Option Greeks Delta vs spot price

Model Thinking

The last chapter offered a glimpse into the Delta option Greek, whilst 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 60 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 30 points.

It is evident that comparing the two thought processes reveals a contrast; the initial one being rather unstructured and spontaneous whilst the second was formed through use of clear metrics and data. Our earlier chapter discussed a formula that anticipated an increase of 30 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 organised.

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:

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

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

Options out of the money (OTM) have a delta value between 0 and 0.5, whilst 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 24,680, the strike under consideration is 24,500, and the option type is CE (Call option, European).

What is the Delta for the 24,500 CE when the spot rate is 24,680?

Since the 24,500 CE is an ITM option, the Delta should be in the range of 0.5 to 1. Let’s assume a Delta value of 0.7 for this example.

What do you estimate the Delta value to be if Nifty spot goes from 24,680 to 24,500?

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

What would be the Delta value if Nifty spot moved from 24,500 to 24,350?

If the spot moves from ATM to OTM, the Delta value should approach 0. Let’s set the Delta at 0.3 for this example.

If Nifty Spot experiences a significant rise and reaches 24,850 from 24,350, how will the Delta be affected?

The spot has increased, causing the option to move from OTM to ITM. As a result, the Delta will increase from 0.3 to 0.75, for instance.

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:

The graph of the Call option’s delta is represented by a blue line, exhibiting values ranging from 0 to 1

The red line illustrates the range of fluctuation of the delta of the Put option, from -1 to 0

Let us understand this better:

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.

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)

Observe the delta line, represented by the blue line. As the spot price increases, the delta also increases

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

Keep in mind that the call option’s delta has a lower bound of 0

When the spot moves from OTM to ATM, the delta starts to rise (considering the option’s increasing moneyness)

Observe how the delta of the option falls within the range of 0 to 0.5 for options that are less than ATM

At ATM, the delta reaches a value of 0.5

As the spot moves from ATM to ITM, the delta continues to increase beyond 0.5

Notice that the delta starts to level off when it reaches a value of 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).

For those exploring equity investment opportunities through a stock broker or consulting with a financial advisor, understanding the relationship between Delta and spot price proves essential when navigating the stock market. Whether evaluating trading calls or utilising a stock screener to identify opportunities, comprehending how Delta changes with spot movements enables more sophisticated options trading strategies and model-based thinking.

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