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frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-10-17 11:22
Bergomi's model is a log-normal model for forward var. To account for skew of VIX options if I'm not mistaken I think he then 'hacks' the model.

I was wondering what happens if you start with a log-normal model for volswaps instead. It seems that then, because forward varswap will be a sum of log-normals, and hence not log-normal anymore, the VIX skew can be accounted for more naturally:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3471156

Note: no numerical tests. As I am a real quant I don't have Excel or python or any such thing installed on my laptop.

One man's Theta is another man's Gamma - Me

Strange


Total Posts: 1597
Joined: Jun 2004
 
Posted: 2019-10-17 18:32
Can we discuss a little, please? :)

E.g. I am trying to understand what dynamics that would imply along the term structure axis. E.g. if 1 month var changes by 1 vol, how much would the 3 month point change by?

"In Russia, every CDS ends in bullet payment"

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-10-19 06:26
I had to take the paper down as I discovered a 'little' consistency error ehemm..
Will let you know when it is fixed and answer your question then. Sorry.

One man's Theta is another man's Gamma - Me

Strange


Total Posts: 1597
Joined: Jun 2004
 
Posted: 2019-10-20 15:17
Thanks! FWIW, I think it's an interesting approach so I am hoping you can figure out the inconsistency.

"In Russia, every CDS ends in bullet payment"

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-10-21 14:37
Thanks for the encouragement.

I have fixed the consistency problem but since a fuck up is usually the mother of even more fuck-ups I am not going to put the paper online just yet.

It has actually become a different (but still log-normal) model, and still giving upward sloping concave skews for options on realized variance, and flexible term structures as well. I did 1-factor for now, but think higher factor model shouldn't be too hard.

Drop me an email and I will respond with the model description and simple Excel prices with skew. Would be nice if you could provide me with some data to test against.

One man's Theta is another man's Gamma - Me

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-10-22 14:23
.

One man's Theta is another man's Gamma - Me

ronin


Total Posts: 512
Joined: May 2006
 
Posted: 2019-10-24 15:00
Why did you remove it? I was looking forward to having a look...

"There is a SIX am?" -- Arthur

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-10-24 18:27
it's embarrassingly trivial.. but here it is for a limited time of 48hrs after which the file will self-destruct.

One man's Theta is another man's Gamma - Me

ronin


Total Posts: 512
Joined: May 2006
 
Posted: 2019-10-24 19:09
It's cute!

I especially like the reference list. Cool

In all seriousness, as the next step you should spend some time looking at the smile implied by the model. What does the smile look like, and how much do you need to tweak it to get it to look realistic?

E.g., I would expect that lognormality of variance implies some built-in persistency of the long dated smile, and this may generate issues with calibration to existing vol surfaces - like vol of var having to decay for long maturities, or something like that. But I am just guessing here.

That's always been my experience with PC's papers - lots of interesting ideas, but most of them don't survive close comparison to actual data.

"There is a SIX am?" -- Arthur

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-10-25 05:22
The reference list is the highlight of the paper, don't dis it. ;) If it ever becomes a serious work I will include Bergomi, Gatheral and other big hitters in the ref.

As you say I need to see if it can match the market. The charts in the note show it can produce substantial upward sloping skews depending on which parameter values I choose. But the lithmus test is actual market data.

I am out of work for several mths now so dont have access to OTC data.

If anyone can give me historical OTC implied vol data for variance options on SPX and/ or SX5E for testing purposes I'd be grateful!

One man's Theta is another man's Gamma - Me

ronin


Total Posts: 512
Joined: May 2006
 
Posted: 2019-10-25 12:39
Sorry to hear that.

I haven't been trading options in a while, so I don't have anything. But CME lets you download last few days' settlement prices, including settlement prices for options on futures - surely that is something to start with. CME website under Market Data > Settlements.

But even that is too aggressive at this stage. Just try playing with the shapes that come out of the model naturally and see how far you can swing them without breaking the model.

"There is a SIX am?" -- Arthur

Strange


Total Posts: 1597
Joined: Jun 2004
 
Posted: 2019-10-25 17:11
Send me an email - I'll ask my coverage for these if you like. Also, at some point lets discuss how the real world dynamics will be reflected in this model

"In Russia, every CDS ends in bullet payment"

Strange


Total Posts: 1597
Joined: Jun 2004
 
Posted: 2019-11-05 01:17
Sooo..
- I got some prices for options on realized var for you but the quotes are pretty wide
- I can send you some EOD prices for VIX options
- Most reliable market for optionality on realized variance would be var/vol quotes (which I have too)

Lemme know :)

"In Russia, every CDS ends in bullet payment"

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-11-05 08:22
Hey that's great! So I dropped you an email couple of days ago. Let me know if you received it. Would love to get the data you have, pls let me know what kind of options quotes you got: options on VIX and/ or options on realized variance / realized volatility.

Thanks a lot

One man's Theta is another man's Gamma - Me

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-11-06 15:06
.

One man's Theta is another man's Gamma - Me

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-11-08 13:49
Boring you guys one final time on this market model of mine which has almost led me into a depression.

- It is a multi-factor model now (you can basically choose the correlation you want between varswaps of different maturities)
- It accommodates instantaneous volatilities of short term varswaps are higher than that of long term varswaps. This is I believe also observed in practice.
- It generates positive upward sloping concave skews as long as the internal consistency conditions, which are also required for positivity of prices, are satisfied.

Here it is:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3483571

One man's Theta is another man's Gamma - Me

ronin


Total Posts: 512
Joined: May 2006
 
Posted: 2019-11-08 14:53
...and even the reference list is padding itself out.

Nice.

My main comment is why this focus on spot starting variance swaps? If you focus on forwards, you get something that is a lot like the libor market model for variance swaps. And that can make everything you are doing a lot simpler.

E.g. the fact that you can't split tenors - it's kind of obvious if you know this is a libor market model, but it isn't obvious for a generic model of spot starting variance swaps. Etc.

Also, I'd still really like to see some skews coming out of the model - not just term structures.

"There is a SIX am?" -- Arthur

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-11-08 15:48
Thanks ronin, reference list especially for you :)

First on the skew: the charts in the paper are skews, not term structures. X-axis the strikes (in variance terms), Y-axis the Black-Scholes IVs coming out of the model. You see that the skews are quite nice and these upward sloping concave skews are typically observed.

On the focus on spot starting: believe me I think I have tried every possible combination possible. In particular, if I model forward starts using displaced diffusion, and again with start and maturity date dependent shifts (so that you have even more freedom controlling the skew), I run into all sorts of issues around consistency. I am a stickler for internally consistent models, hence in the end I went for this one. But I may have very well missed something and directly modelling forward starts is also possible. I don't think so though, not with start/maturity date dependent shifts and basically full freedom in correlation structure.

One man's Theta is another man's Gamma - Me

ronin


Total Posts: 512
Joined: May 2006
 
Posted: 2019-11-09 20:15
> the charts in the paper are skews, not term structures

My bad, sorry about that. As they say - when eveything else fails, read the instructions...

> if I model forward starts using displaced diffusion, (...) I run into all sorts of issues around consistency.

Man - this is sounding more and more like BGM...

If you can resolve those issues, I think you have a pretty interesting model there. The mesh of multi-factor and spot starting will always look a bit patchy, but forward factors coming together would be really interesting.

"There is a SIX am?" -- Arthur

frolloos


Total Posts: 86
Joined: Dec 2007
 
Posted: 2019-11-11 10:34
> but forward factors coming together would be really interesting.

Yes you're right actually. Forward factors are the way to go.

arghhh, I give up, let's all just use the Bergomi model Smiley, there's a reason why that is the market standard.

One man's Theta is another man's Gamma - Me

ronin


Total Posts: 512
Joined: May 2006
 
Posted: 2019-11-11 11:51
Don't - you are onto something.

Where are the consistency issues coming from? Feel free to pm if you want to take it off the forum.

"There is a SIX am?" -- Arthur
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