by John Summa (
Contact Author |
Biography)
After looking at the concept of position Greeks in previous tutorial segments, here we will return to a look at some outright positions in order to reveal how Greeks interrelate, and how their interaction in options strategies can alter the prospects for profit and loss. One key area is highlighted here - how
Theta and
Delta relate and are impacted by changing levels of
implied volatility.
In previous segments the Greeks were largely inspected in isolation (the
ceteris paribus assumption). But if we relax the assumption of all other things remaining the same (
ceteris paribus), then a more complicated picture emerges in terms of the behavior of Greeks.
Take the example of position
Delta. Recall that at different strikes across time the
Delta rises with more time premium on the option. Taking a look at Figure 14, we can subject
Delta to a fall in implied volatility. Remember, when implied volatility falls, so will extrinsic value on those options. The higher the extrinsic value before the fall, the more risk there is in terms of
Vega exposure, so typically higher extrinsic value will mean higher
Vega values. Since options have negative
Vega because they lose value when implied volatility falls, the size of the loss can be measured by looking at
Vega on each option, or if a strategy uses a combination of options, by looking at the position
Vega.
Simulated Changes to IV Levels |
1360 At-the-Money Call Option Strike |
1410 Out-of-the-Money Call Option Strike |
| Delta Values w/ No Time Value Decay |
| 0 |
58.63 |
38.05 |
| -2 |
58.55 |
35.80 |
| -4 |
58.41 |
33.15 |
| -6 |
58.26 |
29.96 |
| -8 |
58.11 |
26.11 |
| -10 |
57.93 |
21.40 |
| Figure 14 : Delta values for S&P 500 futures February call options Deltas and associated changes in implied volatility (IV). S&P 500 futures price at 1361.60. As IV falls, Delta values decline. But the fall in Delta is higher for the at- and out-of-the-money calls. Assumes no time value decay. |
Figure 14 provides a look at
Deltas assuming no
time value decay. The 1410 out-of-the-money call strike
Delta (right-hand column) suffers a significant decline with falling IV (left hand column). This decline is exacerbated when the 8 days have elapsed, as seen in Figure 15. For instance, with no implied volatility changes and no time value decay, the
Delta is 38.05, as seen in Figure 14. But with a fall in implied volatility by 4 points (-4) and passage of 8 calendar days, the
Delta declines to 28.25, as seen in Figure 15, making any long position a more unlikely winner and a short position a more likely winner. Additional declines in implied volatility and time value decay will eventually reduce
Delta to single digits as seen, for instance, in Figure 16. Here, with a -10 fall in IV at 17 days into the trade,
Delta has fallen to just 8.97.
Simulated Changes to IV Levels |
1360 At-the-Money Call Option Strike |
1410 Out-of-the-Money Call Option Strike |
| Delta Values w/ 8 Days in Time Value Decay |
| 0 |
57.57 |
33.60 |
| -2 |
57.45 |
31.14 |
| -4 |
57.32 |
28.25 |
| -6 |
57.18 |
24.84 |
| -8 |
57.04 |
20.82 |
| -10 |
56.87 |
16.13 |
| Figure 15: Delta values for S&P 500 futures February call options with 8 calendar days remaining until expiration and associated changes in implied volatility (IV). S&P 500 futures price at 1361.60. As IV falls, Delta values decline. But the fall in Delta is higher for the at- and out-of-the-money calls. |
Simulated Changes to IV Levels |
1360 At-the-Money Call Option Strike |
1410 Out–of-the-Money Call Option Strike |
| Delta Values w/ 17 Days in Time Value Decay |
| 0 |
56.26 |
26.44 |
| -2 |
56.16 |
23.69 |
| -4 |
56.00 |
20.57 |
| -6 |
55.92 |
17.03 |
| -8 |
55.80 |
13.11 |
| -10 |
55.60 |
8.97 |
| Figure 16: Delta values for S&P 500 futures February call options with 17 calendar days remaining until expiration and associated changes in implied volatility (IV). S&P 500 futures price at 1361.60. As IV falls, Delta values decline. But the fall in Delta is higher for the at- and out-of-the-money calls. |
Simulated Changes to IV Levels |
1360 At-the-Money Call Option Strike |
1410 Out-of-the-Money Call Option Strike |
| Delta Values w/ 25 Days Time Value Decay |
| 0 |
55.20 |
14.96 |
| -2 |
55.10 |
12.11 |
| -4 |
55.05 |
9.14 |
| -6 |
55.00 |
6.17 |
| -8 |
54.95 |
3.5 |
| -10 |
54.90 |
1.4 |
| Figure 17: Delta values for S&P 500 futures February call options with 33 calendar days remaining until expiration and associated changes in implied volatility (IV). S&P 500 futures price at 1361.60. As IV falls, Delta values decline. But the fall in Delta is higher for the at- and out-of-the-money calls. 42.50 is the price of the 1360 call and 18.90 is the price of the 1410 call. Clearly ultimately, more is at risk with the higher priced call (higher maximum potential loss). |
While the
Delta risk is greater for the 1360 call at all time intervals, the
Delta decay rate due to falling IV is much
lower with the closer-to-the-money (in this case slightly in-the-money) 1360 call options, as seen in Figures 14-17. The severity of the decline in
Delta on the 1410 call is revealed in Figures 18-2 and Tables 21-22. The at- to in-the-money 1360 maintains its
Delta values despite declines in IV and
time value. However, because the option has more time premium, there is always more directional risk should the market move the wrong way, a difficult trade-off, particularly for option buyers. (To learn more about time value, read
The Importance of Time Value.)
 |
| Figure 18: Delta values at different days remaining. Assumes no change in volatility levels. |
 |
| Figure 19: Delta values at different days remaining. Assumes -2% points change in volatility levels. |
 |
| Figure 20: Delta values at different days remaining. Assumes -6% points change in IV levels. |
| % Point Change in IV |
33 Days Left |
25 Days Left |
16 Days Left |
8 Days Left |
| 0 |
38.05 |
33.6 |
26.44 |
14.96 |
| -2 |
35.8 |
31.14 |
23.69 |
12.11 |
| -4 |
33.15 |
28.25 |
20.57 |
9.14 |
| -6 |
29.96 |
24.84 |
17.03 |
6.17 |
| -8 |
26.11 |
20.82 |
13.11 |
3.5 |
| -10 |
21.4 |
16.13 |
8.97 |
1.4 |
| Total Rate of Change in Delta |
-43.76 |
-51.99 |
-66.07 |
-90.64 |
| Figure 21: Delta values and total rates of decay of Delta for 1410 call options with changing levels of IV and decays remaining on the option. The highest rate of decline in Delta takes place on the option with eight days remaining, which suffers a 90.64% drop in Delta with a -10 fall in IV in terms of percentage points change. |
| % Point Change in IV |
33 Days Left |
25 Days Left |
16 Days Left |
8 Days Left |
| 0 |
58.63 |
57.57 |
56.26 |
55.2 |
| -2 |
58.55 |
57.45 |
56.16 |
55.1 |
| -4 |
58.41 |
57.32 |
56 |
55.05 |
| -6 |
58.26 |
57.18 |
55.92 |
55 |
| -8 |
58.11 |
57.04 |
55.8 |
54.95 |
| -10 |
57.93 |
56.87 |
55.6 |
54.9 |
| Total Rate of Change in Delta |
-1.1 |
-1.22 |
-1.17 |
-0.54 |
| Figure 21: Delta values and total rates of decay of Delta for 1360 call options with changing levels of IV and decays remaining on the option. The highest rate of decline in Delta takes place on the option with 33 days remaining, which suffers a 1.19% drop in Delta with a -10 fall in IV in terms of percentage points change. Contrast this with the out-of-the-money 1410 call, which suffers the smallest decline in Delta on the 33 -day intervals. However, the magnitudes are much greater: a 43.76% drop on the 1410 call versus a 1.19% drop in Delta on the 1360 call. |
Conclusion
In this segment, at-the-money and out-of-the-money call options are used to contrast the impact on
Delta values resulting from changes to levels of implied volatility and time remaining on the options. It is demonstrated that while more potential dollar risk may reside on an at-the-money call option, it does not experience the corrosive effects of falling implied volatility and passage of time that an out-of-the-money call option does (a put option would similarly face the same conditions). While out-of-the-money options cost less (and therefore have much less maximum risk for a buyer), they display much larger
Delta decay risk.
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Next: Options Greeks: Conclusion »
by
John Summa, Ph.D., is the founder and president of
OptionsNerd.com LLC. He co-authored "
Options on Futures: New Trading Strategies and Options on Futures Workbook" (2001). He is also the author of "
Trading Against The Crowd: Profiting From Fear and Greed in Stock, Futures and Options Markets" (2004), which presents contrarian sentiment trading indicators and trading systems for stocks, futures and options.
Founded in 1998, OptionsNerd.com provides professional training and educational support to stock, options and futures traders. Summa is an economist, author, options trader and former professional skier, and he presents small-group, online and in-person training seminars.
