An iron condor trader asked for advice from a forum's members. He wanted to estimate where the price of the underlying would be when the delta of his sold option reached a certain level. For those new to the Greeks of options, delta can be positive or negative, and measures how much an option's value changes for each point change in the underlying.
That must be someone who adjusts as I do on my iron condor trades, I thought, clicking on the thread and reading through the answers. The questioner was seeking information specific to his trading platform, using that platform to estimate what the underlying's price might be when the deltas approached his adjustment level. Forum members chimed in with suggestions specific to his software but also with more general suggestions.
None, however, mentioned that he needed to factor in possible changes in volatility. I've covered this topic previously, but it's one that needs repeating. Volatility and delta are not independent of each other. Time impacts delta, too, but this questioner wanted to estimate the delta on a specific date, so it was price that was the variable, not time.
As James Bittman explained in his book, Trading Options as a Professional, the absolute value of the delta of any option tends to gravitate toward +0.50 as volatility rises (94-96). What that means is that, if one were trading a far out-of-the-money call with a delta less than +0.50 and volatility rose, that call's delta would move toward +0.50. If one were trading an in-the-money call with a delta above +0.50, that delta would move back toward +0.50. If one were trading an OTM put with a delta in the -0.25 range and volatility rose, that delta would drop toward -0.50, since Bittman was talking about the absolute value.
Bittman called this effect the "fifth rule on deltas." I like this rule because it's easy to remember. The absolute value of deltas rises toward +0.50 as volatility rises.
So, no computation, theoretical or otherwise, of delta can be complete without at least a nod toward the effect that volatility might have on the option. Let's look at some examples. Imagine that 57 days before option expiration and with the OEX at just above 502, an iron condor trader had sold an OEX call with a delta of 0.111 and a put with a delta of -0.107. Imagine that the iron condor trader's plan called for an adjustment when the sold call's delta reached +0.22 and the sold put's, -0.22. What would the OEX's value have to be fourteen days later, 43 days before expiration, in order for those levels to be reached?
Call Deltas Versus Price, 43 Days Before Expiration, Calculated Via OptionsOracle:
That price would be approximately 530.5 when delta would theoretically reach above +0.22 on the target date two weeks later, as long as implied volatility remained the same. But what happens to volatility when prices are rising, unless they're rising rapidly? Volatilities tend to decrease. Based on what we know about the interactions in delta and volatility, we can predict that the price at which the delta reaches +0.22 would actually be different than what was calculated above.
Call Deltas Versus Price, 43 Days Before Expiration, with Implied Volatilities Lowered 10 Percent:
With the IV lowered to 15.216, 10 percent lower, the OEX could reach slightly higher, to 531.95. In this case, the difference wouldn't be much, but it does show the effect of lowered volatilities if they drop as the underlying climbs, as often happens. The iron condor trader who adjusts based on delta would perhaps not have to adjust as quickly as it seemed in the first calculation.
The opposite effect would be seen when the OEX's price is dropping. Particularly if price is dropping quickly, implied volatilities will rise. A trader who is trying to calculate when the absolute value of a put's delta would be at 0.22 would need to factor in an increase in implied volatility. That delta would be reached quicker than expected if the trader forgot to factor rising volatility into theoretical calculations. For example, let's take the case of that put that initially had a delta of -0.107 when sold, at 57 days before expiration when the OEX was just over 502. If implied volatility stayed steady, an unlikely event, that put's delta would not reach a level below -0.22 two weeks later unless the OEX started dropping below 466.60. If the IV kicked up 10 percent while the OEX dropped, however, that -0.22 level would be hit almost 4 points sooner, at about 470.50.
This effect becomes important when making many decisions about options trades. For example, when I enter iron condor trades, I often buy put insurance. These days, I often buy an extra put for each 10-15 RUT iron condor contracts, buying that extra put about 20 points below the long put in the bull put credit spread portion of the trade.
I never buy call insurance, however. Why? If volatility decreases as prices rise toward my sold strike, that further out-of-the-money call insurance I bought might not be providing as much insurance value as it seemed on initial profit/loss charts on OptionsOracle or TOS or BX or other profit/loss charts. The delta is likely being impacted by a possible drop in volatility, so it won't be doing as much delta hedging as I might have hoped. The call insurance's value would also be eroded by the passage of time, of course, so two factors would make it less valuable as insurance than it initially seemed to be. As volatility drops, a long call I bought will become less of a hedge than it was at the time the trade was initiated. If I hedge on the upside, I hedge only on an as-needed basis when deltas are getting too high in the sold call, and I do it with calls one month further out than the ones in the iron condor. I'm not saying that this is the only way to look at buying insurance, as I do know of iron condor traders who buy initial call insurance, but this is the reason I don't. I almost always buy put insurance and never do buy the call insurance.
Of course, profits and losses are impacted by changing volatilities and their impact on deltas, too. If you've got a trade, and you're trying to figure out theoretical profits or losses on a certain day at a certain price point, be sure to lower volatilities a bit if that price point is considerably higher than the current price and raise volatilities a bit if that price point is considerably lower than the current price. How much is "a little bit"? That's more of an art form than a science. Look at the range of implied volatilities for your underlying over at least a three-month period and try to estimate where volatilities might go if prices rise or drop by a considerable amount.
Where do you find the implied volatilities for the past three months or six months or year? I use a primary brokerage for most of my trades and a secondary one for some small trades, and both chart these values. Your brokerage probably does, too. The CBOE offers, as one of its services, an "all-new free service [that] provides basic end-of-day information on a specified underlying--such as last value of IV index." Using the service may require registration with the CBOE, but that's free, too.