*Editor’s note: This article is the final installment of a three-part series on long option strategies. Part 1 introduced an option’s gamma as the “positive side” of negative theta. Part 2 explained synthetic positions, put-call parity and delta-neutral strategies, and how some traders use these concepts to “scalp gamma.” In part 3, we’ll illustrate the process with an example of gamma scalping.*

So you’ve identified a stock in which you believe the implied volatility (IV) is too low. Maybe it’s been fluctuating quite a bit, or maybe you think it is entering a period of uncertainty, but this uncertainty doesn’t appear to be reflected in its IV, so you decide to buy the at-the-money (ATM) straddle, a strategy that rises in theoretical value (TV), all else equal, as IV increases (aka a “long vega” position).

But how long do you wait for this potential volatility spike? A day or two? A week? Expiration of the strikes comprising your straddle? Remember, though this straddle is positive vega, it’s also positive theta—each day this position loses a bit of its TV with the passage of time.

You could, however, try to offset some of this theta by dynamically hedging changes in the options’ delta that may pop up as the underlying stock fluctuates. That’s called “scalping the gamma.”

## Buying Gamma with Straddles

With the purchase of a straddle—a long call and long put of the same strike and expiration date—you’re not just buying vega; you’re also buying gamma. When you buy an ATM straddle, it has a net delta of zero since the .50 delta of the call is offset by the -.50 delta of the put. But changes in the price of the underlying change these deltas, and option traders who actively scalp gamma can potentially use this to their advantage. Let’s illustrate:

Suppose a stock is trading at $50, and you were to purchase 10 of the 50-strike straddle. Using the table below, with the stock at $50, the 50-strike straddle is worth $4.00

Stock Price | 50-Strike Call Value | Call Delta | Gamma | Vega | 50-Strike Put Value | Put Delta |
---|---|---|---|---|---|---|

$48 | $1.19 | .31 | .08 | .04 | $3.19 | -.69 |

$49 | $1.55 | .40 | .09 | .05 | $2.55 | -.60 |

$50 | $2.00 | .50 | .10 | .06 | $2.00 | -.50 |

$51 | $2.55 | .60 | .09 | .05 | $1.55 | -.40 |

$52 | $3.19 | .69 | .08 | .04 | $1.19 | -.31 |

##### Table 1: THEORETICAL VALUE, DELTA, GAMMA AND THETA OF A 50-STRIKE CALL AND PUT. *Sample data for illustrative purposes only.*

If the stock increases from $50 to $51, the straddle’s theoretical value (TV) increases, from $4 to $4.10. But what happens if the stock goes right back to $50 an hour later? Assuming the implied volatility hasn’t changed, the straddle’s TV would right back at $4.00 Easy come, easy go, right? Not necessarily.

## Enter Dynamic Hedging

With the stock at $51, it’s not just the straddle’s price that’s changed; the straddle’s net delta has also changed, from zero to 0.20 (.60 for the call and -.40 for the put). Since you have 10 straddles, that amounts to 2.00 total deltas. If you’re one of those option traders who view delta as a percent chance an option will finish in-the-money, you can look at these 2.00 deltas as a theoretical equivalent to being long 200 shares of the underlying. For more on how this works, please refer to part 2 of this series.

So you could sell 200 shares against these theoretical deltas. But remember: if you don’t happen to own shares, you may need to sell the stock short, and not all accounts qualify. Make sure you know what you can and can’t do in your account before considering this strategy.

Now, assume the stock heads back to $50. The straddle’s TV drops back to $4.00. The straddle delta goes back to zero, so there’s no longer a need for the stock hedge. So you can buy back the shares at $50 for a gain of ($1 x 200 shares) = **$200**, minus transaction costs. Congratulations; you’ve done your first gamma scalp. Call it a day.

But when you call it a day, remember you’ll also call it a loss of the day’s theta, which, from the table above is the theta (of both the call and the put in your straddle, so it’s really twice the listed theta), times the multiplier, times the 10 straddles you’re long:

($0.06 x 2 x 100 x 10) = **$120**

So in this example, the strategy made ($200 - $120) = **$80** on this day, minus transaction costs. If, on the following day, the underlying doesn’t fluctuate enough to get in any “scalps,” it’s another **$120 loss** in TV. And that daily theta number tends to get bigger the closer you get to expiration.

This is the essence of the gamma scalping strategy—trying to earn more in scalps than you lose in theta.

## It’s Dynamic—Up and Down

What if, instead of breaking back to $50 after you sold 200 shares at $51, the stock kept going up, to $52? Sure; you’ve lost $1 on those 200 shares, or **$200**, but look at the change in TV of the straddle—it’s up $0.38, or **$380** on 10 straddles. Plus, the straddle now has a .38 delta (3.80 deltas total, or a 380-share equivalent), and since you only sold 200 shares at $51, you could sell more at $52, and so on.

Alternatively, what if, instead of rallying from $50, the underlying stock initially fell, say, to $48? According to the data in table 1, the TV would rise to $438, and the delta would go to (.31 - .69) = -.38. Using the same math as above, your 10 straddles would now have the equivalent of a 380-share short position. You could consider buying in some shares and try to scalp the gamma in the same manner.

## Summing it All Up—And Maybe Closing it Out

Dynamic hedging can be thought of as a competition between gamma and theta. If a stock moves around enough, and you’re able to scalp enough gamma to offset each day’s theta, you can come out ahead. If not, you don’t. And one more caveat: gamma scalping may require extra diligence and attention. If the stock is fluctuating enough to give you gamma scalping opportunities, you (or at least your orders) need to be in place. And each time you get filled on an order, you should assess your delta position and set new entry and exit points. It’s called “dynamic” for a reason.

And remember the initial premise? You originally bought these straddles in anticipation of a potential rise in implied vol, and the gamma scalping strategy was initiated in order to offset the theta while you waited for an opportunity to sell your straddles at a higher IV level. So you also need to look for potential opportunities to liquidate.

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