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Volatility, the Most Important Variable in the Model When Trading Stock Options

Filed Under Beginner Options Trading 

The only variable we’re not sure of is volatility and that’s why it’s the most important variable in the model. If it’s an unknown variable, then how did we look up volatility numbers for Google and McDonald’s earlier? When we looked those numbers up they were historic numbers; they had already occurred in the past. When the Black-Scholes Model asks for volatility, it really needs to know the future volatility of the stock and not the historic volatility.
 
To understand why, go back to our two-price stock model where the stock could move up or down $5. If this is how the stock has behaved in the past then we would value the $50 call at $2.50. However, suppose we have reason to believe the stock will now move up or down $10 in the future. Now the $50 call is worth $5 and not $2.50. It’s the future volatility of the stock that determines the price of an option and, unfortunately, that is something we will not know until expiration.
 
In order to truly know the value of an option we must know the future volatility of the underlying stock. And that is something that can never be known for sure until expiration.
 
 
Using the Black-Scholes Model
Let’s take a look at how to use a Black-Scholes Model. There are many available online, but one of the best can be found at the CBOEs website www.cboe.com:
 
Figure 6-5: The Black-Scholes Option Pricing Model (Calculator)

Figure 6-5

Let’s assume we are looking at a stock trading for $50. We’d simply type “50” in the “Price” field on the left side of the calculator. If we wish to evaluate a $50 strike, we’d type 50 into the “Strike” field. We’ll also assume that there are 365 days to expiration and that interest rates are 2%, which we type into their respective fields. Last, we’re going to assume that the future volatility of the stock will be 17.62% over the course of the year (you’ll find out why this specific number was chosen shortly). What is the $50 call worth under these assumptions? All you have to do is click the “calculate” button in the middle of the screen and the call and put prices show up on the right by the “Option Value” field (circled).
 
It’s showing us the call should be $3.99 and the put should be worth $3. The reason 17.62% was chosen as the volatility is because that’s the volatility that makes the put worth exactly $3, which fits an example we worked by hand in Chapter Five. If you recall in that chapter, we were trying to figure out what a market maker should charge for a one-year, $50 call with the stock at $50. We also assumed he paid $3 for the put and interest rates were 2%. From put-call parity, we calculated that the market maker should charge $3.98 for the call, and the Black-Scholes Model in Figure 6-2 is coming up with $3.99. So we’re off by a penny, but that is due to differences in the interest compounding assumptions and number of days assumed in a year.
 
Although the Black-Scholes Model makes use of some very complex mathematics, the essence behind the calculations is similar to what we worked through when trying to figure out how much the market maker should charge for a call option.
 
Why do you suppose the call in Figure 6-5 is roughly $1 higher than the put? Hopefully you remember from put-call parity that it’s due to the cost-of-carry on the stock. If interest rates are 2%, it will cost $50 * .02 = $1 in lost interest to buy and hold the stock for one year. In other words, if you pay $50 for stock and hold it for a year, you could have had $51 at the end of the year if you had left the money in a risk-free account instead. So there is a $1 cost of carry on a $50 stock over a year if interest rates are 2%. That’s why the call is priced $1 higher than the put. The Black-Scholes Model is a complex form of put-call parity with volatility as the key ingredient.
 
 
Why You Need to Understand Volatility
This chapter is by no means meant to be a comprehensive lesson on volatility. However, most beginning option books do not even mention it, and that’s a huge disservice to new traders and investors. If you don’t understand the role of volatility, you can end up with unpleasant surprises as we will now demonstrate.
 
Many option traders believe option trading is a relatively easy task and that you buy calls when you think the stock is going up and buy puts when you think it’s going to fall. After all, that’s all that’s needed to trade stocks. When most traders make the switch to options, they apply this same directional procedure to the options market. However, this approach ignores the time value of calls and puts in terms of volatility and unexpected, almost paradoxical, losses can occur as the following real-life example shows.
 
On September 16, 2004, Atherogenix (AGIX) was trading for $18.81 as shown by the quotes in Figure 6-6. At the time, there was tremendous bullish news on the stock regarding a new heart medication. Most option traders who were bullish might have been tempted to buy the $20 call since it was the next-highest strike from the (then) current stock price. Figure 6-6 shows the $20 call (circled) would cost $4.80, or $480 per contract.
 
Figure 6-6: AGIX Option Quotes

Figure 6-6

On September 22, just six days later, the stock had risen significantly from $18.81 to $21.18, which is a 12.5% gain in a short time. It certainly sounds like it should have left the trader with a nice profit on the leveraged $20 call, but Figure 6-7 shows that is not what happened. The $20 call was bidding only $4.70, which left the trader with a 10-cent loss for being correct on the direction of the stock!
 
Figure 6-7: AGIX Option Quotes (Six Days Later)

Figure 6-7

Direction Versus Speed
What happened? How did this call option lose money even though the stock’s price went up? Loosely speaking, the reason is because options are two-dimensional assets. That is, option traders must not only guess the direction of the stock correctly but they must also guess how quickly the stock’s price will get there – the speed.
 
Stock traders, on the other hand, only need to correctly guess the direction; they are dealing with a one-dimensional asset. It doesn’t matter how long it takes for the stock to move, just as long as it moves in the right direction.
 
As an analogy, you car moves in one dimension – horizontally. An airplane, on the other hand, can move in two-dimensions – horizontally and vertically. It is this second dimension that makes flying an airplane so much more difficult than driving a car. Just because you may have driven a car accident-free for 20 years does not mean you should just jump into an airplane and start flying. There is a second dimension you’re not used to dealing with. Likewise, just because you may have been trading stocks successfully for 20 years does not mean you should just jump into the options market and start trading options based on direction. That’s an equally bad idea.
 
In this example, the $20 call option trader got the stock direction right but not the speed; it took too long for the stock to get there. If the stock had moved to $21.18 in a shorter time, say a day or two (rather than six), the $20 call would certainly have made money. It is this second dimension of speed that makes options trading so much more difficult than stock trading. Notice that a stock trader would have made money by purchasing the stock for $18.81 and selling at $21.18. The speed at which the stock rises doesn’t matter. So while both traders guessed the stock direction correctly, only the stock trader made money.
 
This example shows that call options are not necessarily a direct substitute for stock. If you think a stock is moving higher, you cannot just buy a call in place of the stock and expect to make money if you are correct. Yet most option traders mistakenly apply this one-dimensional stock trading technique to options and, consequently, end up losing money. What is responsible for this speed component? It’s the time premium of the option. If the time premium is relatively high, then the breakeven price is pushed too high and the option may lose money even though the underlying stock moves favorably. In order to prevent that from happening, option traders must learn to separate the price of an option from the value.
 
 
To be continued…..

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