A recent article introduced negative theta—that is, options positions that lose theoretical value each day due to the passage of time. The article demonstrated how this theta “cost” actually provides a potential benefit in the form of long gamma.

Some professional option traders will buy gamma and dynamically hedge it as the underlying stock fluctuates, as a way of locking in potential gains, or perhaps to cover the cost of the theta.

Over the course of two articles, you’ll learn how some option traders look at an option or option position’s delta as a “theoretical equivalent” position in the underlying, and how that assumption can allow them to dynamically hedge an option position. Or, in trader terms, to “scalp the gamma.”

## But First, a Bit of Option Theory

To understand dynamic delta-hedging, it might help to get a refresher on synthetic positions and, specifically, to familiarize yourself with put-call parity. Put-call parity defines the relationship between puts, calls and the underlying stock, and mixing and matching any two of them, in the correct manner and ratio, can give you a position with the same risk/reward profile as the third.

For example, if you’re long one call and short one put of the same strike and expiration date, you have a position that has the same risk/reward profile as owning 100 shares of the underlying. And why 100 shares? One options contract gives the owner the right to buy (call) or sell (put) 100 shares of the underlying asset. The table below shows six basic synthetic positions.

## Delta in a Whole New Light?

Delta, in its most basic definition, is an option’s sensitivity to changes in the price of the underlying. But some professional option traders have additional definitions of delta:

- a theoretical equivalent position in the underlying (more on that in a moment)
- a percent chance that an option will be in-the-money (ITM) at expiration
- a hedge ratio

Let’s explain:

A call with a delta of 1.00 (called a “deep ITM call”) moves 1:1 with the underlying stock, and assuming its delta stays at 1.00, it will likely be exercised into 100 shares on or before expiration.

By contrast, a call option that is way out-of-the-money (OTM) has no theoretical value. Its bid-ask spread is zero bid at $0.01, and it has essentially a zero delta. So long as its theoretical delta remains at zero, fluctuations in the underlying have no effect on the option price.

Of course, nothing is certain but death, taxes and expiration. If the underlying were to rally far enough, a zero-delta option might come to life. And if a stock were to have a steep pullback, a call option that was once a 1.00-delta “sure-thing” can become anything but. It’s rare, but it does happen.

So if a zero-delta option mirrors the risk profile of a zero-share position, and a 1.00-delta option mirrors the risk profile of a 100-share position, does a .50-delta option have the risk profile of a 50-share position?

Technically, no. At expiration, an option is either in-the-money (1.00 delta in the case of a call; -1.00 in the case of a put) or out-of-the-money (zero delta). But from a theoretical standpoint, that 50-delta option has a 50% chance of being ITM at expiration. As such, some option traders might “hedge away” the delta to become what’s called delta-neutral. Remember that put-call parity.

## The Volatility Play

Why might an option trader wish to hedge delta? Suppose, for example, you think the implied volatility (IV) of the options on a stock is too low. Maybe you believe the underlying stock is about to enter a period of excessive fluctuation, which might lead to a rise in volatility. In this case, you might consider buying options to become what’s called “long vega.” In this case, you’re willing to accept the volatility risk, but not necessarily the delta risk.

So perhaps you consider a trade that, initially anyway, has no delta, such as an at-the-money straddle or an equivalent-delta strangle. With such positions, you’d be long vega and flat delta. You could sit on this position and wait for a rise in IV, but remember: with a long options position, time decay, theta, is working against you, each day eroding the theoretical value of the position.