Delta Neutral - Options - Accurate - Black Scholes

General
1

Hello ,

@nithin - please advise

I am trying to be as delta neutral as possible , for weekly bank nifty options short strangle.
Least affected by movement either side.
Wondering for intraday purpose - delta would be relevant or should look at premium amount and distance-to-strike.

Using the black scholes calculator requires three inputs :

  1. Annual Volatality for Weekly Bank Nifty Options.
    What should this value be , and where can I check this.
    Any reference with VIX. Implied vs Historical ?
    How accurate is the IV auto calculated by the broker , specially as days to expiry become 1 or 2.

  2. Time to expiration in days.
    Say on Monday 12:00 noon , should I put 3 or 3.2 for Thursday 3:30 PM expiry
    What about previous Friday ? 5 or 6 or 7 days.

  3. Risk free rate. What about this ?
    Presently putting 7%. Where can I check this.

Secondly ,

  1. Role of Price :
    Does the option price play any role in being delta neutral.
    I shouldn’t be averaging , based on price at different strikes right ?
    IE : 2 qty at 75 is equal to 1 qty at 50 and 1 qty at 100.
    Can I turn blind on the price ?
    At equal strikes calls are substantially pricier than puts.

  2. Role of distance from Strike
    Being equal distance from Strike also doesnt mean being delta neutral right ?
    say 200 points away for CE and PE - would not be delta neutral right ?
    From observation : at equal distance from the strikes the Call is priced more.
    Shouldn’t it be the PUT more expensice than Call.

The Risk free rate and time to expiry , dont seem to have a very major impact.
However , the IV does. and it changes very spontaneously.
Please advise , how price / strike / delta judgement - can be used to enter into 'as delta neutral" as possible.

Can I rely completely on the delta values from the Black Scholes Calculator to be direction indifferent.

2

i think better you tag @nithin sir for its answer…

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thanks for the advice. did do so now. any other option experts , i can tag ? @goldb

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IV for BN weekly options available on the NSE India option chain, time to expiration is the number of calendar days to expiry and the risk-free rate is the RBI 91 day treasury bill rate available on the RBI site, currently at 6.1908%. More on greek calculation

Change in price changes volatility which affects delta value. Usually, puts have higher inherent IV and are usually pricier but the call seems to be more expensive in your case. It’s possible. The aim is to be as delta neutral as possible. Choosing equidistant strikes from ATM strike with favorable option prices gets you close to delta neutral.

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5

thanks @Srinivas

So ,

Say Current Bank Nifty Spot Index (Not futures) : 25000
Can I sell : 24800 PE and 25200 CE and assume to be delta neutral.
strike : equal distant
premium-price : not looking
delta : this suggests otherwise , this says to be 24800 PE and 25300 CE to make delta zero.
hence confused.
also , this changes as days to expiry get shorter ,
what would you do ? go with strike price or go with delta value.

Second , what to do in case :

  1. Bank Nifty Spot Index : 25025
  2. Bank Nifty Spot Index : 25075
    If I want to be around 200 points OTM.
    Can we play with the quantity ratio.

Can we overlook the premium-price completely for our purpose ?
most times the difference is quite large.
The idea is to gain from theta decay / reduction in price.

6

Check this scenario below:

image

Strikes equidistant from Dec future price are delta neutral. But then after tomorrow, the options will start to follow the Jan future price. I’m a little confused here too.

@iSTFF, need some assistance here.

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@Srinivas , thanks for the screenshot. perfect. now it will help to understand.

  1. I look at the Spot Index only. Never consider the future price.
    Whats the point of looking at Jan 25th-2018 future month future , as we are dealing with 4th-Jan weekly product.
    That’s correct ?

  2. As per screenshot , you can see - that at 200 points away , there is substantial difference in the CE / PE price.

  3. Bring in Delta to the picture : you can use an excel calculator for black scholes.
    Can you please check and post. also mention IV , days and risk-free-rate you used.
    Accuracy of the delta will make a difference.
    but the changes in delta are too spontaneous , wonder if we should use it.

possibly on tuesday and wednesday with only 1or2 days to expiry - the relevance of the delta calculated will be lost.
someone knowledgeable on this can advise.

@Abid_Hassan @VelmuruganSengottai

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Hey @Srinivas, strikes equidistant from the future/spot on Call and Put sides may not have same Delta values. The reason is due to differential IV values that you have also mentioned above. As for the above, yes you are right, from what I have witnessed for a long time, the premium pricing will soon start following the Jan BankNifty futures value especially if it moves significantly away form the spot price.

@adityaparakh, does your strategy require that you keep maintaining a Delta neutral position? If yes, then you should keep a hard-focus on Delta values to maintain neutrality. Else, If you chose to use strategies like Strangles or Iron Condors, then you need not focus too much on absolute Delta values (you can chose equidistant strikes from the future/spot).

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@iSTFF , @Srinivas

No , I don’t require continuous delta neutral.
I am trying out Intraday Short Strangle on Bank Nifty Weekly Options.

1. Should we consider the Spot Index or the month end Future price for reference ?
2. Can I overlook the premium price completely and focus only on the distance-to-strikePrice?
3. Above screenshot = 25200/25700 or 25300/25700 which would be a suitable delta neutral pair for Jan 4th 2018.
Since both Spot Index and JanFuture are approx 25500 , being equi-distant would mean 25300/25700.
However , if you calculate the Delta from Black Scholes it will advise - 25200/25700. I am referencing delta value from another broker as well. And there are variations.

10

Ok, since it’s a Strangle on the BN weeklys, equidistant Call/Put strike should do.

  1. Although the BN weekly Options are Options-on-index (unlike Gold options on MCX), theoretically, the spot price should be considered. However, my personal observation is that when there is much divergence in the Spot-future prices then Options usually follow the future pricing (If you don’t agree then I would strongly suggest that you look at this phenomenon for a few months to convince yourself if this correct or incorrect). My assessment is that if future prices move away from the spot price significantly and if the Options premium pricing follow the spot price theoretically, then significant arbitrage profiting opportunities arise among the Futures & Options combined (not getting into details about it here). Such arbitrage profiting naturally pushes Options premium prices to follow the future instead of the spot price.

  2. Yes, for Strangle I do the same.

  3. From above screenshot 25300/25700 looks fine. Actually, in the last half hour today BankNifty fell quite a bit so the IVs of PE options swelled quite a bit as traders started to aggressively bid for the Put options, hence the higher premium value of 25300PE.

Note: The above is for educational purpose only, they are not recommendations for initiating a trade.

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@iSTFF

“much divergence” - can we say around 30 points or more ? between spot index and month end future.
Can I forget about Spot Index altogether then and merely look at the month end future price.
Be it week 1 2 3 or 4 - I am supposed to look at the month end future price.
And from that future price , be equidistant from the strike.

We will not look at the (any day of the week) :

  1. delta - be it from excel-calculator , zerodha-web-calcualtor , other-broker-inbuilt.
    There are variations among them and it only adds to errors.
    Can I understand that this dynamism in the IV , leading to changes in the delta , is the reason that we are preferring to look at the equidistant-from strike and not the delta ?
  2. premium-price . blind to this even if substantial difference.

This is alright : ?
At 25525 , a combination of 100 units of 25300PE and 25700CE - 50 units + 25800 CE - 50 units
At 25575 , a combination of 100 units of 25400PE and 25700CE - 50 units + 25800 CE - 50 units

Thanks a lot. Really appreicate. Disclaimer was not required. Really appreciate.

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  1. i look at both future price and the spot price (
  2. instead of complicating things , if i want to go for strangle , i will try to pick the strikes of PE and CE which has more or less values ( like if CE is trading for 100Rs , i am ok to pick a PE with any values from 85Rs to 120Rs kind )
  3. from my expereince , for intraday trades i dont think black scholes might be any use . We have to still use our judgement and pick the startegy correctly . for iron condor or iron butterfly , pick the wing based on your risk appetite .

PS:-

  1. i met one poster through tradingqna and he is consistently profitable in simple short straddle / short starngle and he had shown me the P/L report as well
  2. for me intraday seems to be working ( iron condor/butterfly , starngle , straddle … short or long based o n situation ) and overnight BN directional postions are totally inconclusive
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  1. based on @iSTFF s observations it makes sense to look a month end future only.
    if its close to Spot - it will be same. if its away - options will follow future price.
    I feel a convinced about this. just awaiting his confirmation.

  2. likewise , as he said , looking at price is not the right way.
    probably better to stick to strikes than confuse with premiums.
    being equally priced is not a sign of being delta neutral or equi-distant.

  3. i was hoping that black scholes would help in accuracy as it factors in premium / iv / time to expiry everything.
    but seemingly the practical approach is to look only at the distance-to-strike.

14

Yep, looking at the future price is ok.

Variation is Delta value calculations could be due to different values of IV and risk-free rate that different sources use. Basically Strangles don’t need absolutely precise Delta calculations, so equidistant-from strike approach can be used for simplicity. If equi-priced premium approach is followed then it’s also fine. Up to you! No hard rule.

I didn’t understand this part. Could you please elaborate?

Yes, it’s alright. (Extra 1 leg brokerage though :wink: )

Just my personal Risk Management style, please don’t take it otherwise. :slight_smile:

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Thanks @iSTFF ,

Will look at future price.
Will not look at delta.

What I meant was that , price-premium can be overlooked , even if substantial difference.
But equi-priced-premium can also be used ?
Wouldn;t it defeat the purpose of direction neutral.
Like in the above case :
25300/25800 would be distance-to-strike based.
25200/25800 would equi-priced based.

Only can be direction neutral within minimum impact , right ?

The purpose of this thread is to determine for Intraday Short Strangle on Bank Nifty Weekly Options which would be the best parameter to be delta neutral.
“Premium-Price” vs “Distance-To-Strike” vs "Delta"
Theoritically Delta is most applicable as it factors in all parameters , but practically it seems that the inaccuracies we face in calculation and dynamic change in IV , hence delta itself , leads to it being a lesser preferred choice.
Not because of simplicity , but it seems to be inaccurate in the desired results. @iSTFF
Between the “Premium-Price” vs “Distance-To-Strike” , the latter seems logical.

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Hey @adityaparakh

Sorry about joining the party late. Ill take a swing at your questions.

I will answer what seems to be the single biggest source of confusion

You have to use the futures price for equidistance. Because theoretically, the futures is the expectation of spot at the time of expiry!

If you are trading the month end option, put the underlying price as month end future price. And when you are using this in a pricing model, using r=0. Try it, seriously :slight_smile:

If you are trading weekly options, then you a weekly future price which does not exist. You can use the Put Call Parity formula on weekly options to arrive at this number

Equation reads C-P = D(F-K)
F = Future, K = Strike C= Call Price P= Put price
D= e^-rt where r = 6% (Repo Rate) t = 7/365 (this will be roughly equaly to one). 1.001 for 7 days

So C-P = F-K

So if 4th Jan 25500 Call = X
So if 4th Jan 25500 Put = Y

Actually what, do the math :slight_smile:

Wondering for intraday purpose - delta would be relevant or should look at premium amount and distance-to-strike.

Distance of future to strike.
(Although at a theoretical level, implied volatility does have a bearing on delta. But let’s not go there)

Where to get volatility?
NIFTY option chain. Although in weekly options, IV has hardly any meaning when its just three days to go because Vega (change in option price with change in vol) is very low.
Also, in weekly options, only ATM has any significant Vega.
IV makes sense for longer time options near the money.

How accurate is the IV auto calculated by the broker , specially as days to expiry become 1 or 2.
Not sure which broker :slight_smile:

Time to expiration in days. Say on Monday 12:00 noon , should I put 3 or 3.2 for Thursday 3:30 PM expiry
Doesn’t matter much. Like I said, if you are trading options it is much better to think in terms of “Not going above/ below this level” than thinking “Theta of x and Vega of Y”.

What about previous Friday ? 5 or 6 or 7 days.
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Risk free rate. What about this ?
Repo Rate works. But there is an even better idea.

If you are trading the month end option, put the underlying price as month end future price and interest rate = 0. Try it. Seriously!

If you are trading weekly options, then you need to derive a meaningful value of a weekly future, had the weekly futures existed. We already figured how to do this in the beginning of the post

You will arrive at a theoretical future. Use that future price with r=0 in Black Scholes.

Secondly ,

Role of Price :

Does the option price play any role in being delta neutral?
Not really, Although, theoretically, yes. But you should ignore that. Look at distance of strike from future price.

I shouldn’t be averaging , based on price at different strikes right ?
IE : 2 qty at 75 is equal to 1 qty at 50 and 1 qty at 100.

Can I turn blind on the price ?
Not sure what this means

At equal strikes calls are substantially pricier than puts.

Role of distance from Strike

Being equal distance from Strike also doesnt mean being delta neutral right ?

say 200 points away for CE and PE - would not be delta neutral right ?

From observation : at equal distance from the strikes the Call is priced more.
Shouldn’t it be the PUT more expensice than Call.
It could be because you are using the spot instead of future,. Try using the future, / calculated weekly future, it should correct this.

The Risk free rate and time to expiry , dont seem to have a very major impact.

However , the IV does. and it changes very spontaneously.

Please advise , how price / strike / delta judgement - can be used to enter into 'as delta neutral" as possible.

Can I rely completely on the delta values from the Black Scholes Calculator to be direction indifferent.
As long as your inputs are right. The biggest catch here is getting the future right

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@adityaparakh please feel free to write to me on abid at sensibull dot com if you need more explanation on this. I have skimmed through the question and answer a bit.

It is a fairly good question, and I am sure a lot of others have the same questions.

In the process, I could get a better understanding of options! Thanks!

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@Abid_Hassan, thank you very much :pray:

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@Srinivas

Anytime mate! I consider this my job :slight_smile:

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@Abid_Hassan , Wow , Thanks a lot.
Really informative.

So In Crux :
In reference to Intraday Weekly Bank Nifty Options Short Strangle ,
To try to be delta neutral , it is not essential to look at delta-values or the premium-price.
Dont look at Delta - cause vega is too low.
Dont look at premium price - as it wont effect delta-neutrality for practical pusposes or taking position.

It is rather important to be equidistant from weekly-future price.
To determine this future price :
For 25500CE = Rs.127 , 25500PE = Rs.173 ,
127-173 = F - 25500 , Hence F = 25454
where the option prices are weekly ones. Choice of strikes of Options ? Closest to Spot ?

If I use : 25600CE=Rs85 and 25600PE = Rs.228 ,
85-228 = F-25600 , Hence F=25457 Close enough.
D will always be considered to be 1. All Days of Week / All 4 weeks ?

From this F value , we become equidistant and we are good ?
Spot : 25490 , MonthFuture : 25498 , Weekly F : 25454
A 200-250 point OTM position would 25200PE/25700CE based on calculated Weekly F.

This F value , is more appropriate than SpotIndex or the Month End Future value ?

As to determine the F value , and take our position we are not looking at all at the Spot or the Month-End-Future. !?
The price of the options plays more role. This F becomes our only input for the OTM Strangle position.

Secondly a lesser significant question :
Say , Weekly F is 25525 , what would be an ideal combination to make a good balanced strangle average 200 points away
and least effected by moves either side.
And for 25575 ?