The experience level of our subscribers ranges from the newbie options trader to those who have studied Augen's work on volatility trading and could teach me a thing or two. For the benefit of the newer trader or the trader who isn't accustomed to paying attention to the Greeks of options pricing, it's time for a brief review. I'll try to scatter these articles among those meant for experienced traders. I'll start with a brief introduction to delta, in preparation for a more complex article that will appear next week.

Hopefully, these introductory articles will provide a glossary of sorts that helps interpret the discussion in the more advanced articles. I'll occasionally be drawing from James Bittman's Trading Options as Professional and my first purchase of an options-trading tome, Lawrence McMillan's Options as a Strategic Investment.

These articles are meant as an introduction only. Those wanting further information are encouraged to read those or other books on the Greeks of options pricing. Alternately, both the CBOE and the OIC's educational arm,, provide free basic online courses on options pricing.

Delta and theta are probably the most frequently watched Greeks and the first studied by new options traders who want to learn more about options pricing. Delta describes how the price of the option theoretically changes with price movement of the underlying. For example, a call with a delta of 74.68 (or 0.7468, if your quote service does not apply the 100 multiplier) will presumably rise $74.68 for each call contract purchased if the price of the underlying immediately moved one point. Commissions would of course have to be subtracted to determine the actual benefit. Deltas for calls range from near 0.00 up to 100, or 1.00, if your quote service doesn't apply the 100 multiplier. A deep-in-the-money call would have a delta nearer 100; an at-the-money call, near 50; and a far out-of-the-money one, nearer 0.00.

Profit-and-Loss Chart for a Call Option with a Delta of 74.68, OptionNet Explorer Chart:

The chart shows a current $2.00 loss. That's including a $1.00/contract commission cost to buy to open the trade and then sell to close it. Some brokerages charge more; some less.

In this case, delta is positive, at 74.68. Deltas can be positive or negative. Long call purchases have positive deltas. The option gains value when the underlying climbs, as long as other inputs into the pricing stay constant. The position loses when the underlying drops, as long as those other inputs stay constant.

Long put purchases have negative deltas. Those puts lose value if the price of the underlying climbs. They gain value if it drops. This holds true as long as the other inputs into option pricing remain constant.

However, notice at the far right-hand side of that chart that the curve steepens and its angle nearly aligns with the expiration chart's 45-degree angle? Also, see how the curve flattens to the left-hand side of the current price and then doesn't change much with a change in price? Those changes in the shape of the curve points out something else we should know about deltas. The delta you see when you buy an option holds true only over a short distance of price changes. Delta itself changes a little with each one-point move in price. The change is usually not appreciable over a few points, but it is noticeable over a large distance in price movement. A future article will describe how we can predict how much delta will change.

If price movement beyond a few points changes delta, what else might change delta? In the kind of constant interest rate environment that we've had over the last several years, the biggest additional factors that might change delta are the passage of time and a change in implied volatilities. Let's experiment with the chart first by rolling the date forward by five days into the future.

Same Call Option with Time Rolled Forward Five Days:

In the legend below the chart, the boxed section shows us that delta has risen from the original 74.68 to 76.69. The option will be slightly more sensitive to price movement than it was initially as long as other inputs also stayed the same. In this case, the difference isn't large. This is, however, because some of the extrinsic value has leaked out of that in-the-money call, and it's moving more in lockstep with the underlying.

What is the effect of a change in implied volatility? Some may first need an explanation of implied volatility. McMillan described it as a prediction of the volatility of the underlying stock, and notes that it is determined by using prices currently existing in the options market at the time, rather than using historical data on the prices changes of the underlying stock (971). Most brokerages and quote services will tell you the implied volatility of an option you're considering. Contact your brokerage's help desk if you can't figure out how to find it.

Same Call on Day Trade Initiated, with a Decrease in Implied Volatility:

I put the date back to the original date, because we want to isolate the effect of lowering the implied volatility. Delta has increased from the original 74.68 to 77.66, with the only change being a decrease in implied volatility.

It might be interesting to look at what happens to a put's delta when implied volatilities decrease. Remember that a long put's delta will be negative. I chose an available put with a delta that had an absolute value as near the call's 74.68 as possible, a put with a delta of -76.53. Now let's roll the implied volatilities down the same amount and see what happens.

Put with Original Delta of -76.53, with Implied Volatilities Rolled Lower:

The put's delta has changed from -76.63 to -80.58, with the only change being the decrease in implied volatility. It, too, is more sensitive to price movement than it was originally. In this case, the put's delta was lowered from a negative number to a more negative number.

About now, the newbie options trader may be wondering how to memorize the effect of changes in implied volatility on deltas. Bittman offers a handy way to predict the effect of changes in volatility on deltas without separately memorizing the effect on calls and puts. Deltas change toward +/- 0.50 when volatility increases and away from +/- 0.50 when volatility decreases (98), he says. In this case, Bittman's discussion does not include the 100 multiplier, so here's a translation with the substitutions made: Deltas change toward +/- 50.00 when volatility increases and away from +/- 50.00 when volatility decreases. Our call's delta moved away from +50.00 when volatility was rolled lower, and our put's delta moved away from -50 when volatility was lowered.

If you sell a call or put instead of buy it, the sign of the delta changes. A sold call would have a negative delta, for example. Complex positions such as butterflies or spreads may have positive or negative deltas, depending on how the position is constructed.

If you're not used to dealing with the Greeks of options, your head may be spinning by now. If your brokerage has that capability, put up simulated call, put and complex options positions. Roll the date forward and watch the effect on delta. Roll implied volatilities up and down and watch the effect. You'll get a better feel for how it works that way than in just reading these words. If your platform doesn't have this capability, you can try something like freeware OptionsOracle or the CBOE site. Bittman's book is a great reference book, replete with lots of charts, but it can be a bit dense. You have lots of options for learning about delta, pun intended.