  # Derivatives: Exploring Delta and Gamma in Options Trading

Drawing Parallels

Throughout the last several sections, we’ve comprehended how Delta of a choice functions. As we know, Delta exemplifies the alteration in premium for any switch in the underlying cost.

If the Nifty spot value is 8000, then it’s evident that the 8200 CE option is out-of-the-money (OTM), which means its delta could range anywhere from 0 to 0.5. To continue this conversation, let us fix this value at 0.2.

If Nifty spot experiences a surge of 300 points, it would no longer be OTM for the 8200 CE option. It would instead become slightly ITM and as such its delta value would alter from 0.2 to around 0.5 to 1.0; let’s approximate this at 0.8.

This alteration in the root cause means that Delta’s value is no longer static; instead, it evolves in accordance with alterations to the underlying and the premium. Just like velocity alters according to time and distance travelled, so too does Delta shift its value.

An option’s Gamma tells us the response of its delta to a shift in the underlying. It is the answer to how much the delta of an option will be affected by a change in the underlying.

Let’s now make a comparison between velocity and acceleration, on one hand, and Delta and Gamma, on the other.

1st order Derivative

• Change in position over time is captured by velocity, which is the 1st order derivative.
• The change in premium corresponding to alteration of the underlying is measured by delta, thus it is referred to as the first derivative of the premium.

2nd order Derivative

• Acceleration, which represents the change in velocity over time, is captured as the second-order derivative of position.
• Delta captures the effect of a change in the underlying value on the option premium, and Gamma is thus referred to as the second derivative of the premium.

As you can imagine, computing Delta and Gamma values (and all other Option Greeks) necessitates a hefty amount of number crunching and advanced calculus (like differential equations and stochastic calculus).

Do you know why derivatives are called derivatives? The reason is that their value depends on the underlying asset that it represents.

The value that the derivatives contracts take from their related underlying is gauged by using the mathematical concept of “Derivatives”, thus why Futures & Options are known as ‘Derivatives’.

If you’re curious, there is an alternate world where traders utilise derivative calculus to discover trading possibilities continually. Generally known as ‘Quants’, these investors have a quite distinguished name. Quantitative trading is the reality behind the ‘Markets’ mountain.