical Volatility

Historical Volatility looks at how much the underlying asset has actually moved in the past.

For example, if a stock has shown annualised volatility of 25% based on its historical price data, that tells us about the size of its previous price movements.

Historical volatility is therefore based on actual past behaviour.

It can be useful for understanding how risky or volatile an asset has been historically.

However, past volatility does not guarantee future volatility.

Expected Future Volatility

Historical data tells us what has already happened.

But option prices are concerned with what may happen in the future.

Suppose a major event is expected to happen next week.

Traders may expect the underlying to move significantly during that period.

The expected future volatility can therefore be different from the volatility observed in the past.

This difference is extremely important for option pricing.

A Simple Analogy

Imagine a company is about to release an important product.

Its previous products were moderately successful.

That gives us some information about its likely future performance.

But suppose analysts are now expecting the new product to become a major success.

The market's expectation about the future may therefore be very different from what its past performance suggests.

The same idea applies to volatility.

Historical Volatility = What happened

Expected Volatility = What may happen

Implied Volatility

Implied Volatility (IV) is the volatility level that is implied by the current market price of an option.

In simple terms:

The market gives an option a particular premium.

If we put that premium into an option pricing model along with the other required inputs, we can determine the volatility level that would produce that premium.

That volatility level is called Implied Volatility.

So IV is essentially the market's volatility expectation reflected through option prices.

Why Is Implied Volatility Important?

Suppose an option is trading at a high premium.

The underlying price alone may not explain the entire premium.

The market may be expecting greater future movement.

This expectation can result in higher implied volatility and therefore a higher option premium.

Similarly, when expectations of future movement decline, implied volatility may fall and option premiums may decrease.

This is why an option's premium can change even when the underlying price remains relatively stable.

Historical vs Implied Volatility

The difference can be understood simply:

Neither should automatically be considered "correct".

They answer different questions.

Why Does This Matter for Vega?

Vega measures how much the option premium changes when volatility changes.

Suppose an option has a Vega of 0.15.

If volatility increases by 1 percentage point, the option's theoretical value may increase by approximately 0.15.

If volatility decreases by 1 percentage point, the theoretical value may decrease by approximately 0.15.

This is why understanding the type of volatility being considered is essential when studying Vega.

Volatility and Time to Expiry

The effect of volatility also depends on the amount of time remaining until expiry.

Consider an option with:

• 30 days to expiry
• 15 days to expiry
• 5 days to expiry

An increase in volatility generally increases the premium in all three cases.

However, the impact is usually greater when more time remains until expiry.

For example, the source compares a rise in volatility from 15% to 30% and observes that the premium response is much larger when 30 days remain than when only 5 days remain.

What Happens When Volatility Rises?

For both Call and Put Options:

Volatility ↑ → Premium ↑

And:

Volatility ↓ → Premium ↓

This relationship generally holds regardless of whether the option is a Call or Put.

The difference lies in how strongly the premium responds, which is where Vega becomes useful.

Vega in Action

Suppose an option has:

Vega = 0.15

If volatility increases by 5 percentage points:

Expected Premium Change = 0.15 × 5 = 0.75

The option's theoretical premium may therefore increase by approximately 0.75 points, assuming other factors remain unchanged.

If volatility falls by 5 percentage points, the theoretical premium may decrease by approximately 0.75 points.

What This Means for Option Buyers

For a long option position, rising volatility generally works in the trader's favour.

Therefore, a trader buying an option would ideally want:

Underlying to move in the expected direction

and, from a Vega perspective:

Volatility to increase

On the other hand, falling volatility can reduce the premium even if the underlying moves in the expected direction.

What This Means for Option Sellers

For an option seller, the situation is reversed.

The seller generally benefits when volatility falls because the option premium can decline.

Therefore:

Long Option → Positive Vega

Short Option → Negative Vega

This is why option sellers often pay close attention to whether current volatility appears high or low relative to expected future conditions.

A Critical Point

A trader can be correct about the direction of the underlying and still have an option position that performs poorly.

For example:

• You expect the market to rise.
• You buy a Call.
• The market rises as expected.
• But implied volatility falls sharply.

The decline in volatility can reduce the option premium and partially or completely offset the benefit from the underlying's movement.

This is why option trading requires more than simply predicting direction.

Practical Insight

Before buying or selling an option, consider three things together:

Direction + Time + Volatility

Ask:

• Where do I expect the underlying to move?
• How much time is left?
• What is the current volatility?
• Do I expect volatility to rise or fall?

This gives a much better understanding of how the option premium may behave.

Common Beginner Mistake

A common mistake is assuming:

"If my market direction is correct, my option trade must make money."

That is not necessarily true.

Changes in volatility and time can significantly affect the option premium even when the underlying moves in the expected direction.

Key Insight

Historical volatility tells us about the past. Implied volatility reflects what the current option price suggests about future volatility. Vega helps measure how sensitive the option premium is to changes in that volatility.

Understanding these three ideas is essential for analysing option premiums properly.

Key Takeaways

• Volatility can be viewed through historical data and future expectations.
• Historical Volatility is based on past price movements.
• Expected Future Volatility represents what the market may experience going forward.
• Implied Volatility is derived from the current option premium and reflects market expectations.
• Historical and implied volatility answer different questions.
• Higher volatility generally increases both Call and Put premiums.
• Lower volatility generally decreases option premiums.
• The impact of volatility is generally greater when more time remains until expiry.
• Vega measures the rate of change of option premium for a change in volatility.
• Long options have positive Vega, while short options have negative Vega.
• A trader can correctly predict the underlying's direction and still lose money if volatility moves unfavourably.