Forums > Pricing & Modelling > Calculate volatility from straddle's price?

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 HockeyPlayer Total Posts: 125 Joined: Nov 2005
 Posted: 2017-09-28 18:29 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.
 HockeyPlayer Total Posts: 125 Joined: Nov 2005
 Patrik Founding Member Total Posts: 1353 Joined: Mar 2004
 fomisha Total Posts: 31 Joined: Jul 2007
 Posted: 2017-09-29 15:33
 NeroTulip Total Posts: 1010 Joined: May 2004
 Posted: 2017-10-02 03:44 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. "Earth: some bacteria and basic life forms, no sign of intelligent life" (Message from a type III civilization probe sent to the solar system circa 2016)
 fomisha Total Posts: 31 Joined: Jul 2007
 Posted: 2017-10-25 21:01 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 non-trivial to interpret the implied vol when you compare it to any "realized" quantities.
 logos01 Total Posts: 5 Joined: Jul 2014
 Posted: 2017-12-18 10:54 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 Total Posts: 1540 Joined: Apr 2004
 Posted: 2017-12-19 01:59 @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 Total Posts: 5 Joined: Jul 2014
 Posted: 2017-12-19 11:24 @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
 Posted: 2017-12-19 19:15 @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
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