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DocToc
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Joined: January 20th, 2010, 9:32 am

norm swaption volatility

September 22nd, 2012, 2:38 pm

a few short questions about the above concept:why is normalised vol so important - i.e. why do most brokers etc pay much more attention to this qty rather than black vol..?It is apparent that black vol is directly related to the level of rates so that higher swap rates such as 1m30y tend to have lower black vols than say 1m5y mainly because of the leverage effect..Obviously this impairs you from being able to see relative value between these trades (in a vol sense because they'd just be straddles anyway), therefore it is quite important to have a measure of value indep of the level of rates - this is one of the reasons normalised vol is important right? (Correct me if I am wrong)For gamma trades such as 1m10y normalised vol is a nice qty to give you annualised break evens or daily break evens as well..How is it useful for Vega trades such as 10y10y vs 10y30y..?However even though individually these make sense and are reasons to look at normalised vols i cant really merge the two points together..? Some people like to normalise their deltas and vegas..at the moment with rates so low is there really a distributional justification for this? if not, is this just a preference? Also, say I have a 10y10y swaption straddle, in a normal model this trade has no delta. therefore, locally (at least) it is only a function of normal vol..Is this another reason why bp/normalised vol is quite important when trading straddles? In a black model because of the lognormal distributional assumptions the straddle immediately has a +ve delta (even though this is relatively small) it is still an imperfect measure..Let me know if these assertions I am making are correct or just misguided as I seem to get a lot of conflicting/incorrect or just misleading comments where I work.Thanks
 
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lepolo7
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Joined: September 20th, 2010, 5:42 am

norm swaption volatility

September 28th, 2012, 4:23 am

the normalised vol is important in the gamma area ie for options with a maturity lower than 2 years.The curve is so steep in the short term, it is better to look at the bp per annum vol than the log vol, with the log vol, the standard deviation of the underlying is proportional to the forward.the difference between norm vol on 1m30y and 1m5y comes from the fact that the 30y is usually less volatile than the 5y (kind of mean reversion, just check it with the historical vols)The normal vol is much less important in the vega area (options above 2 y maturity)The delta Log is completely wrong for ATM straddles, especially with low rates/high log vols, using norm vols will give a better result : zero. In fact the ATM delta is between -3% and +5%, but you have to use a SABR model to compute itThe norm vol is usefull in the gamma area where you will be able to perform relative value analysis and compare the implied and historical vols, it is less effective for the vega area, above 10 year, witht eh actual low rates, the probabilities of negative rates will exist with a normal model