Volatility and Option Premium

Options and Volatility

Volatility and Premium
Volatility and Premium. Pixabay.com

The market price of call options and put options vary over a wide range, depending on how likely it is that the underlying stock will undergo a larger, rather than a smaller, price change on any given day. Let's see if we can bring that statement to life so that you get a true sense of how implied volatility works.


When we talk about the volatility of any stock, we are referring to a measurement of how much the closing price varied from day to day -- over a specific period of time in the past (when the data was collected).

In general, when we talk about an option having a specific volatility:

A stock trades with a 25 volatility. Translation:

Approximately 68% of the time, after one year, the stock price will be within ± 25% of unchanged.

After one year, the stock price will be within 50% of unchanged, about 95% of the time.

Because the data comes from price changes in the past, this number is referred to as the stock's . When traders use this number to estimate the future volatility of the stock, they understand that the future probably will not repeat the past. However, unless there is some special situation, that historical volatility gives us a reasonable guess for the future volatility.

When we buy and sell options, their value in the marketplace depends heavily on that future volatility estimate. Why?

  • When someone buys an option, the plan is to profit when the stock price changes and moves in the correct direction (higher for calls and lower for puts). If the stock is not expected to be very volatile, then there is only a small chance that the stock price will change by any meaningful amount -- especially when the option expires in one or two months. Such options carry a low premium (market price). 
  • When someone sells an option, the plan is to profit when the stock price fails to change by very much.

Consider the option seller. For this example, assume that the seller is not hedged and that the trade is a sale. The seller must be compensated for taking risk -- specifically that the stock price will change in the right direction for the option buyer.

For example, if XYZ is $68 per share and our naked seller writes one XYZ Oct 70 call option, the seller faces a financial loss when the stock runs through $70 and continues to move higher. The not-very-volatile stock is unlikely to reach $70 and very unlikely to get very much above $70 in a short time. Thus, the call seller does not demand a high premium when selling the call option.

Now contrast this with a scenario in which XYZ is a volatile stock and it is fairly common for the price to change by $2 on any given day. The option buyer knows there is a very good chance that the stock will move above $70 per share -- perhaps it may happen in a day or two. And if it can move $2 in one day, there is a good possibility that the stock may move past $80 or even $90 in the next month or two. That makes the option far more valuable and the trader who wants to own that option is willing to pay a significantly higher price. 

And the seller? He/she knows that it is very possible to see the option become worthless if the stock price declines pretty quickly (large downside move). However, trouble looms if the stock price begins to rally. This volatile stock may move much higher very soon and I hpoe it is obvious that there is a lot of money at risk when selling this option.

Thus, the seller demands a premium commensurate with that risk. NOTE: Selling unhedged (naked) call options is considered to be a very risky proposition because the potential loss is infinite. For that reason, most brokers allow only their most experienced traders to adopt that strategy. I urge you to avoid the sale of naked options. The sole exception occurs when you sell naked puts and want to buy the underlying stock at the strike price. 


Example: Volatility affects option price

Stock Price = $68.00
Time to expiration 90 days
Call option; strike price = 70

Volatility Estimate:   20           30           40           60           80
Value of Call:         $1.86      $3.19     $4.53      $7.23     $9.91

As you can see from a single example, as the stock becomes more volatile (or is expected to become more volatile) the theoretical value of an option increases significantly. Remember that stocks move down as well as up, so that both puts and calls increase in value as the underlying stock becomes more volatile.

The calculations were made using a free calculator available at the CBOE website.

Takeaway: New option traders must learn not to judge whether options seem to be expensive or cheap based only on the premium. The value of any option is very dependent on the nature (volatility) of the underlying stock.