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pj


Total Posts: 3415
Joined: Jun 2004
 
Posted: 2018-11-06 19:08
Recently got involved into (erhm) a discussion over the
market practices of the swaption cube interpolation.

I was told that Free AKS SABR
was the standard way to deal with the current negative rates.

Somehow, I wasn't convinced.

So for those in serious business (not of the China lost wax casting factory or Best concise book on telecommunications)
and who are still visiting this phorum.

What would the recommended way of creating a volatility cube from
normal volatility surfaces and (optionally) normal cap surface be?

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

nikol


Total Posts: 553
Joined: Jun 2005
 
Posted: 2018-11-06 22:58
Please, articulate what bothers you in the approach.

What if you think of IR as an expected rate of cash flow arrival/departure to/from your book? How will that change the concept of negative rates?

pj


Total Posts: 3415
Joined: Jun 2004
 
Posted: 2018-11-07 06:51
Wait, I am not against the negative interest rates, nor
the volatility cube.

I am just asking, what method
the people in the know are using to build it.
The cube from normal volatilities that is.

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

frolloos


Total Posts: 48
Joined: Dec 2007
 
Posted: 2018-11-07 10:55
I would be interested to know the answer to pj's question as well. Recently there have been some papers on local and local stoch vol for rates, but I am not sure those are actually or already being used for the swaption cube.

ronin


Total Posts: 361
Joined: May 2006
 
Posted: 2018-11-07 12:39
I am not particularly in the know these days, but you haven't got any other replies...

This normal/lognormal thing isn't particularly new. I saw something like that 15 years ago when I was a junior quant - the bank where I worked had a model with lognormal high forwards, normal low and negative forwards, and some smooth splicing in between. It wasn't even new then.

But it wasn't the market standard. The market standard seemed to be vanilla SABR, then shifted SABR, then no idea - I have been doing other things in the meantime.

"There is a SIX am?" -- Arthur

nikol


Total Posts: 553
Joined: Jun 2005
 
Posted: 2018-11-07 15:21
@pj

I didn't say 'negative rates' is a misconception (sorry for using word 'concept' then).

As @ronin mentioned the most appealing 'traditional' model is a mix of normal (at around zero) and log-normal (at rates larger than 200-500 bps).

Log-normal at zero produces singularity, which is difficult to comprehend.

pj


Total Posts: 3415
Joined: Jun 2004
 
Posted: 2018-11-07 16:25
what about shifted lognormal volatility surfaces with SABR?

(if I understand well, linear is gone out of fashion)

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

ronin


Total Posts: 361
Joined: May 2006
 
Posted: 2018-11-07 17:05

Yes, that's what I meant by "shifted SABR".

Instead of S^beta, it's (S-S0)^beta.

That was more-or-less standard the last time I looked, a few years ago. I don't know if anything new came up since then.

"There is a SIX am?" -- Arthur

mtsm


Total Posts: 220
Joined: Dec 2010
 
Posted: 2018-11-07 19:36
Shifted SABR is pretty much market standard if you ask me. Look no further.

In the SABR world, no piece of work outside of the original Hagan work really made it to the top. I feel I have discussed this so many times and I am not even an expert, but basically the bottom line is that these shitty parametric stochastic vol models are merely interpolation devices.

pj


Total Posts: 3415
Joined: Jun 2004
 
Posted: 2018-11-08 11:23
@mtsm

Thank you very much. One more (final) question.

How the shifts are determined in real life?
A predetermined shift per currency?
Or something more convoluted?

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

nikol


Total Posts: 553
Joined: Jun 2005
 
Posted: 2018-11-08 11:29
Shifted SABR is applicable alongside strike.

Is there any standard method to interpolate across tenor of underlying and swopt maturity?

ronin


Total Posts: 361
Joined: May 2006
 
Posted: 2018-11-08 11:57
> How the shifts are determined in real life?

That's up to you and your data set. Either you calibrate all parameters at the same time, or you freeze some and calibrate others, or what ever else you feel like today.

There is no "market standard calibration method".

"There is a SIX am?" -- Arthur

pj


Total Posts: 3415
Joined: Jun 2004
 
Posted: 2018-11-08 13:49
I have heard of CHF volatility shift hardcoded to 2% used.


The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

ronin


Total Posts: 361
Joined: May 2006
 
Posted: 2018-11-08 14:18

+2%?

Unlikely. Maybe -2%.

But I don't have any (recent) direct knowledge of CHF.

"There is a SIX am?" -- Arthur

nikol


Total Posts: 553
Joined: Jun 2005
 
Posted: 2018-11-08 17:30
You can try inflation rate as it is stipulated by Fisher.
https://en.wikipedia.org/wiki/Fisher_equation

Inflation can be positive and negative (deflation).

In general IR has 5 components:
- risk free (flat constant)
- inflation/deflation --> this is the main source of shift
- cost/revenue of liquidity -> locally it is inventory thing and globally it is systemic factor vs global defaulted cash amount/rates
- cost of credit (~CVA/ELoss) / always positive
- cost of capital (risk of all above) / always positive

Personally, I dont like 'calibration' of the shift. It must be exogenous observable parameter, i.e. inflation.

ronin


Total Posts: 361
Joined: May 2006
 
Posted: 2018-11-09 22:40
@nikol, just no.

The problem with cut-off at zero is that it is too aggressive. Your cut-off at inflation forwards would be even more aggressive. It would make the problem worse, not better. Real rates actually turned negative long before nominal rates - by more than five years, if I remember correctly.


"There is a SIX am?" -- Arthur

nikol


Total Posts: 553
Joined: Jun 2005
 
Posted: 2018-11-10 00:02
Yes, actual rates became negative long before it started to be a problem for the banks.
But real rates are the actual 'zero' (ground). When you set it, everything becomes log-normal.

Negative rates in EU market indicated that the money market contracted due to demanded increase on capital and liquidity buffers for regulated institutions. With increase of capital (and liquidity) requirements more money mass got locked up although formally the money mass was still circulating around.

Look at evolution of capital ratio and liquidity coverage ratio. These are vessels full of illiquid liquidity:
banking-sector-performance

At the beginning NSFR shortfall was 1.8 trillion. At jun-17 it is 'tiny' 50b. Same is with LCR shortfall. To get liquidity banks are forced to fill HQLA's with govies, which 'pay' negative rates (price of liquidity).

PS.
Another mechanism of negative rates: in the situation, when assets suitable for HQLA (govies) are limited, they becoming "hot" and overpriced, hence negative rates.

5 components of IRates are part of the rate quoted to customers. Banks account these components in the pricing.
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