One of the biggest mistakes new options traders make is buying a call option in order to try and pick a winner. After all, buying calls maps to the pattern you're used to following as an equity trader: buy low, sell high, in that order.

Options are trickier. Sometimes the underlying stock moves in the expected direction, but the option doesn't, or even vice versa. Options with different strikes move differently when the underlying price moves up and down, and also as the option approaches expiration. Is there any mathematical way to estimate how much your option might move as the underlying moves?

The answer is delta _ it provides part of the reason for how and why an option's price moves the way it does. There are many different definitions of delta, but the explanation that follows is the primary one.Delta is the amount a theoretical option's price will change for a corresponding one-unit (point/dollar) change in the price of the underlying security _ assuming, of course, all other variables are unchanged.

Keep in mind that delta is determined by using a pricing model, hence the term theoretical in the definition above. So although this is how the marketplace expects the option's price to change, there is no guarantee that this forecast will be correct.

Imagine a stock is at $40 and we're looking at the two-month, at-the-money (ATM) call with a strike price of 40 and a current price of $3. If the stock goes from $40 to $41 right now, so the only thing that changes is the stock's price, how much would you expect the call option's price to move?

The call price should increase by about 50 cents, to $3.50. How do you know? One way would be to look up the option's delta, +0.50, which you can find in the Options Chains under the Quotes + Research tab.Using the definition above, if the stock goes up $1, the call price should go up roughly by the amount of delta. Hence, it should go from $3.00 to about $3.50. This also works in reverse. If the stock went down by $1 instead, the call option should go down approximately by the amount of the delta, 0.50 or 50 cents, to a price of $2.50.

When looking up delta at Ally, you will notice that calls have a positive delta. One way to explain this is call prices tend to increase as the underlying increases. You may have also noticed that put deltas are negative. This is for a similar reason; puts typically increase in value as the stock decreases. These are the delta signs you'll get when buying these options. However, when selling these options, delta signs reverse. Short call options will have a negative delta; short put options will have a positive delta.

Delta is dynamic

What if the stock moves from $41 to $42? Would the call option move another 50 cents, or more or less?

The answer is more than 50 cents. That's because delta is dynamic: how close or how far away the stock is from the strike price determines how the option will react to stock price movement. Since movement from $41 to $42 would mean the call option was becoming more in-the-money (ITM), the delta will increase to reflect that. In this case, we estimate the delta to be about 0.60 or 60. Using the increased delta to calculate, the new price of the call option should be about $4.10 ($3.50 + $0.60).At-the-money (ATM) call options, like our first example, usually have a delta around 0.50 or 50. (By the way, traders will often remove the decimal and just say the delta is fifty.) In-the-Money (ITM) call options usually have deltas between 0.50 and 1.00 (or 50 and 100), and out-of-the-money (OTM) call options usually have deltas between 0.50 and 0 (or 50 and 0), obviously never going below zero.At-the-money put options have a delta around -0.50 or -50. Deltas of ITM puts typically range from -0.50 to -1.00 (-50 to -100). Put options that are OTM often have a delta ranging from 0 to -0.50 (0 to -50).

Using delta to predict price movement as expiration nears

Let's take a look at a different example:

Many first-time options buyers will gravitate toward the 133 strike call, because it's the cheapest. However, if you understand delta you'll see why it's so cheap.

It's cheap because its delta is only 0.05 _ that is, this call option wouldn't move much for a one-point move in the underlying. Why is its delta so low? Because the strike is so far away from the underlying price, the odds of the underlying finishing above $133 in 11 days are very small.

If you were lucky enough to get a one-point movement up tomorrow in this stock, delta suggests the option price should move only about five cents. In the real world, though, it might not move at all. Sure, it will move according to delta, but the option also lost one day of time value, as measured by a Greek called theta. When you factor in time decay, you'd be lucky if the option was still trading for 15 cents.

If a one- or two-point increase in the stock is expected before expiration, the 127 strike calls will most likely benefit you more than the cheap option (133 strike).

What's the moral of the story? It's crucial to understand how your option will move relative to the stock price. Without understanding delta, it's hard to know which option will reward you the most if your forecast for the underlying security is correct.

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