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An Introduction to Volatility in Trading Stock Options

Filed Under Beginner Options Trading 

An Introduction to Volatility
 
 
In Chapter Two, we talked briefly about volatility and how it affects an option’s price. It was there we found out that the uncertainty of stock prices – the volatility – is what gives an option its value. The higher the volatility of the stock, the higher the option’s price. However, the definition alone is not enough to trade options successfully. New and experienced traders must understand the role it plays in determining the fair value of the option as well as how it is possible to lose with options even though the underlying stock moves in their favor.
 
 
The Frog and the Roo
To understand the role of volatility and option prices, imagine that you are at a carnival with a very unusual game – a frog jumping game. A frog starts in the middle of a floor and can only jump left or right. The frog moves randomly, jumping right or left with equal probability. At the end of one minute, the frog’s final destination is marked and you are paid $1 for every foot the frog is to the right of the starting point. If the frog happens to land anywhere to the left of the starting point, you win nothing:

frog

How much would you pay to play this game? There is no right or wrong answer but think about it for a moment and pick a number that you think sounds reasonable. Now let’s change the mechanics of the game a bit. Imagine there is another game that is played with the same set of rules except this one uses a kangaroo:

Roo


How much would you pay to play this game now? As before, there is no right or wrong answer but think again for a moment and come up with your best estimate as to what this game is worth to you. It should be obvious that no matter which price you chose for the frog you should be willing to pay a higher price to have it replaced by a kangaroo. Why? Because the kangaroo has the ability to jump further, and that means you could win far more money, so the game is worth more to you. Notice that while both games offer potentially different rewards, neither has a mirror-image downside risk. In other words, you do not lose one dollar for every foot to the left of the starting point — once you place your bet that’s the most you can lose. So the only thing that matters to you is the upside potential. The game with the most upside is the one that is worth the most. It is the asymmetrical payoffs of these games that makes the kangaroo game more valuable.
 
In order to understand how volatility affects options prices, just replace the frog and kangaroo with at-the-money calls on two different stocks. One stock hardly moves like a big blue-chip stock such as General Electric (GE). The other bounces all over the board like Google (GOOG). Which call is more valuable to you? It’s the one that has the highest ability to move; in other words, it is the stock with the highest volatility. If you own a call option, you’re not as concerned with the downside risk as you are when holding a stock. If you own a stock, you can make dollar-for-dollar on the upside but also lose dollar-for-dollar on the downside. Put-call parity showed us that when you buy a call option, you are doing the same thing as someone who buys stock and buys a put option. In other words, call options provide downside protection so we are not concerned with the downside in the same way as when you own stock. Likewise, if you own a put option, you are doing the same thing as someone who shorts stock and also buys a call to protect them from the upside risk. Therefore, when you own an option, your maximum loss is limited. What determines the value of the call (or put) is the likeliness for the stock to make large moves – the volatility.
 
We can mathematically measure the volatility of a stock. The calculation is quite easy, although tedious, but is not really necessary to understand for our purposes. Just be aware that we can measure how far a stock price typically moves from its average. Volatility is typically measured in percents; the bigger the percentage, the more volatile the stock. A high-volatility stock is one that exhibits large price swings throughout the day or over time. Conversely, low-volatility stocks are those whose prices do not move much. The volatility range is not limited to 0 and 100 like many might suspect when dealing in percentages. Most stocks will probably fall in the 15% to 30% categories while 50% and higher would probably constitute a relatively-high-volatility stock. However, ranges can extend into the thousands during unusual circumstances.
 
One of the exercises in Chapter Two asked you to look up at-the-money quotes for Google and McDonald’s and see which is more expensive and then asked why. If you did that exercise, you found that the options on Google were far more expensive than for McDonald’s. From the brief discussion on volatility in that chapter, you should have realized that Google options are more expensive because the stock is more volatile. Now let’s see if we can gain a better understanding of what we meant. Take a look at Figure 6-1, which shows historic price charts for Google and McDonald’s over the same six-month time frame:
 
Figure 6-1

Figure 6-1

Think of the pictures as roller coasters. You can see the Google is a much “wilder ride” since there are bigger drops between the peaks and valleys. McDonald’s, on the other hand, had a relatively steady climb and doesn’t exhibit price swings like Google. Another way we can tell that Google is more volatile than McDonald’s over this time period is by the heights of the individual bars. The heights of those bars are determined by the high and low stock prices during the day. It is evident that the bars are much taller for Google than for McDonald’s, on average, and that means Google had much larger price swings during the day. So whether you look at the charts intraday or across time, Google had bigger price fluctuations than McDonald’s and that means we’d expect it to have a higher volatility number. Granted, these two charts are on different scales but they still give a good visual representation of the concept of volatility. If we were to look up actual volatility numbers during this time frame, we’d find that Google had 40% volatility while McDonald’s had 20%, which confirms what we just visually interpreted.
 
It’s important to understand that high volatility does not necessarily mean better performance. Higher volatility just means that there are larger price fluctuations over the time period; it says nothing about the performance of the stock. In fact, in Figure 6-1, you can see that Google had a low around $360 and a high of about $490 over the time period, or a 36% increase. McDonald’s had a low and high of $34 and $45 respectively, or 32%. So the performances are similar even though the volatilities are vastly different. The higher volatility for Google just means that the movements across the chart exhibited bigger “jumps” than were realized for McDonald’s.
 
In the same way, the kangaroo game is more volatile than the frog game. This simply means that the sizes of the jumps are much bigger for the kangaroo so there is more potential for upside gains. But this doesn’t necessarily mean that the kangaroo will always win. It is certainly possible for the frog to win. High volatility just means there are bigger fluctuations during the day and across time; it says nothing about performance.
 
 
A Simple Pricing Model
The size of the jumps – the volatility – in a stock’s price is the key to determining what an option is worth. In order to gain a better understanding of how volatility affects an options price, let’s make a very simple model and assume that a stock is trading for $50 and that it can only rise or fall by $5 at expiration with equal probability. (To make the calculations simple, we’ll assume there is no cost of carry; that is, interest rates are zero.)
 
This means that only two final prices are possible, $45 and $55. What is the $50 call option worth? We can figure that out intuitively. Half the time it will be worth $5 (the call has $5 intrinsic value) when the stock ends at $55, and half the time it would be worth nothing when it ends at $45 (the $50 call expires worthless).
 
Now let’s consider some prices to pay for the call. If you pay $5 for the $50 call then half the time you’ll break even and half the time you’ll lose $5. This means you can’t win but could certainly lose, so $5 is too much to pay for the call. What if you paid $1? In this case, you’d make a $4 profit half the time and lose $1 half the time, which means you’ll make money for sure over the long run. This price is certainly a good deal for you, but that also means you’ll likely get outbid by another trader so it will be too low a price in an actual market.
 
 

To be continued…..

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