Level Up Your Options Knowledge (To Synthetics and Beyond)

Synthetic, pieced together, made by humans to imitate something else. In your closet, synthetics are clothes that can be mixed and matched to accessorize and slenderize. And in the options world, synthetics are what result from the mixing and matching of calls, puts, and stocks.

There’s a tight relationship between the right to buy a stock (a call option), the right to sell it (a put option), and the stock itself. This relationship allows you to combine any two to mirror the risk profile of the third. Sound complicated? Maybe so, until you break it down.

Synthetics: Piece by Piece

Consider a long call position at any given strike. At expiration, if the underlying stock price is higher than the call’s strike price, you could exercise the call and take a long position in the stock, if you wanted to own the stock. If it’s below the strike at expiration, it expires worthless.

Now, look at a short put position at the same strike. If the stock price stays above the strike price through expiration, the option expires worthless. If it drops below the strike prior to or at expiration, the put would likely be assigned, and you’d be buying a long stock position.

Suppose you’re long the call and short the put—same strike, same expiration date. At every point above and below the strike, one of the two options will be in the money (ITM) and could result in a long stock position if exercised or assigned. A long call paired with a short put mirrors the risk profile of a long stock position, so it’s a “synthetic” long stock.

It’s easier to see this visually (see figure 1).  

What about prior to expiration? Is the position fully synthetic then as well? For that, let’s turn to delta.  

If you’re long the stock, it’s 1.00 delta. If you hold 100 shares, for every dollar the stock rises, the value of the position increases $100. If it goes down $1, you’re down $100. That’s pretty simple. Likewise, if you’re long a deep ITM call, it’s essentially 1.00 delta and moves basically one-to-one with the stock. A put with that strike has a significantly lower chance of finishing ITM, so it likely has a near-zero delta.

Now suppose it’s an at-the-money strike. It’s 50/50 whether the call or put will be ITM at expiration. So, the call has a 0.50 delta, and the put delta is -0.50. Think of this as a 1.00 delta sandbox. At any point, the call delta minus the put delta (a double negative, so add them together) is always 1.00. If a call has a 0.30 delta, the corresponding put will be -0.70. If the call is 0.40, the corresponding put will be -0.60, and so on.

Again, if you’re long the call and short the put at any strike, either you could exercise the call and become long the stock, or you could get assigned the put and be long the stock. Not both. But it’s pretty much certain to be one of the two.

The Big Six

Let’s go a step further. If a long call paired with a short put is a synthetic long stock, then a short call with a long put is a synthetic short stock. Now move them around to and from different sides of the equation (like you did in algebra class) to get these six basic synthetics.

And remember: A standard U.S. equity options contract is deliverable into 100 shares of the underlying stock. So, for these six synthetic combos, it’s one call, one put, and 100 shares of stock (see figure 2). 

Speaking of algebra, this relationship has a name and a formula. It’s called the put-call parity theorem. Here’s what it looks like:

        S + P = C + K, where S = stock price, P = put premium, C = call premium, and K = strike price

The prevailing price of the underlying stock plus the put premium equals the strike price plus the call premium. Want to see it on the thinkorswim® platform? Take a look at figure 3.  

For the 51 strike:

$51.51[S] + $0.96[P] = 52.47

$1.47[C] + 51[K] = 52.47

Rearrange the equation using basic algebra and you arrive at the other five equations. And using put-call parity, you could double-check if you’re getting in at a fair price.

For example, suppose you want to synthetically get long by using the 51 strike. You’d buy the call and short the put. Using the mark prices in figure 2, the call is $0.51 higher than the put price. And with the stock at $51.51, the 51-strike call is ITM by $0.51.

C – P = S – K

Same formula—just rearranged algebraically. 

And if you’re looking at deltas, note that the absolute value of the call and put deltas add up to 100. At each of the strikes in Figure 3, buying a call and selling a put will give you a delta of 1.00. 

As a retail option trader—maybe one who sticks to basic strategies such as covered calls or vertical spreads—your entry and exit targets and overall strategy are working for you. And you might be thinking, “So what?”

Two answers.

First, if you trade options, you’re already benefiting from synthetic relationships. Behind the scenes, market makers use them to keep bid/ask spreads as tight and liquid as possible. It keeps things from getting out of whack.

Second, once you’re comfortable with synthetics, you might find—as many advanced traders do—you can potentially use them to more effectively and efficiently pursue your options trading objectives.

Accessorize With Synthetics

Synthetic Stock Position

Say you’ve got a stock in your portfolio that you’ve owned for a long time. You think it could be headed for a pullback, but selling it might be a taxable event. You could shed some delta with a synthetic short stock position, and when your target’s been met—for better or worse—you could undo the synthetic hedge, keeping the long position intact. 

Alternatively, suppose you want to short a stock but can’t (or don’t want to) go through the borrowing process. A synthetic short stock position might be the answer. But keep in mind, like the short stock strategy, the short call component of this synthetic (if not covered by long stock in the account) is subject to unlimited risk of loss.

Covered Call Dressed Up

The synthetic short put combines a short call and a long underlying. And that’s another name for a covered call—one of the more common strategy choices out there. Selling a cash-secured put at the same strike is a synthetic way to get the same risk/reward profile in one trade. 

Convert It

Say you bought a put and it went your way—the stock dropped $5. You’re sitting on a nice winner, but you’re worried the stock might drift back higher. So, you buy the stock. You’ve now turned that position into a synthetic long call. Now, suppose the stock rallies. You could close out the stock and put or sell the corresponding call to lock in a synthetically flat position (long stock, long put, short call).

You get the idea. There’s a whole wardrobe’s worth of strategies that are only possible once you’ve opened yourself up to the world of synthetics. Consider trying one on in paperMoney®. You might find it fits your strategy objectives like a pair of spandex shorts.