# Delta as a Probability Tool: Assessing Option Profitability

Delta as a probability

We can finish our conversation on Delta by looking at a fascinating way to use it: determining the likelihood of an option contract finishing in the money.

Let me explain – When a trader purchases an option, regardless of whether it’s Calls or Puts, what exactly are they hoping for?

To provide an alternative example, let’s say you purchase the Nifty 9000 PE when the spot price is trading at 9100. In this scenario, the 9000 PE is an out-of-the-money (OTM) option. Your expectation is that the market will decline, resulting in a profit from your put option.

As the spot price decreases below the strike price, the option transitions from being OTM to in-the-money (ITM), which increases the potential profit. To estimate the probability of this transition, you can utilize the option’s delta.

Assuming the 9000 PE has a delta of 0.3, which is typical for a slightly OTM option, you can convert this delta into a percentage. In this case, a delta of 0.3 translates to a 30% probability of the 9000 PE becoming an ITM option.

It’s important to consider this scenario as it reflects the realities of the market. However, let’s now shift our focus to a different situation.

For instance, let’s analyse the 8400 CE, which is trading at Rs.4/-, while the spot price is at 8275. With only two days remaining until expiration, the question arises: should you invest in this option?

From a trader’s perspective, this might seem like a small investment given the premium of only Rs.4/-. On the other hand, if the speculation proves to be correct, there is potential for significant profit.

However, let’s engage in “model thinking” to evaluate whether this is a prudent course of action.

Considering the 8400 CE as a deep out-of-the-money call option with a delta of approximately 0.1, we can infer that there is only a 10% chance for the option to expire in-the-money.

Furthermore, with just two days remaining until expiration, the case against buying this option becomes even stronger.

By analysing these factors, we can make a more informed decision about whether to pursue this option strategy.

A smart investor will never purchase this option, but it makes perfect sense to sell it for the premium. Looking at the facts – there is only a 10% chance for this option to end in-the-money, or put another way, a 90% chance of settling out-of-the-money – it’s clear why one should boldly take on this trade!

The delta of an ITM option is usually close to 1, which indicates that there’s a strong likelihood for it to remain ITM at expiration. Consequently, if you’re considering writing/shorting ITM options, consider that the chances are already stacked against you!

It’s essential to understand the numbers and wear your ‘Model Thinking’ hat before taking a trade, as this is what smart trading is all about – making sure the odds are in your favour.

I trust that this has helped you gain a reasonable idea about the initial Option Greek – the delta.

Now let’s understand about Gamma in the next chapter.