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### origins of interest rate skew

Posted: **February 5th, 2011, 10:23 am**

by **unkpath**

I would like to put together a collection of documents, papers, book discussing the causes of interest rate skew for USD. I am thinking of various macro causes and technical effects.Any references?Many thanksnkpth

### origins of interest rate skew

Posted: **February 5th, 2011, 4:19 pm**

by **unkpath**

So, it is known that at times there are certain prevalent actions in the market that will be interpreted as vol/skew drivers. Say, there is some mortgage convexity related market activity in european swaption space, then it is known that this can affect the vol surface. I wonder where such market effects on the vol surface are documented, qualitatively and quantitatively.Thanks.

### origins of interest rate skew

Posted: **February 5th, 2011, 4:52 pm**

by **Martinghoul**

I am not aware of anyone documenting such effects and trying to catalogue them rigorously. It's a whole bunch of anecdotal knowledge and intelligence, based on mkt experience.

### origins of interest rate skew

Posted: **February 5th, 2011, 11:55 pm**

by **Gmike2000**

the skew is influenced by supply and demand on the micro level (the level of the mkt maker)from a macro perspective, however, the skew tends to follow the (probability weighted) local vol that the fwd realizes during the life of the option. for example in the current low rate environment, (normal) vol compresses as the fwd approaches zero (and vice versa). the skew reflects that behaviour, of course. if it didn't, there would be an opportunity for vol arb.

### origins of interest rate skew

Posted: **February 6th, 2011, 2:51 pm**

by **unkpath**

hi m, I think that dealer research is probably full of these considerations. So my question is if people remember some very relevant piecespublished here and there?For example I would cite a paper by Fei Zhou, Lehman, Volatility Skews, 2003, which certainly discusses some skew folklore.Gmike, right, so supply and demand on the micro level is an effect of the causes I am interested in. Also, can I ask you to elaborate a bit on what you explain and which sounds very interesting. Do you mean to say that skew is the future expectedlocal vol realized by the fwd? Can you restate that idea a bit more precisely? So imagine, you take the implied vol at some OTM strike today. What is that the weighted average over?As to low rate environement. Are you saying that skew is basically lognormal in such an evironement?Thanks for your comments guys, v. interesting.QuoteOriginally posted by: Gmike2000the skew is influenced by supply and demand on the micro level (the level of the mkt maker)from a macro perspective, however, the skew tends to follow the (probability weighted) local vol that the fwd realizes during the life of the option. for example in the current low rate environment, (normal) vol compresses as the fwd approaches zero (and vice versa). the skew reflects that behaviour, of course. if it didn't, there would be an opportunity for vol arb.

### origins of interest rate skew

Posted: **February 6th, 2011, 3:12 pm**

by **Martinghoul**

I don't think the zero bound effects on skew are that interesting, personally. Given that we have seen what happens in the yen mkt, you can make all sorts of predictions and tweak your models accordingly. For instance, changes to SABR beta and variations of absorbing SABR are used by many at the moment to price recvr skew. What's more interesting is payer skew and the various effects one can observe there. For instance, in the yen mkt one can observe what some people call "hypernormal" payer skew. Periodically, I have seen bids for very high strike payers come and go in the USD mkt. Is that just price-insensitive demand from non-fixed income investors or is the USD mkt transitioning to a Japan-like steady state? Who knows...

### origins of interest rate skew

Posted: **February 6th, 2011, 4:46 pm**

by **Gmike2000**

hi unk, what i meant was just looking at a very simple measure of realized vol and plotting that versus the level of the forward, you see that currently vol rises when fwds go up and vol falls when fwds come down. i am talking bp vol (normal vol). so all i meant was that the skew has to reflect that behaviour, so e.g., it is natural that payer skew should currently be higher than receiver skew and indeed it is what you can see in the markets. some people say skew is at historical extremes, but it is just because rates are so low and the fwds are behaving this way.

### origins of interest rate skew

Posted: **February 9th, 2011, 10:02 pm**

by **gammaslide**

hi mike,you mentioned plotting realized vol vs the fwd..shows vol rises when fwd go up and vice versa.Taking eur swaptions as an example definitely back in end 2008 when the fwds were rallying 15y15y etc.. vol went through the roof (e.g.3m30y vol..)Isnt the implied vol of OTM receiver higher in eur than OTM payer due to the street being short otm receivers from dutch pension funds?Not the case in GBP and USD right? In GBP is payer skew just high because of rate shocks that happened ages ago?thanks guys

### origins of interest rate skew

Posted: **February 9th, 2011, 10:04 pm**

by **gammaslide**

and by the way quick question..are all usd ir options desks using sabr most likely to have Beta at 0 at the moment?

### origins of interest rate skew

Posted: **March 9th, 2011, 8:16 pm**

by **gammaslide**

Hi..I was just browsing and realized I hadn't quite got a full picture on my question before..also mike you mentioned "just looking at a very simple measure of realized vol and plotting that versus the level of the forward, you see that currently vol rises when fwds go up and vol falls when fwds come down. "I'm struggling to understand whether this should be reflected in higher payer skew or if this is an expected long-term relationship then it should be reflected in an upward sloping backbone (sabr).I know this is not possible mathematically in the sabr approx, but shouldn't a good model be able to accommodate this..?Appreciate your helpthanks

### origins of interest rate skew

Posted: **March 10th, 2011, 2:46 pm**

by **Gmike2000**

This is a very good question and I was often wondering about the same thing. In a way it should be reflected in both the skew and the backbone, but i really don't know to what extent. Certainly, the backbone must reflect this behaviour. But also the skew must reflect the fact that vols would realize at higher levels if the forwards move to high strike regions. And vice versa. My suspicion is that SABR models (and people who naively use SABR) only care about the "local" behaviour of vol and fwd (local meaning within a std deviation of ATM...at most). And then they disregard that their skews do not make sense "globally", meaning they trust SABR to extrapolate correctly to very high and very low strikes. But SABR extrapolates incorrectly. I know many people are aware of this and correct for that. But I am also sure many do not correct for it.

### origins of interest rate skew

Posted: **March 11th, 2011, 7:42 pm**

by **gammaslide**

gmike exactly.I think the limitation of not having an upward sloping backbone, exacerbates the payer skew wouldnt it?A backbone is a long-term relationship between atmvols and fwds, but if over next two years we have a gradual blow-up then higher fwds mean higher atm vols.And it leads me to ask why do people use a zero beta in low rates like yen, if anything isn't a flat backbone (beta = 1) the next best thing?

### origins of interest rate skew

Posted: **March 12th, 2011, 11:06 am**

by **Martinghoul**

This is well known to most reasonably sophisticated mkt participants. As to the choice of beta, I have seen 1 used for JPY.

### origins of interest rate skew

Posted: **March 12th, 2011, 12:40 pm**

by **gammaslide**

QuoteOriginally posted by: MartinghoulThis is well known to most reasonably sophisticated mkt participants. As to the choice of beta, I have seen 1 used for JPY.martin is that an exception? I'm trying to get a feel for the level of subjectivity in choosing the underlying level of lognormality/normailty in their distribution by imposing this parameter on their sabr model.

### origins of interest rate skew

Posted: **March 12th, 2011, 1:50 pm**

by **Martinghoul**

QuoteOriginally posted by: gammaslideQuoteOriginally posted by: MartinghoulThis is well known to most reasonably sophisticated mkt participants. As to the choice of beta, I have seen 1 used for JPY.martin is that an exception? I'm trying to get a feel for the level of subjectivity in choosing the underlying level of lognormality/normailty in their distribution by imposing this parameter on their sabr model.It's not an exception, as far as I can tell. Subjectivity is always present, because parameter choice is made to allow you to intuitively understand PNL.