Delta value not correct

Hello sir/madam
Again i see problem with Delta mentioned for various strike prices. I had bought the call option 20600 CE expiry 21 Dec 2023, seeing it is having delta near to 0.9. Now as the market has soared well beyond 600 points and the delta is being shown as 1. Still the move of 150+ points is only giving profit of around 4200 INR instead of 7500 INR. There is something amiss here. I think the delta is not being right. Though it is showing delta as 1. Actually it is working as 0.5 as per my calculation. Please have a look at this. It is causing me losses. Requested to sort out this issue in future also so that such incidents dont repeat.

Hi @anuragbhardwaj07 -
I’d like to run these calculations myself…can you provide me a couple of data points? In particular:

  • What date did you enter into the position (and around what time)? I will use that to get a better approximate price of the underlying on entry.
  • What was the price of the call option on entry?

Thanks!

Hello @mike . Great to hear from you…
I am here with my datas and i have done my calculations once again and by the end of market session the delta is being averaged out at 0.86 for today.

Data for reference
Entry 20600 CE @ 9:16 am on 14th Dec 2023 .
at price 576.95 INR .

But do have a look if i am missing out on something or perhaps ignoring some parameters.

Please let me know if your calculations shows any anomaly.

Regards
Anurag

Let me take a look into this. It will take several days for me to be able to diagnose to see if there is any issue. For reference, the model I use is showing slightly different (but not impactful) Black-Scholes values than what we have in-app so I want to ensure everything is correct. If anything, it may be some assumption differences in what I am quickly calculating vs. in-app.

Going through your example, the LTP today for the 20600 strike is 915.15 which is a gain of 338.20 based on your entry price of 576.95. The Nifty was right around 21100 at 9:16 yesterday looking 1-minute candles so the gain was 356.65 based on the close today of 21456.65. So, your contract gained in value at a rate of 95% of the value of the Nifty’s gain. When you do these calculations overnight, you also need to account for theta decay. In this case, technically, you are looking at 2 days of time decay because you held all day yesterday and all day today.

Another thing to remember is that the LTP <> the price you get when you trade (or mark-to-market price). For instance, the +/-2 strikes from current ATM have had an average volume of 1.84M contracts; this is a volume of >2000x the 20600 strike. As I write this, for the 20600-strike, the LTP is at the ‘ask’ but the bid is R9 lower (which is what you would receive if you exit your position).

Realistically, liquidity is the likely reason why the option isn’t moving in “lock step” with the underlying. If you look at the IV values of the adjacent strikes, you can see that the 20600-strike has IV of 1-2% lower than the nearby ones. This means that it is incorrectly priced due to illiquidity; the 20600-strike should be priced higher.

Lastly, based on your initial feedback about being a delta of 0.50: the ‘50 delta’ will always be the ATM strike. Delta is a rough approximate of the likelihood that the particular strike will end in the money. Intuitively, a 50-delta means that there is a 50% likelihood that the strike will be in the money on expiry and 50% likelihood that the strike will be out of the money on expiry. This will only occur for ATM strikes.

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Actually on day 1 of holding the call option It did was moving Sluggishly as compared to actual movement of nifty.
But i really appreciate your detailed analysis and valuable explanation into the matter.
Even i was clueless when the data for moments comform to the delta of around 0.5 which is for ATM strike price only.
Your reply was really detailed and insightful. Do let me know if you find something along the way. Thanks a lot for your valuable time.
Have a good day!

No problem at all! If I find something I will let you know. Either way:

  1. The challenge with trading ITM (as well as OTM) contracts is that the price will be sluggish compared to the Nifty and contracts that are near-the-money. This is simply liquidity…they aren’t being traded so the displayed price will appear ‘off’. However, on average, market dynamics will correct it.
  2. IMO - you are doing the right thing by trading ITM options. These will have higher win rates and while your ROI will be lower, your primarily goal in trading shouldn’t be big, irregular wins but rather smaller, consistent wins.

Thanks!

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Okay. Guess i am on the right track and more so…with helpful folks like you.
One last thing i would like to ask…
I was actually holding 19200 CE and was rolling over the same until last week. After that i decided to go for 20550 CE observing it is also having close to 1 delta. Do i lose much if i hold 20550 CE instead of 19200 CE. I think both must be having the same time decay and would behave more or less like futures. But there might be some elementary differences between real deep ITM and deep ITM. Let me know your thoughts. Thanks a lot.

Hi @anuragbhardwaj07
Here is some rough data that I’ve mocked up.

This is a 19200-strike and 20200-strike assuming 6 days until expiry and 18% IV. Theta moves in an asymmetric curve where the most negative impact is when the contract is at-the-money. As you can see in the plot, there isn’t much of a difference in theta between a deep ITM contract (20200) and a very deep ITM contract (19200). However, the very deep ITM contract will have slightly lower theta. The intuition behind this is that theta technically only impacts the extrinsic value of the option. A deeper ITM option will have a greater proportion of its value as intrinsic value as compared to a less deep ITM option. Since theta only impacts extrinsic value, the less deep ITM option will have slightly higher time decay. The benefit of a less deep ITM option is that it is more liquid and with more extrinsic value, it can be more impacted by favorable changes in volatility (albeit small).

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Okay. I see. It made a lot of sense to me. Thanks for all the wisdom you shared. Have a good night and take care.

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