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The Least You Should Know about Option Pricing

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For the last several articles, I've discussed "the least you should know" before trading options. Now it's time to delve into the Greeks of options. Don't worry that the article will be too technical, however. We're not going to delve too far into the Greeks.

Knowing something about the Greeks of options might have helped a trader who contacted me recently. This trader had gone long (bought) an SPX put. That put was so far out of the money that the trade had little chance of profiting even if the SPX did drop. One look at the Greeks would have explained why, if the trader had only understood them.

The trader contacted me soon after the SPX had begun moving down from a recent high, puzzled because the put's price had not changed. The answer to the trader's puzzlement lay in one of the Greeks, the delta.

Stated a bit simplistically, the delta of an option describes how much the option could be expected to move with the movement of the underlying. Another way of looking at the delta is to consider it the chance that the option will expire in the money.

For the benefit of newbies, an in-the-money condition occurs when the underlying has moved above the strike price of the option if it's a call and below the strike price if it's a put. For example, if the SPX is at 1402 and a call has a strike price of 1400, it is two points in the money. If a put has a strike price of 1400 and the SPX is at 1402, the put would be out-of-the-money. If 1402 was the SPX's settlement price obtained the Friday of opex week, the call would have been worth $2.00 x 100 (multiplier) = $200.00, but the put would have expired worthless.

The delta of this subscriber's put was -0.07. That meant that the option never had much chance of going into the money. If the delta of an option can be considered to be the chance that the option would expire in the money, that option had only a 7 percent chance of expiring in the money. The converse of that is that it had a 93 percent chance of expiring out of the money.

There was worse news for the trader who had hoped to benefit from a short-term move in the SPX. For every point the SPX dropped, the option's price could be expected to gain only about $0.07 (-$1.00 change in the SPX's price x -0.07).

Options traders should be aware that delta doesn't stay the same as the underlying's price changes. As the underlying moves closer to the strike price, the absolute value of the delta increases. As the underlying moves farther away from the strike price, the absolute value of the delta decreases. So, if the SPX had been moving closer to the put's strike price, the delta's value might have changed from -0.07 to -0.09, for example. It then might have moved about $0.09 for every point the SPX dropped. However, without the world coming to an end and the SPX suddenly crashing, the delta of that put was unlikely to change too much.

Even if delta does change with the price action, the delta at the time an option is purchased provides traders with a fairly good estimate of how much the price might change if the SPX were to move to the trader's targeted price. That's important to know. If traders are buying a call with the thought that the SPX might be about to move up, and they expect the move to be under five points, that call better have a fairly high delta at the time it's purchased. When I was still trading intraday moves and hadn't switched to spreads, I liked a delta around 0.70, at least, for such short-term moves.

The SPX had dropped three points since the subscriber had bought the option, but the $0.21 gain that the delta predicted wasn't big enough to span the SPX's rather wide bid/ask spread and make the selling of the option profitable. The option was just too far out of the money to benefit by a small movement in the SPX without other forces, such as a big swing in the volatility, helping it along. That wasn't happening that day, as the VIX stayed low.

If the subscriber had instead bought an option with a delta of about -0.70, a three-point drop in the SPX's price might have raised the options price by about $2.10, give or take a little since the delta would have been changing slightly as the price dropped. If the subscriber had been adept at getting between the bid and the ask, that should have been enough to make selling that option profitable after the three-point drop. If the trader who had written me had understood this basic fact about options' Greeks, a different put might have been chosen.

Let's backtrack now and talk a little about the other Greeks. Greeks are the various risk measurements for options. Delta, gamma, vega or tau, theta, and rho comprise the various Greeks for options. While it's probably wise for all options traders to review the Greeks and obtain a basic working knowledge of what each represents, traders don't have to contemplate all this information each time an option is traded unless they're employing advanced strategies. To trade profitably, however, traders do need to understand roughly how the delta works.

Why was that delta negative in the example provided? The great Lawrence G. McMillan summarizes delta by saying that it measures "how much current exposure" an option trader's "option position has as the underlying security moves." Delta is considered positive for calls, which means that when the price of the underlying such as the SPX moves higher, the price of the call would, too. Delta is considered negative for puts, which means that as the price of the underlying moves higher, the price of the put moves down, moving opposite to the price of the underlying. When price drops, that negative delta is multiplied by a negative price change and the result is a gain in the put's price.

Delta ranges in value from 0.0 to 1.0 for calls and -1.0 to 0.0 for puts. That far out-of-the-money SPX put that the subscriber had bought had a delta of -0.07, a teeny delta. Options that are far out of the money have small deltas. Options that are at the money, so that the underlying is trading near the strike price of the option, have deltas near 0.50 or -0.50, in the case of a put. Options that are deep in the money have deltas that are closer to 1.0 or -1.0, in the case of a put.

For example, on November 2, with the SPX trading at 1366.31 shortly after noon, a November 1365 put would have been slightly out of the money. The delta of the November 1365 put was -0.44, as shown on the chart below, found at the CBOE site.

Price and Greeks Information for SXYWM, the SPX Nov 1365 Put:

Most online brokerages that cater to options traders will provide their customers with information about each option, including the delta of that option. For those who need another source, the CBOE's quotes provide it, too, as seen above. It's free from CBOE, although delayed. Even the delayed information will give you a fairly good idea of the current delta unless prices are moving quickly, and traders can sign up for a paid version that provides real-time quotes. Still, delayed is better than none if it's going to save traders from buying a put with a delta of -0.07. Obviously, deep-in-the-money options are more expensive, so options traders always balance the leverage that cheaper out-of-the-money options provide them against the propensity for more expensive in-the-money options to move more in lockstep with the underlying's price movement.

All kinds of strategies revolve around the delta of an option, including the delta-neutral combination plays that some advanced options traders employ. Traders who are interested in such strategies might consult a more advanced text or even the CBOE site. The purpose of this article is not to delve into such advanced tactics, but rather to suggest that traders need to know the basics of delta as they choose the option they'll buy.
 

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