Throughout the last several sections, we’ve comprehended how Delta of an option functions. As we know, Delta exemplifies the alteration in premium for any switch in the underlying cost.
If the Nifty spot value is 24,000, then it’s evident that the 24,400 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 450 points, it would no longer be OTM for the 24,400 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.
For those exploring equity investment opportunities through a stock broker or consulting with a financial advisor, understanding the relationship between Delta and Gamma proves essential when navigating the stock market. Whether evaluating trading calls or utilising a stock screener to identify opportunities, comprehending how Gamma measures Delta’s rate of change enables more sophisticated options position management and risk assessment.
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