How Volatility Effects Option Pricing

By: Jon Najarian

The following is an excerpt from Jon Najarian's Dr. J's Little Black Book

The most basic way to price an option is to start with a strike price.  If IBM is trading, for example, at $90 a share, and you decide to buy a call – or in Wall Street parlance, to go long a call – at the $95 strike price, you are buying the right, but not the obligation to own IBM for $95 a share until that option’s expiration.  Now, take that $95 and multiply it times the interest rate that you would have to pay if you borrowed money from the bank, say 8 percent.  If you’re not borrowing the money, multiply the strike price times the interest rate you would get paid if you put your capital in a certificate of deposit (CD) today, say 1.8 percent.

For the sake of illustration, let’s pick an interest rate of 8 percent to borrow money to buy the $95 call: $95 x 0.08 = $7.60.

Now, multiply that by the number of days for the life of the option, such as 30 days for a one-month option: $7.60 x 30 = $228.00.

Then divide that by 360, for the approximate number of days in the year (you could use the exact 365, but nobody on Wall Street does): $228.00 / 360 = $.063.

This would give you the value for that $95 call, assuming there were no volatility considerations.

But that’s like computing the value of a piece of property based on square footage alone – and not taking location into account, like 500 square feet of land in a remote part of Utah versus 500 square feet in Central Park.

As market makers, professional traders, and sophisticated retail investors know, the biggest component in the price of an option is volatility.  In the simplest of terms, volatility is a measure of risk.  The more volatile something is, the greater the risk.  Put another way, if the price of something is bouncing around like crazy – up one day and down the next – there is greater risk that you could be caught short or long with the price moving against you.  The volatility increases your risk.

At the same time, volatility is an estimate of what the expected range is for whatever stock or commodity you’re trading.  Again, if a stock has some pretty wild gyrations in price, such as eBay or Google, it has a relatively high volatility and its projected trading range will likely be wide.  By the same token, a stable stock with little change in price, such as a utility stock, would have low volatility and a comparatively narrower expected price range.

Here’s an analogy to illustrate the concept of volatility.  Everybody (particularly any parent) knows it costs more to insure a 16-year old boy who is driving the family car than for the 30-year old man who is married and is the father of two children.  Why?  Volatility!

The 30-year old man with a wife and two kids is less likely to engage in “volatile” behavior such as drag-racing with is friends, or drinking and driving to impress his girlfriend.  Thus, the range of expected events – in this case the chance of an auto accident – is far greater with the 16-year old boy than with the 30-year old father.  So what does the auto insurance company do?  It charges more to insure the 16-year old because the likelihood of an accident is greater, which would result in the insurance company having to pay for damages and/or injuries.

To bring our analogy back to the market, the 16-year old driver might be the equivalent of an Internet stock, the price of which is bouncing around in a volatile fashion.  The 30-year old station wagon driving Dad might be IBM.  IBM, with its far lower volatility, usually will trade in a narrower range than the high-flying Internet stock.

Based on the volatility, we can project how a stock is likely to trade in a day – say, with a price range of $3 a share.  That volatility won’t tell you the price at which the stock is likely to close.  But it will tell you where it’s likely to trade based on past price patterns and current volatility.

Using a bell curve model, you could predict that about 66 percent of the time, the stock would trade in a $3 range, 95 percent of the time in a $5 range, and 98.6 percent of the time in a $10 range.

For example, let’s say IBM stock is trading at $114, with normal weekly volatility around 40 percent.  Its bell curve points are likely to show, for example, a $13 range 66 percent of the time, a $25 range 95 percent of the time, and a $39 range 98.6 percent of the time.

But before earnings, IBM could reflect a weekly volatility of around 70 percent.  At that time, its bell curve points are likely to show, for example, a $22 range 66 percent of the time, a $45 range 95 percent of the time, and a $67 range 98.6 percent of the time.

With higher volatility there is a greater probability that a particular price point will be hit.  Think of the 16-year old driver… what is the chance that the volatility of youth will result in a fender-bender?

To buy an option on a volatile stock, you would have to pay a higher premium than for a less volatile issue.  Why?  Because the seller – like the insurance company offering coverage on a teenage driver – wants protection from the risk of an event.  In the case of an option, the seller wants to ensure that the premium paid will balance the risk involved in hedging the exposure the seller takes on should that option be exercised.

If the option is exercised, the seller may be obligated to sell the stock at a considerably lower price than the prevailing market (in the case of the seller shorting a call option), or buy the stock at a considerably higher price (as could be the situation faced by a put seller) than the prevailing market.