8. What is volatility? - The basics and the theory

(1). The important factor that affects the price of options

An option's premium is a sum of intrinsic value and time value, do you remember?

Option's Premium = Intrinsic Value + Time Value

Yes. I remember. I guess.

Intrinsic value is calculated by [underlying asset's price - option's strike price] in a call option, and [option's strike price - underlying asset's price] in a put option.

As you can see, intrinsic value of an option is determined by the price of an underlying asset and the strike price of the option.

Only in-the-money options have intrinsic value.

That's correct.
Then, how is time value determined? What affects the amount of time value?

Well, you told me "the longer the time to exercise, the higher the time value" in the previous lesson.

* Options of near expiration month
Options with far expiration month
  1. With short period of time until expiration, there is little chance that a stock price moves significantly.
  2. Traders have low expectations that the value of the option will increase before expiration.
  3. Time Value is low.
* Options of far expiration month
Options with near expiration month
  1. With long period of time until expiration, there is good chance that a stock price moves significantly.
  2. Traders have high expectations that the value of the option will increase before expiration.
  3. Time Value is high.
There is, however, another important factor that affects time value.
The factor is called Volatility.


Volatility. I know it's hard to pronounce.

Perfect understanding of the mathematics of volatility is not required. The emphasis should be on how you use it to make a profit anyway.
So you don't need to perfectly understand what I will explain in this lesson. Just grasp the outline of what volatility is, and you will be OK in a real trading situation.

(2). What is volatility?

An option's premium is affected by the following factors.
(The first 2 factors determine intrinsic value, and the other factors determine time value.)
Factors which determine a premium
  • Price of the underlying asset
  • Strike price of the option
  • Time left until the expiration
  • Interest rate (*)
  • Volatility
(*) Interest rate has the smallest effect on the option's premium among these factors, and can be almost neglected.

Volatility is a percentage of price movements.
The bigger the price movements, the higher volatility.

* The relationship between stock price movements and volatility

High volatility High volatility
Well... I got the idea, but I'm not sure what it has to do with options.

It may be helpful to put yourself in option buyers' place to understand that.
Suppose that there are two kinds of stock. One stock moves a lot, and the other doesn't.
If you would buy the option on either of those stocks, which stock would you choose?

Let me see... When I buy an option, there is an unlimited profit if the stock price moves a lot to a good direction. And if the stock price moves a lot to a wrong direction, there is a limited risk.

But if the price moves a little, a buyer of an option cannot gain a profit even if the direction is good.
I see! The option of the stock with big movements (high volatility) is more valuable to a buyer, isn't it?

Yes! You got the point!
Conversely, the option of the stock with small movements (low volatility) has a little value to a buyer of the option.

High volatility

-> High option premium

Low volatility

-> Low option premium

(3). Historical Volatility vs. Implied Volatility

There are two kinds of volatility. One is Historical Volatility, and the other is Implied Volatility.

Historical volatilili...
I'm getting tired of saying these words.

Some option traders use "Volty" instead of Volatility. Use this word if you like.
You don't need to care too much about the technical terms, but it is necessary to understand the difference between the two.

Alright. I'll do my best.

Let's start with Historical Volatility, or "HV" which is a frequently used abbreviation for it.

HV is the percent amount of a price movement based on the past price movements in the given time period.
The volatility I mentioned above, to be exact, is also HV .

The chart below shows the Japanese stock index "Nikkei 225" and its HV.

* Historical Volatility vs Index Price

index vs HV

When the index moves sharply, the HV surges.

That's the characteristic of HV.

Now that we learned HV, let's move on to Implied Volatility, or "IV".

Compared with HV which is just an average amount of change based on the past price movements, IV is calculated from the premium of options in the market.
IV is a very important factor in options trading.

Really? Tell me more.

To understand IV, you should first know the idea of Theoretical Price of options.
Theoretical price is the "reasonal price" which is calculated in a certain formula.

The formula consists of underlying asset's priceoption's strike pricetime left until expirationinterest rate、and finalyHV.
Theoretical options price is calculated from these factors.

The real premiums of options, however, don't always agree with the theoretical prices.
Theoretical price is just a "guide" for traders who want to know what price is reasonalbe for the option they are buying or selling.

* Calculating Theoretical Options Price
  • Price of the underlying asset
  • Strike price of the option
  • Time left until the expiration
  • Interest rate
  • Volatility (HV)
Based on the factors on the right, theoretical options prices are calculated by a mathematical formula. "Black–Scholes model" is one of the standard formulas in this calculation. (*)
※ Black–Scholes model
The model was first articulated by Fischer Black and Myron Scholes in 1973. Even today, it is the most widely used option's model to calculate theoretical prices.
Next, arrange the above formula as follows to find IV.
  1. Take away HV from the formula.
  2. Replace theoretical price with the actual premium of the option traded in the market.
What do we get as a result? All the factors except Volatility are fixed. (option's premium, price of the underlying asset, strike price of the option, time left until the expiration, and interest rate)

Therefore, a "measured" value of volatility at any particular time can be back-calculated by using the same formula.

* Back calculate volatility from the actual option's premium
  • Price of the underlying asset
  • Strike price of the option
  • Time left until the expiration
  • Interest rate
  • Actual Premium
Because all the factors except volatility are fixed in the market, a "measured" value of volatility can be back-calculated.
The result we get is implied volatility (IV) of the option.
IV is the value of volatility which is determined by the actual option's price (premium), compared with HV which is the statistical value gained from past movements of the underlying asset.

In other words, IV is an estimate of the future volatility by option traders.

When traders expect the future price of the underlying asset to move rapidly, the option's premium becomes high, and thus IV becomes high.
Conversely, when traders expect the future price to move a little, the option's premium becomes low, and thus IV becomes low.

In this sense, IV is a future estimate (expectation) by traders, compared with HV which is a pure statistic in the past.

In options trading, IV is used to determine which option is expensive or cheap.

I got HV is a past statistic, and IV is a future estimate by traders.

Do I get to see IV in a real trade?

You can refer to IV in a trading screen of a broker, like the screen below.

* Trading Screen of Broker
Option Trading Screen

Now I get IV matters in a real trade.
I wonder why I have never heard of IV or HV as a stock trader.

Institutional investors, bankers, and other big players in the market do consider volatility to manage their risk even if they trade only stocks. For indivisual stock traders, however, volatility is not always considered.

Since the change of a price is essential in options trading, volatility cannot be ignored if you are to win.

I see.
It's a little intricate, but I'll try hard to remember it.

Just get the outline of the mechanism explained above, and you'll be a step ahead in understanding volatility strategies of options trading.

In the next lesson, I'll show you how to take advantage of volatility in a trade.