Greeks: Inter-Greeks

The key assumption that we’ve made up until this point is that everything has remained constant except for the Greek that we were analyzing. Of course, this never happens in reality and its tremendously important to understand how the Greeks interact with each other.

Example: Change in Delta

Let’s take a look at an example that shows the change in Delta given a simulated decline in implied volatility. When implied volatility falls, the extrinsic value of an option falls, since there’s less of a chance of reaching a strike price. High extrinsic values equate to more Vega exposure when they begin to fall, since Vega measures the decay of that value over a set period of time.

Change Implied Volatility Levels At-the-Money Call Option Strike Delta Out-of-the-Money Call Option Strike Delta
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

The key takeaway from this table is that Delta values decline as implied volatility falls, while the fall in Delta is the highest for at- and out-of-the-money calls, assuming no time value decay.

Changing a Variable: Add Time Value Decay

Next, let’s add in eight days in time value decay to see how it further affects these prices.

Change Implied Volatility Levels At-the-Money Call Option Strike Delta Out-of-the-Money Call Option Strike Delta
0 57.75 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

The impact of a -2 change in implied volatility can be seen when looking at the out-of-the-money call option Delta that moved from 38.05 to 35.80 in the first table, but that decline was exacerbated after eight days where the Delta moved down to 31.14. Additional declines in implied volatility with time decay will eventually reduce the Delta even lower – especially for at- and out-of-the-money calls like these.

While the Delta of the at-the-money call options is greater, the Delta decay rate due to falling implied volatility is much lower with at-the-money calls than out-of-the-money calls (see chart below). Since the at-the-money option has more time premium, there’s always more directional risk should the market move the wrong way, which is a difficult trade-off for option buyers. (See: The Importance of Time Value).

The Bottom Line

The interplay of Greeks can be very complicated in practice, but understanding how each Greek functions can help make sense of the situation. In the example above, we looked at how at-the-money and out-of-the-money call options’ Delta values change based on implied volatility and time decay. We also demonstrated that, while more capital is at risk with at-the-money call options, it does not experience the corrosive effects of falling implied volatility and passage of time that out-of-the-money goes options experience. These are the kinds of trade-offs that options traders must learn to understand and navigate to be successful.

 


Go to Part 9 – Conclusion