Can someone explain how these FNO margins work?

Here are a few example of margins in some common scenarios involving NIFTY options for the current week, calculated using Angelone fno margin calculator:

Selling a naked ATM PUT:

Strike Type Qty Premium Span Exposure Total
23100.00 PE SELL 75 -9277.5 158127 34671.15 192798
TOTAL -9277.5 158127 34671.15 192798
MARGIN BENEFIT 0

Selling a PUT Spread:

Strike Type Qty Premium Span Exposure Total
23100.00 PE SELL 75 -9277.5 158127 34671.15 192798
22800.00 PE BUY 75 2846.25 0 0 0
TOTAL -6431.25 21546.75 34671.15 56217.9
MARGIN BENEFIT 136580

Selling a naked ATM CALL:

Strike Type Qty Premium Span Exposure Total
23100.00 CE SELL 75 -11602.5 161509.5 34671.15 196181
TOTAL -11602.5 161509.5 34671.15 196181
MARGIN BENEFIT 0

Selling a CALL Spread:

Strike Type Qty Premium Span Exposure Total
23100.00 CE SELL 75 -11602.5 161509.5 34671.15 196181
23400.00 CE BUY 75 3285 0 0 0
TOTAL -8317.5 22195.5 34671.15 56866.7
MARGIN BENEFIT 139314

Selling the ATM Straddle:

Strike Type Qty Premium Span Exposure Total
23100.00 CE SELL 75 -11602.5 161509.5 34671.15 196181
23100.00 PE SELL 75 -9277.5 158127 34671.15 192798
TOTAL -20880 161509.5 69342.3 230852
MARGIN BENEFIT 158127

Selling the ATM Straddle with hedges (probably called Iron Butterfly):

Strike Type Qty Premium Span Exposure Total
23100.00 CE SELL 75 -11602.5 161509.5 34671.15 196181
23100.00 PE SELL 75 -9277.5 158127 34671.15 192798
22800.00 PE BUY 75 2846.25 0 0 0
23400.00 CE BUY 75 3285 0 0 0
TOTAL -14748.75 22195.5 69342.3 91537.8
MARGIN BENEFIT 297441

Can someone with deeper understanding of derivatives explain how the margins and margin benefits calculated in each cases, with formulas if possible?

How would the calculations change for a different expiry or a different index/stock option?

Are these margins same across all brokers?

How much money one needs to have in their account if they want to trade each of these scenarios?

Not many know the exact formula and there is no need to know also to be a successful trader, if you are a beginner then there is absolutely no necessary to know these things.
Can check this about SPAN. You can google if you want to know more about SPAN.

Yes.

What ever final margin numbers you posted that is required to enter, after taking position one should maintain M2M ,means any loss, so it is suggested to maintain minimum of 20% extra than margin required to enter.
Your queries looks like you are a beginner , no need to worry about calculations of margins, just see how much margin is required and maintain 20% extra always, with experience you will get an idea how they will change according to situation.

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Margins specified by the exchanges are the same but levied by the brokers have slight variations.

Also, the same position could have an extra margin requirement on expiry day.

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Thanks for explaining. Actually I am writing a backtest for a strategy for a client.

The account starts at 2L, goes down to 1.4L after a few bad months and then recovers and gains to reach 5L eventually. Currently, I am only checking if the account contains more money than the max loss in a hedged selling position. But this is flawed since there is a chance that during the drawdown, the account may not have enough money in the account to even place the trade. So I am trying to get the formula so I can make sure that all the trades taken during the backtest were actually placeable accounting for the margin requirements.

Thanks for replying. I was aware about changes in rules and lot size over the years, but not about the changes for expiry day. It looks like it is a bit more complicated that I thought it would be.

This is probably why even online backtesting platforms like algotest/opstra/stockmock don’t account for the margin requirements during backtests. But this limits the reliability of a backtest for option selling.