Delta Hedge vs Straddle?

CyJackX said:
Ah, yes, didn't think about this...

A straddle offsets both delta and gamma.
A synthetic straddle offsets delta, but not gamma.
A synthetic position is therefore more responsive to moves in the underlying.
Thanks.
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No, it's exactly the same... a delta-hedged call has the same delta, same gamma, same vega as a straddle....

Although, you need to trade 2 SPX calls with 1 SPX future... or 2 SPX calls with 2 ES futures to get a full straddle. Otherwise it's half a straddle.

1 ATM call has the same gamma as 1 ATM put, so 2 ATM calls have the same as 1 straddle or 2 puts...
 
Yup, the exposures are identical. For futures, your cash treatment would be the same too. However, for a stock option synthetic straddle vs natural one would get you into a bunch of bizarre and obscure things - funding, short rebates, margin requirements etc.
 
JackRab said:
No, it's exactly the same... a delta-hedged call has the same delta, same gamma, same vega as a straddle....

Although, you need to trade 2 SPX calls with 1 SPX future... or 2 SPX calls with 2 ES futures to get a full straddle. Otherwise it's half a straddle.

1 ATM call has the same gamma as 1 ATM put, so 2 ATM calls have the same as 1 straddle or 2 puts...
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I'm trading 1 SPX Option with 1 ES to get my full straddle.

I had to think about it for a second, but I see what you're saying with the gamma; it doesn't offset, long options are always positive gamma. Hm...

In any case, I'll still probably stick to this strategy for my intraday trading, as it allows me to hedge/scalp with ES while maintaining a longer term directional play while also being a minimum of commissions and spreads.
 
CyJackX said:
Ah, yes, didn't think about this...

A straddle offsets both delta and gamma.
A synthetic straddle offsets delta, but not gamma.
A synthetic position is therefore more responsive to moves in the underlying.
Thanks.
More...

"offset" is not the word you want to use here..

put+call straddle is more responsive to underlying price changes
as i said, gamma is your friend

straddle and synthetic straddle can have the same delta at the moment of its entry
but the other greeks will be different (gamma, vega, ..)

it will behave differently as the price, time, volatility start to move

:]
 
A call and same strike and expiry put have the same gamma and vega etc.
The only thing is you need 2x the amount if you only trade a call or a put vs the straddle.

If you buy 2 ATM puts and hedge it with 100 stocks, you have 0 delta.
Same if you buy 2 ATM calls and hedge it with -100 stocks
same if you buy 1 ATM call and 1 ATM put... (straddle)

They are all the same.

If stock moves up, and that ATM put has a delta of -20 x 2... you will be +60 deltas incl hedge.
The ATM call would have a delta of +80 x 2, and you will be +60 deltas
The straddle will have a delta of +60 (+80 for call - 20 put).

So still the same delta position.

Call vega/gamma = put vega/gamma... that's a fact, since they both rely on the same probability distribution and therefore have the same characteristics.

For instance, if the ATM call = 1.00 and has a vega of 0.10.... the IV rises 1 point, and the new value of the call will be 1.10.
The ATM put has to have the same vega, otherwise put/call parity doesn't hold anymore... and that put rises as well with 0.10.

Same goes for all other strikes.
 
Spot 100
Call 90 = 12.00 with 0.05 vega
Put 90 = 2.00 with 0.05 vega

IV rises 1 point...
Call 90 = 12.05
Put 90 = 2.05
Put/call parity still holds...

If the put would have a different vega, say 0.03...
Put 90 = 2.03
And you can arb by + stock at 100, - call90 at 12.05, +put90 at 2.03... wait till expiry and pocket 2 cents.
 
JackRab said:
If you buy 2 ATM puts and hedge it with 100 stocks, you have 0 delta.
Same if you buy 2 ATM calls and hedge it with -100 stocks
same if you buy 1 ATM call and 1 ATM put... (straddle)
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ok, i got it
you are using 100 stocks as your base for comparison

while i'm comparing: (2 calls + -100 stocks) with (2 calls + 2 puts)
since the stocks is the optional

thanks for explaining your context, JackRab
;]
 
water7 said:
ok, i got it
you are using 100 stocks as your base for comparison

while i'm comparing: (2 calls + -100 stocks) with (2 calls + 2 puts)
since the stocks is the optional

thanks for explaining your context, JackRab
;]
More...

So basically you are trading 2x the size with the 2 straddles compared to 2x hedged calls. That will be the difference.

2x hedged calls = 1 straddle
2 straddles = 4 hedged calls (or 4 hedged puts)
 
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