Option Greeks Delta vs spot price

The last chapter offered a glimpse into the Delta option Greek, while also providing a deeper view into model thinking. What I mean by that is the previous chapter exposed different options trading views – hopefully you now have a better understanding of how to examine options beyond just one dimension.

Moving ahead, if you hold a bullish view on the markets, your trading strategy might not involve straightforwardly “purchasing a call option or earning a premium by selling a put option.”

You may want to consider taking a bullish view on the market with an expectation of a 40 point increase. To capitalise on this move, investing in an option that has a delta of 0.5 or higher would be wise, as it should yield at least 20 points.

It is evident that comparing the two thought processes reveals a contrast; the initial one being rather unstructured and spontaneous while the second was formed through use of clear metrics and data. Our earlier chapter discussed a formula that anticipated an increase of 20 points in the option premium.

Option Delta * Points change in underlying= Expected change in option premium

The above formula is only the first step in the game. As we uncover more of the Greeks, our evaluation process becomes increasingly quantitative and trades become more logical. Numbers and equations will drive our strategy from here on out, leaving little room for ‘casual trading thoughts’. Some people are successful with that approach, but it’s not for everyone. Taking a numerical perspective gives you much better odds – the kind of edge that comes from developing model thinking.

When analysing options, it’s important to keep the model thinking framework in mind; this will give you a structure to make your trades organized.

– Delta versus the spot price

Earlier, we analysed the importance of Delta and delved into how one can use delta to forecast changes in premiums. To quickly refresh your memory here is a brief review of the previous chapter –

1. A Call option demonstrating a delta of 0.4 conveys that its premium is affected by a 1-point fluctuation in the underlying; the option will increase or decrease by 0.4 points respectively.
2. A Put option’s delta is negative. For example, if the delta of a particular Put is -0.4, then a one-point movement in the underlying asset will result in a 0.4-point change in the price of the option.
3. Options out of the money (OTM) have a delta value between 0 and 0.5, while the at the money (ATM) option has a delta of precisely 0.5, and those in the money (ITM) possess a delta ranging from 0.5 to 1.

Allow me to draw insights from the third point mentioned and draw some conclusions. 

Let’s take the Nifty Spot at 8305, the strike under consideration is 8250, and the option type is CE (Call option, European).

1. What is the Delta for the 8250 CE when the spot rate is 8305?

Since the 8250 CE is an OTM option, the Delta should be in the range of 0 to 0.5. Let’s assume a Delta value of 0.3 for this example.

2.           What do you estimate the Delta value to be if Nifty spot goes from 8305 to 8250?

As the spot moves from OTM to ATM, the Delta value should increase. Let’s assume the Delta to be 0.5 for this case.

3.           What would be the Delta value if Nifty spot moved from 8250 to 8200?

If the spot moves from ATM to ITM, the Delta value should approach 1. Let’s set the Delta at 0.8 for this example.

4.           If Nifty Spot experiences a significant rise and reaches 8350 from 8200, how will the Delta be affected?

The spot has increased, causing the option to move from ITM to OTM. As a result, the Delta will decrease from 0.8 to 0.4, for instance.

5.           What conclusions can be drawn from these four points?

The change in the spot value influences the moneyness and Delta of an option, impacting its pricing and risk profile.

This is an essential point to note – delta is a variable and will alter when the underlying’s value shifts. Consequently, if an option has a delta of 0.4, its worth will be subject to fluctuations depending on the value of spot.

Examine the chart below for a depiction of delta relative to the spot price. It is a general representation and not pertinent to any specific strike or option. There are two lines easily distinguishable on it –

1. The graph of the Call option’s delta is represented by a blue line, exhibiting values ranging from 0 to 1.
2. The red line illustrates the range of fluctuation of the delta of the Put option, from -1 to 0.

This chart is captivating and we should start by simply examining the blue line, disregarding the red line. The blue line symbolises the delta of a call option. As you look over the graph, there are certain notable elements to consider; here are some of them: as the spot price fluctuates, this can also result in a change to the moneyness of the option.

1. Take a look at the X-axis, where the moneyness increases as the spot price transitions from OTM (Out of the Money) to ATM (At the Money) to ITM (In the Money).
2. Observe the delta line, represented by the blue line. As the spot price increases, the delta also increases.
3. Notice that at OTM, the delta remains relatively flat near 0. This indicates that regardless of how much the spot price falls (moving from OTM to deep OTM), the option’s delta will remain at 0.
   1. Keep in mind that the call option’s delta has a lower bound of 0.
4. When the spot moves from OTM to ATM, the delta starts to rise (considering the option’s increasing moneyness).
   1. Observe how the delta of the option falls within the range of 0 to 0.5 for options that are less than ATM.
5. At ATM, the delta reaches a value of 0.5.
6. As the spot moves from ATM to ITM, the delta continues to increase beyond 0.5.
7. Notice that the delta starts to level off when it reaches a value of 1.

1.   This suggests that once the delta surpasses ITM and reaches deep ITM levels, its value remains constant at the maximum value of 1.

Similar characteristics can be observed for the Put Option’s delta (represented by the red line).