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# Number Sense/Option Sense

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In the past, I occasionally wrote for the educational market. "Number sense" was a term sometimes bandied about when I was writing for mathematics programs.

Today, let's develop a little number sense or perhaps option sense that will help make decisions about buying and selling options. The article is intended to encourage subscribers to develop an innate feeling for "if the underlying's price does this, the option's price will do that."

That innate sense is an important tool for traders to develop. Too many times, traders can doom a play by having the right idea and choosing the wrong option or the wrong time to sell that option.

We're going to perform some calculations on the option price calculator found on the left-hand sidebar on the www.ivolatility.com site. Click on "Basic Calculator" and you'll see the free version.

After you've agreed to ivolatility.com's terms, here's what you'll see:

Basic Calculator:

iVolatility.com has grouped the inputs for an option's price on the left-hand side. After the inputs are keyed in and "Calculate" is punched, the calculator churns out call and put values and the Greeks on the right-hand side. For the purposes of this article, we're going to be concerned with the price of the option only. We're getting a feel for where the option's price will go if the underlying's price changes in certain ways and over certain periods of time.

That agreement iVolatility.com makes you sign affirms that although the calculations are as accurate as possible, the calculator can't be counted upon to churn out the exact value for an option's price. I found that to be true when I ran through dozens of calculations when I was thinking about a hedging procedure I wanted to try on a spread play. The pricing wasn't what I anticipated when it came time to hedge.

However, the options calculator did provide some idea of where prices might be, and it's great for something else: getting a feel for how pricing changes as conditions change. That's the feeling, the sense, that I want subscribers to develop.

Let's try it. This article was first written on Friday, July 13, with the calculations below made at that time. Periodically, I'll update with some actual prices that I captured this week, so we'll see how the action and the anticipated prices matched.

Imagine that on Friday, July 13, 2007 of the week before option expiration, you bought an ATM SPX JUL call about 1:00 in the afternoon, anticipating an afternoon run higher. You spent 11.70 (estimated cost when splitting the bid/ask a conservative 70/30 in the favor of the seller) for a 1550 call with the SPX then at 1549.24.

That afternoon run occurred. Yippee! You were right. By 3:51 in the afternoon, the call you'd bought earlier was quoted at 13.10 bid and 13.90 ask. You should be able to sell it for at least \$13.30, collecting a handsome profit for your afternoon's work. That's conservative. You probably could have gotten more.

Should you take that profit Friday afternoon or should you hold that option into the next week? The SPX is on a run, you reason, but what if it settles into a typical pattern for the SPX and consolidates a few days before a brief dip to the 10-sma, only then initiating another strong rise?

On that Friday, the 10-sma was at 1526.34, but it was rising and you anticipated that it might have risen to about 1528 within two or three trading days. Would you be stopped before the next run higher, if the SPX indeed dipped to that 10-sma before surging higher again into the end of opex week?

I think we intuitively know the answer to that question, but let's use the calculator to make that determination. I first ran the calculation for Friday, July 13, to see if I came up with a figure near the 11.00 bid x 12.00 ask that the 1550 was quoted at about 1:00 that afternoon. I did that to determine an estimate for the volatility that would be used for all further calculations, just to keep everything but price and days to expiration steady. That's not a real-world happening, of course, because volatility will change as price does, but we don't know how it might change.

SPX JUL 1550 Call Price on 7/13/07

The figures may be somewhat difficult to read because of the newsletter's requirement that charts and tables are kept at a certain width, but I input the then-SPX price, the 6 days to expiration, and a volatility of 14.48. iVolatility.com input the 5.32 for me. I'll explain some of those inputs.

We all know that expiration for the SPX options is Saturday, July 21, but the options chains I consult actually figure it from the last day it trades, which would be Thursday, July 19. Those options chains showed 6 days to expiration on Friday, July 13, 2007.

When using a volatility rate of 14.48 percent, iVolatility.com's calculated call price of 11.78 was between the actual 11.00 bid and 12.00 ask of that option at 1:00 that Friday. It was close to the estimated 11.70 at which I thought a trader might be expected to get a fill. So, the inputs chosen worked well, and the 14.48 volatility figure appeared valid.

How did I get the figure for the volatility percentage? Easy. Sometimes I estimate until I come up with the known option price. If you don't have a clue as to where you'd start that estimation, iVolatility provides that information, too, in two different ways.

Notice the bold words "Implied Volatility" on the bottom right-hand side of that chart? You can fill in some of the parameters for the underlying and then put in a known price for an option, and iVolatility.com will return a volatility figure for you. You can then use that figure for further calculations with the same option.

Volatility Calculation:

This returns a volatility figure of 14.38, a little lower than the figure I ended up using. I'll explain why later, after I've introduced the second way that ivolatility.com helps you determine volatility figures. In addition to the calculation we just performed, you can find "Basic Options" on the left-hand sidebar on iVolatility.com's main page. Clicking on that brings up a page that provides all the information you would ever want to know about historical and implied volatility on near-term options. iVolatility calculates volatility figures as of the close of the previous day, as well as providing historical information about the SPX's options' volatility. As of the close on 7/12/07, ivolatility.com pegged the July 1550's volatility at 13.02 percent.

After I had found these two estimates, I ran the figures through the calculator again to verify. Both that figure and the calculated 14.38 delivered call prices that were too low when compared to the actual price I thought someone would pay for the option, so I edged the volatility higher by trial and error until I came up with a figure that delivered the right price for buying an option.

Update: It's important to note that this volatility we're using now returns a price that would be paid to buy an option and not one that you'd necessarily receive to sell one. That would typically be a bit lower than the figure the calculator will now be churning out. Using hindsight, I probably should have also figured out a volatility estimate that would produce a call price that approximated the one at which the option could be sold, but that's hindsight.

If you do not feel comfortable fiddling around with this number, iVolatility will input the closing value from the day before as the volatility percentage default. You'll still be able to see how an option moves.

Now we can use these same inputs to determine what might happen to that call price if the SPX trades sideways into Wednesday of opex week and dips down momentarily to test the 10-sma before another hoped-for strong climb on Thursday. (Update: this several days of consolidation and subsequent dip to the 10-sma on Wednesday is actually what did happen.) Would you be stopped that Wednesday if the SPX traded sideways then dipped to 1528?

Again, I think we know the answer to this question intuitively, but let's run the numbers. I'll input "1" for days to expiration because that's the number of days the option will still trade on Wednesday, July 18, as explained earlier.

Estimated SPX JUL 1550 Call Price on 7/18/07

Yikes! That's obviously not something you want to do, to let an \$11.70 option sink to \$0.14, the call price ivolatility.com calculated. We knew intuitively that we wouldn't want to hold on through that test without running this calculation, but it goes against human nature sometimes to sell at a loss on a Friday when a bounce and higher prices are anticipated by the end of the next week. If traders aren't practiced at running these calculations, at developing this intuitive feeling for what will happen with option prices over time and with certain movement of the underlying, those traders might translate "higher prices" into "higher option prices," not realizing what will happen in between.

To me, this holding on no matter what seems to have increased since the early 2000's, when the SEC changed the rules for active traders with accounts smaller than \$25,000. Those rules now limit the number of round-trip options trades to three a week, I believe, so if a trader has already bought and sold options twice that week, that trader may be averse to selling a call at a loss when a bounce is anticipated later.

Okay, so let's imagine on this Friday, July 13 that someone held on all the way through an imagined 10-sma test on Wednesday and then the anticipated bounce did occur from the 10-sma. (Update: The SPX did bounce from its 10-sma, although the 10-sma was higher by Wednesday than I had anticipated.) Imagine that bounce brought the SPX all the way from a test of the 10-sma on Wednesday morning up to 1556 by Thursday afternoon. (Update: the high Thursday was actually 1554.31.)

As you can guess, the calculator delivered a price of \$6.00 if the SPX closed at 1556 on Thursday of opex week, the last day it traded. This was the amount by which that 1550 strike would have been in the money. Someone who bought the option for \$11.70 on Friday, July 13 and held on when the SPX was just below 1550 would have lost a hefty amount, even though the SPX closed expiration week in this example more than six points higher than the point at which the call had been purchased and high enough that the option was in the money. (Update: Traders would have lost even more if they hadn't sold at the close on Thursday and had held on through Friday morning's settlement. The Friday-morning settlement figure for the SPX was 1553.69, so that the cash-settled JUL 1550 call would have delivered 3.69 into a trader's account for an option purchased for 11.70.)

I deliberately chose an easy example, one that worked intuitively, but I'm still often surprised by the number of traders who accurately predict what will happen in the markets but not with their option's price. That's why building up number sense by playing around with an option calculator can be so important.

Updating this example, by Wednesday, the 10-sma had risen to 1533.32, higher than I had anticipated. The SPX did exactly what I thought it might do (and warned it might do in my Thursday, July 12 Wrap). It consolidated sideways to sideways up for a few days and by Wednesday, the third day of consolidation, it dipped toward that 10-sma, achieving a low of 1533.67 that day. Having just moved to a new town a few days earlier, I was in and out of my study all day, so I didn't capture the option price at the exact test of the 10-sma. However, I did catch it at 12:22 EST, with the SPX at 1535.08, and the JUL 1550 call was 2.00 bid by 2.60 ask at that moment. Presumably, it was lower when the SPX dipped lower to that final 10-sma test. Although this 2.00 x 2.60 price was far higher than the calculated 0.15 price when I had estimated that the 10-sma might have risen only to 1528 by Wednesday, most traders still would have been stopped long before the decline of their 11.70 option to somewhere between the 2.00 bid and the 2.60 ask.

What if you predicted a different scenario on Friday, July 13 as this article was first roughed out? What if you thought the SPX was going to make a run toward 1560 Monday before dropping back and eventually hitting the 10-sma sometime during opex week? What if you bought that 1550 call at 1:00 EST Friday, July 13 and decided Friday near the close that you wanted to hold out for that anticipated 1560 test on Monday, hoping you could safely exit for even more profit than offered to you Friday near the close? How would the option price compare to Friday's closing price?

Estimated Price If the SPX Hits 1560 on Monday, July 16, Calculated on Friday, July 13:

Remember that we set up this calculator so that it's giving us the price at which we'd likely buy an option, not sell it. The person selling to close that 1550 call would likely receive less money, perhaps around \$14.20. Still, the holder of that option would likely profit if the SPX were to reach 1560 on Monday, as long as the volatility stayed the same. (Update: the SPX high on Monday was 1555.90, but I didn't capture the call price that day.)

What if volatility didn't stay the same? What if volatility had dropped as the SPX edged slowly higher all day Monday? What if it dropped to 13.00, certainly not impossible? The calculator returns a price of \$13.86, so that a profit could likely be found.

That's not too bad. It might be worth a try, you reason. But how certain are you that the SPX will climb to 1560 on Monday? What if the SPX doesn't climb on the subsequent Monday, but sinks just a few cents at the open, say back to 1552.00, sits there while the volatility declines to 13.00? What would your option be worth? You shouldn't lose too much by taking that chance, should you?

Depends on what you call "too much."

Estimated Price if the SPX Consolidates at 1552 on Monday, July 16, While Volatility Sinks to 13.00:

Yikes again! The option's price fell to \$8.71, and, the way we set it up, that's the price to buy the option. A seller would likely collect less, perhaps \$8.50 or so.

Do you want to risk a decline of \$3.20 (11.70 - 8.50) from the price you paid for the option and \$4.80 (13.30 - 8.70) from the price you could have received selling it Friday afternoon, just to potentially make \$2.50 (14.20 - 11.70) above your original purchase price if the SPX climbs to 1560? Some would, and some wouldn't. Unless traders develop some number sense about options, though, they might not know what they're risking.

The point is that running the numbers through the calculators gives you a feel for the way the options price might react under certain conditions. These prices might not be completely accurate, as iVolatility wants you to acknowledge before it allows you to even view the free calculator, but developing this kind of number sense can prove invaluable as you make decisions. I've seen too many people make too many wrong decisions just for lack of this kind of number sense.