
I understand how to take a bid in a call options and turn it into a bid in volatility terms. How do I take the straddle's bid price and turn that into a bid in volatility?
Will doing so be dangerous on expiry day?
Pointers appreciated, I was surprised not to see this discussed here or on quant.stackoverflow. 





Phun's answer here was helpful: Quant.StackOverflow
I'm still interested in comments about expiry day. 



Patrik

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As that answers says, as a straddle only has 1 strike level involved the only implied vol to talk about in the markets I've familiar with is the implied vol for that strike.
The closer it gets to expiration the less meaning will thinking about it as implied volatility be. If you make it more extreme  you're 10min before expiration, do you care about implied vol, or do you care about the the distance to the strike and the jump risk?
I find it useful to think about what you'd want to charge if you had to be the seller of any optionality and why that is. So if you have to sell a straddle 10min before expiry, you probably care a lot more about the distance to the strike and the likelihood of a jump of that size over the next few minutes. Talking about implied vol in an annualized standard deviation perspective is pretty meaningless way to think about the risk you'd get short. You can still come up with some number to stick into some formula to come up with the actual price you wanted to charge anyway, but it's not very helpful way to reason about it on its own.

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fomisha


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As T>0, both numerator and denominator >0, making the expression undefined. Therefore volatility becomes meaningless, and you are better off thinking only in terms of jump risk, as Patrik says. 
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fomisha


Total Posts: 34 
Joined: Jul 2007 


For European options, it's trivial to translate between the call, put, and straddle prices using PCP. If you have one, you can easily calculate the value of any other. The corresponding vol is the same for all of them. There is nothing dangerous in calculating an option price from a vol or v.v. It might be quite nontrivial to interpret the implied vol when you compare it to any "realized" quantities. 



logos01


Total Posts: 5 
Joined: Jul 2014 


a specific quantity of straddles is very close to a the initial price of a volatility swap. The exact quantity is described in Carr and Lee Robust replication of volatility derivatives. So by trading straddles you trade the future realized volatility approximately. Note that this is different from the implied volatility, which will be strike dependent. 




granchio


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@logos01: do you mean (1) that the PL of an atm straddle + the PL of delta hedging it until expiry is ~ equivalent to a volatility swap (in appropriate ratio) ?
Or do you mean (2) the naked straddle (i.e. without delta hedging)?
If (1), then it seems to me it's nothing new (there are early results showing the expected standard deviation of PL etc) but to me the main issue is that it will be heavily path dependent, wouldn't it? e.g. the straddle loses gamma, so PL basically stops as you move far away from the strike, the volswaps keeps on paying... 
I struggle to see how it could be (2) e.g. take a process with no drift and high vol... but if it is then it's interesting.

"Deserve got nothing to do with it"  Clint 


logos01


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Joined: Jul 2014 


@granchio, the original question is how to convert a straddle bid to a vol bid. So it is (2), without delta hedging. And the quantity is sqrt(pi/2)/S0 straddles at strike K=S0 




granchio


Total Posts: 1540 
Joined: Apr 2004 


@logos01: just to clarify:
leaving aside the original question,
are you saying that the Carr shows that the expected PL of a naked straddle is similar to the expected PL of a volatility swap ?
EDIT: if you add an email to your profile I'll PM you

"Deserve got nothing to do with it"  Clint 

