1. Options Greeks: Introduction
  2. Options Greeks: Options and Risk Parameters
  3. Options Greeks: Delta Risk and Reward
  4. Options Greeks: Vega Risk and Reward
  5. Options Greeks: Theta Risk and Reward
  6. Options Greeks: Gamma Risk and Reward
  7. Options Greeks: Position Greeks
  8. Options Greeks: Inter-Greeks Behavior
  9. Options Greeks: Conclusion

by John Summa (Contact Author | Biography)

Perhaps the most familiar Greek is Delta,which measures option sensitivity to a change in the price of the underlying. Delta is most likely the first risk parameter encountered by a trader of outright positions. When contemplating how far out-of-the-money to buy a put option, for example, a trader will want to know what the trade-off is between paying less for that option the farther it is out-of-the-money in exchange for lower Delta at these more distant strikes. The eye can easily scan the strike chain to see how the prices of the options change as you get either deeper out-of-the-money or deeper in-the-money, which is a proxy for measuring Delta.

As can be seen in Figure 2containing IBM options, the lower the price of the option, the lower its Delta. The left hand green shaded area shows the strikes (calls on top ranging from 130 to 90 strikes, and puts below ranging from 130 to 95). To the right of the green shaded area is a column containing option prices, which is beside a middle column showing the Deltas (125, 110 and 100 call strike Deltas are circled). Finally, the right-hand column in the white area is time premium on the options.

Figure 2: IBM Delta values across time and along strike chain as taken on Dec. 28, 2007. Months in the green-shaded area across top and strikes in green-shaded area along left side. The price of IBM when these values were taken was at 110.09 at close on Friday, Dec. 28, 2007.
Source: OptionVue 5 Options Analysis Software



Circled items in Figure 2 indicate Delta values for select IBM call strikes. For example, the first set of circled values (January call options) is 90.2 (100 call strike), 52.9 (110 call strike) and 2.27 (125 call strike). The highest Delta value is for the in-the-money 100 call and the lowest is for the far out-of-the-money 125 call. At the money is indicated with the small arrow to the right of the 110 call strike (green shaded area). Note that the Delta values rise as the strikes move from deep out of the money to deep in the money.

One interpretation of Delta used by traders is to read the value as a probability number - the chance of the option expiring in-the-money. For instance, the at-the-money 110 call with a Delta of 52.9 in this case suggests that the 110 call has a 52.9% probability of expiring in-the-money. Of course, underlying this interpretation is the assumption that prices follow a log-normal distribution (essentially daily price changes are merely a coin flip – heads up or tails down). Of course, in short- and even medium-term time frames, stocks or futures may have a significant trend to them, which would alter the 50-50 coin flip story.


Delta values on options strikes depend on two key factors – time remaining until expiration and strike price relative to the underlying. Looking again at Figure 2, it is possible to see the effect of time remaining on the options. Figure 2 provides Delta values for January, February, April and July options months. The yellow highlighted area is for the 110 call option strike across months, which is the at-the-money strike. As is clear from the Delta values along the yellow bar (i.e., all the at-the-money options), Delta increases slightly as the option acquires more time on it. For example, the 110 call option for January 2008 has a Delta of 52.9 while the July 2008 call option has a Delta value of 56.2.

These differences, however, are small compared to the differences in Deltas on options across these months that are deep in-the-money and deep out-of-the-money. The out-of-the-money 125 call options, for example, have a Delta range from 2.27 (January) to 29.4 (July). And the 100 in-the-money call options have Deltas ranging from 90.2 to 72.8 for the same months. Note that the in-the-money Deltas fall with greater time remaining while the out-of-the-money call options rise with more time remaining on them.




The put Deltas, meanwhile, are also shown in Figure 2 (but not highlighted) just below the calls. They all have negative signs since put Deltas are always negative (even though position Delta will depend on whether you buy or sell the puts). The same relationships between strikes and time remaining apply equally to the puts as they do to the calls, so there is no need to repeat the analysis for the puts on IBM. As for position Deltas, long puts have negative position Delta (i.e., short the market) and short puts positive position Delta (i.e., long the market).

Strategies Position Delta
Long Call Positive
Short Call Negative
Long Put Negative
Short Put Positive
Long Straddle Neutral
Short Straddle Neutral
Long Strangle Neutral
Short Strangle Neutral
Put Credit Spread Positive
Put Debit Spread Negative
Call Credit Spread Negative
Call Debit Spread Positive
Call Ratio Spread Negative
Put Ratio Spread Positive
Call Back Spread Positive
Put Back Spread Negative
Calendar Spread (Near) Neutral
Covered Call Write Negative
Covered Put Write Positive
Figure 3: Delta risk and common strategies for options. The position Deltas in this table represent standard strategy setups. Long and short straddles and strangles assume equal Delta valueson the strikes.


A summary of position Deltas for many popular strategies is seen in Figure 3. A few assumptions were made for several of the strategies to allow for easy categorization. For instance, the call and put ratio spreads assume that the spreads are out-of-the-money and have smaller Delta on the long leg compared with the position Delta on the short legs (i.e., 1 long leg and 2 short legs). Additionally, the calendar spread is at-the-money. And the straddles and strangles are constructed with Deltas on the puts and calls being the same.

Conclusion
The options Greek known as Delta is explained, providing a look at Deltas horizontally across time and vertically along strike chains for different months. The key differences in Deltas inside this matrix of strike prices are highlighted. Finally, position Deltas for popular strategies are presented in table format.

For more insight, see Going Beyond Simple Delta: Understanding Position Delta and Capturing Profits with Position-Delta Neutral Trading.
Options Greeks: Vega Risk and Reward

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