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I got a request in a comment on a post I wrote last week about Apple (NASDAQ:AAPL) options to explain how "maximum pain" works, or at least how Optionistics calculates it.

Why, a commenter asked, would Optionistics put the so-called "maximum pain" point at 560? After all, the April open interest was highest at the 600 strike for calls and at the 550 strike for puts as you can see here:

Yet Optionistics had predicted a maximum pain "strike peg" of 560 with a strike price "bias" of 533. Clearly, you simply cannot look at open interest alone to determine these levels.

While I don't necessarily subscribe to the theory of maximum pain, I don't think I've seen it explained in a way that makes it intuitively easy to grasp. Even Optionistics' explanation tends to focus on "obligations" to buy and deliver shares of stock, which may be correct, but not easily understood.

So here's an analogy that I hope makes the concept clearer. So let's get started by pretending that you and I are both rich - really rich.

Own all the calls -- or own all the puts?

Let's say you happened to own all the April AAPL calls as of Friday morning. That's right all of them - every last one of those 656,000 contracts was yours. You obviously wanted the stock to close at the highest possible price at expiration.

If Apple had closed at 960, your 218 165-strike calls would be worth about $17 million in intrinsic value. Your 265 170-strike calls would be worth about $21 million, etc.

Go all the way up the chain, and you'll see that your four 950-strike calls would only be worth $4,000, but who cares? All those call options in the entire April chain would be have worth $23.7 billion in intrinsic value. But if Apple had closed at 165, all of those calls would be completely worthless.

Now let's say I was on other side. I happened to own all the 544,000 April put contracts that were open. If Apple closed at 165, my 20 900-strike puts would be worth $1.5 million, etc.

There weren't as many puts at high strike prices as open interest compared to calls, but I'd still have $860 million in those 19,780 600-strike puts I owned. With AAPL at 165, I'd have about $18 billion in intrinsic value from all the puts in the chain. But if AAPL closed at 960, all my put options would be worthless.

Clearly, our positions are quite opposite-and there's little chance that AAPL would reach either 165 or 960 - so both of us would probably have to compromise on some other expiration outcome.

But I need to pose just one more slightly different scenario to truly get at the concept of maximum pain.

Owning BOTH calls and puts

I figure if I can afford to own all the calls or all the puts, I could certainly afford both.

So let's pretend I own the entire options chain. What's the best outcome for me? Either a really high price or a really low price, but certainly not something in the middle.

The worst possible outcome for me would be an expiration with AAPL closing at around 560. At that level, based on all my open interest, the intrinsic value of all my calls and all my puts would be worth "only" $2.45 billion.

And that's the point of maximum pain. I created my own chart to show where this level was as of Friday morning for the April options based on open interest when the market opened.

Why is this so painful? Probably because those options cost way more when I bought them. After all, these options are expiring, so there's little time, nor time value left.

Or another way to view this is to flip the chart around. What's the "maximum pleasure" (or really, "minimum pain") if I happened to be short all those April calls and puts?

The best possible outcome is the same, 560. And the theory of maximum pain relies upon the premise that sellers of options do better than buyers of options - and that collective market action will drive the price to a level where option sellers minimize their pain and maximize their pleasure.

The important thing to remember, however, is that the pain or pleasure isn't all that much different at wide ranges below and above the so-called strike pin. You can see that if you zoom in on come of the more relevant strike prices

For example, the agonizing "pain" at 560 was only about 1% greater than for 570 or 550. That's a 20 point range where the pain was pretty much the same.

Strike price: Where's the bias?

Okay, so what's this "strike price bias" stuff that Optionistics refers to? Let's go back to the example of where I own all the puts and you own all the calls.

While we each want the stock to move sharply one way or the other, there's a level at which we'll both come out with the same amount of money in terms of intrinsic value.

As of Friday, that was around 533. At AAPL closing at 530, I'd have a bit more intrinsic value with my puts than you'd have with your calls. At a close of 535, you'd have a bit more than me. And that's the strike price "bias."

This chart shows where these levels converged based on Friday's open interest data - plus showing the maximum pain level.

And here's a zoomed in version to show more relevant strike prices.

Least gain or most lost.

So all in all, think of maximum pain at the specific point where the owner of the entire options chain would gain the least (and those short all those options gain the most) at a specific expiration close for the stock.

And think of the strike price bias as the point where someone who owns all the puts would have the same intrinsic value as the person who owns all the calls.

Yes, I realize that owning all the options is a ridiculous concept. If I owned all the options, I'd have nobody to sell them to. And if I were short all those options, I'd have nobody to buy them from me.

As I mentioned earlier, the maximum pain theory is interesting, but I'm not convinced that it does much good when there's less than a 1% difference between strike prices for a stock like Apple.

But I do look at the graphs sometimes. And when you review them for future expirations, thinking in these terms of owning the entire options chain might help you understand how these figures are calculated and what they mean, if anything at all.

Source: Understanding Maximum Pain: A Look At Apple Options Expiration