Gamma in option trading What Is Gamma in Investing and How Is It Used

Do you recollect studying calculus in secondary school? Does the concept of differentiation and integration sound familiar? When we were in school, ‘Derivatives’ held a different meaning. It was just the process of working through challenging integration and differentiation equations.

Let me try to jog your memory – the aim here is to get the point across without getting too deep into the nuts and bolts of solving a calculus issue. It’s essential to keep on reading, as this discussion is specifically related to options.

Consider the following scenario:

The car starts at zero kilometres and travels five kilometres in the first 12 minutes. After another eight minutes, it covers an additional three kilometres, reaching a total of eight kilometres.

Let ‘x’ represent the distance and ‘dx’ represent the change in distance. The change in distance, or ‘dx’, is calculated as 3 (8 – 5)

Similarly, let ‘t’ represent time and ‘dt’ represent the change in time. The change in time, or ‘dt’, is 8 (20 – 12)

Dividing the change in distance by the change in time gives us the velocity, denoted as ‘V’

V = dx / dt = 3/8

The velocity is expressed in kilometres per minute

To convert 3/8 to KMPH, we need to adjust the unit of time to hours. Since 8 minutes is equivalent to 8/60 hours, we can substitute this value back into the equation.

V = 3 / (8/60) = (3 × 60) / 8 = 22.5 KMPH

Hence, the car is moving at a velocity of 22.5 KMPH (kilometres per hour)

It took the car 20 minutes to cover the first eight kilometres. Suppose the car continues for another six minutes, reaching the fourteenth kilometre marker.

The speed of the car during the first part of the journey was 22.5 KMPH. By calculating the change in distance (dx=6) and the change in time (dt=6) during the second part, we can determine its velocity

The velocity for the second part is calculated as 6 KMPH (dx=6 and dt=6)

Let’s introduce ‘dv’ as the change in velocity, which represents acceleration.

The change in velocity can be determined by subtracting the initial velocity (22.5 KMPH) from the final velocity (6 KMPH)

The change in velocity is 6 KMPH – 22.5 KMPH = -16.5 KMPH

The negative sign indicates a decrease in velocity, suggesting deceleration

Whilst the change in velocity indicates deceleration, it’s important to note that this example focuses on velocity changes within a specific context. This explanation helps provide insights into the concept of acceleration, although seemingly unrelated to the concept of Gamma.

We made things much easier by assuming that acceleration is constant. Of course, in reality, this isn’t the case as you naturally accelerate at different speeds. If such a problem involves changes in one variable due to another, one must delve into a branch of calculus which is known as Differential Equations.

Let’s consider the following now:

Distance travelled (position) changes according to velocity, which is referred to as the 1st order derivative of position.

Change in Velocity = Acceleration

Acceleration is the rate at which velocity changes, which is itself the rate of change in position.

Therefore, Acceleration can be said to be the rate of change of Velocity or the second derivative of Position.

Bear in mind the 1st and 2nd derivatives as we continue to analyse Gamma.

For those exploring equity investment opportunities through a stock broker or consulting with a financial advisor, understanding the mathematical foundations of Option Greeks proves essential when navigating the stock market. Whether evaluating trading calls or utilising a stock screener to identify opportunities, comprehending calculus concepts enables deeper appreciation of Gamma’s role in options pricing dynamics.