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frolloos


Total Posts: 99
Joined: Dec 2007
 
Posted: 2020-01-13 10:05
I can have multiple LSV models that exactly fit the same observed vanilla smile. I can then choose one of these perfect fitting models (or all of them) to then price and hedge exotics. *Slight* issue is for exotics I will have multiple prices and hedges that are all consistent with the vanilla smile.

Or I can choose a robust approximation for the exotic in question, and if it is a good enough approximation it is probably almost unique, and almost model independent. It may under or overvalue the derivative because it doesn't take into account model specific parameters and forms, but at least I know that and I can add whatever premium I think is applicable for the product.

What I mean is for exotics, including vol derivatives, or in my case especially vol derivs, I would probably go for the simple robust price and hedge instead of a particular model. I do not understand the obsession with specific and fancy models - maybe because they are too technically challenging for me, to be fair. But honestly, I really think robust approximations are also just more elegant.

What is the general view on this here and among practitioners on the street?

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

nikol


Total Posts: 915
Joined: Jun 2005
 
Posted: 2020-01-13 10:32
If your models fit static quotes equally well, then look into their comparative dynamics (hedging, PnL etc) to see the difference. Remember premise of SABR paper. Authors have demonstrated where local vols fails and how their model will help.

Strange


Total Posts: 1620
Joined: Jun 2004
 
Posted: 2020-01-13 21:03
It's a very tricky question and pretty much anyone who has ran an flow exo book has faced some form of this problem. My preference has been to use specialized models/approximations for each product, plus product-specific overhedges if there is a good intuitive overhedge. Most of the arguments for "one great model" is the ability to extract relative value which I found it be very fishy.

Also, for liquid pricing you want to be matching the market, even if the market is wrong. Unfortunately, that means that you want to own, calibrate and use a market-consensus model whenever someone is asking for price of something that actually has a market once in a blue moon (e.g. KO/FI fwd variance).



"In Russia, every CDS ends in bullet payment"

frolloos


Total Posts: 99
Joined: Dec 2007
 
Posted: 2020-01-14 16:02
Thanks guys - I am thinking / mulling over your answers. Probably my question is too broad, as the choice of model or approximation, right or wrong, is likely to depend on what desk you're at, what you're trying to do, what regulations you fall under, what product you're trading, and how your existing book looks like. Quite a lot of parameters there.

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

nikol


Total Posts: 915
Joined: Jun 2005
 
Posted: 2020-01-14 17:02
"Strange" is correct in one thing - missing information by desk traders. They might be like famous blind wisdom men investigating an elephant and touching only one part of his body.

How do you account for simple fact that, for example, (A) nearly 100% of certain exotic IR-products are sold by banks to private customers meaning that banks are short? Is this specific market in equilibrium such that its implied IR-vols can be equally applied to the other market (B) where banks are vega-short in EQ/IR-hybrid exotics and where EQ-delta is fully hedged/protected? And, to make it worse, the banks think that they their IR-delta exposure in exotics offsets their (C) balance sheet gap. AND quants/traders from all three (A,B,C) desks, those with specific knowledge, vaguely know each other (for whatever reason including Chinese Walls), while high management thinks that all three desks work in unison and offset each other's exposures nicely.

Offset thing still might be the case (with risk of not knowing), but huge directional bets in IR-exotics will introduce inventory-based systemic shifts to the prices. Some narrow looking trader might see such biases as an opportunity.

Strange


Total Posts: 1620
Joined: Jun 2004
 
Posted: 2020-01-14 23:01
"Offset thing still might be the case (with risk of not knowing), but huge directional bets in IR-exotics will introduce inventory-based systemic shifts to the prices. Some narrow looking trader might see such biases as an opportunity."

Prevailing flows, desk positioning and prevailing positioning are the few bits of information that the dealer desk actually has (and other people don't). A good exotics trader will take both into account whenever he's forced to price things and should skew his markets accordingly (of course, it's common not to have a choice and being forced to trade, but still). If someone is leaning his book in that direction, it's likely an intentional bias. Of course, the model might be an excuse - "oh, var/vol is much cheaper in MY model so I sold a few million Vega" etc.

As a side note, how these trades impact the banks balance sheet, regulatory capital should not really be the traders concern. The desks job is to make money within the constraints such as funding levels, risk limits etc. The attenuation of the exposures at the institutional level should be dealt with via things like funding costs, capital charges etc. I've yet to see that done well, to be honest.

"In Russia, every CDS ends in bullet payment"

ronin


Total Posts: 527
Joined: May 2006
 
Posted: 2020-01-16 12:24
@frido,

I am wondering if you have something backwards here.

Vanillas are the same thing as terminal distributions / unconditional forward distributions. If you have an exotic that only depends on unconditional densities, you can statically replicate it with vanillas and everybody is happy. And any two models that agree on the vanillas will agree on your exotic as well, modulo issues.

If you have an exotic that depends on something else - conditional densities, marginal densities etc - then you have to price and risk manage that dependence.

With that in mind, what does "robust model-independent approximation" mean to you?

To me, it sounds a lot like what the rest of us call a "model".


> at least I know that and I can add whatever premium I think is applicable for the product.

I don't think anybody would argue with that. Rule 1 of trading exotics is "hedge what you can, reserve for what you can't".


"There is a SIX am?" -- Arthur

frolloos


Total Posts: 99
Joined: Dec 2007
 
Posted: 2020-01-16 16:12
>With that in mind, what does "robust model-independent approximation" mean to you?

>To me, it sounds a lot like what the rest of us call a "model".

I guess it depends how you define a "model". First of all, in the beginning there was a model, and then we all know the model started leading its own life which made us all smile. So let's take as given the observable vanilla smile.

Given that smile, for path-independent claims, Carr-Madan can be used to hedge a claim without making any further assumptions. That is how I like to look at model-independent.

Next, let's look at a path-dependent claim, such as my long-time obsession the volatility swap. Turns out, it is model-independent too, to a large extent at least. Started with Carr-Lee's work, but a bit impractical given the infinite number of options to be traded daily, and now with the zero vanna stuff I did perhaps a bit more practically feasible (see also my recent post today in books/research paper forum).

Knowing this, would I now use a model to price and hedge a volswap? Probably not, why would I if I know that I will be approximately right (and maybe more right than quite a few models) by just using the info in the vanilla smile.

I am basically wondering, whether other exotics (path-dependent ones) really require a model as well. Of course a model such as a particular LSV implementation is required for exact fit to the vanilla market, but that's not so interesting (albeit necessary maybe).

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

ronin


Total Posts: 527
Joined: May 2006
 
Posted: 2020-01-16 19:16
Well done on the paper! Will read it in detail later.

I think I get your point. But the leap from "volswaps are path independent" to "all exotic payoffs are path independent" is pretty big. Too big, in my book.

When I was trading this stuff, our books were full of autocallables and reverse convertibles. It felt like we never traded anyting else. I imagine most retail facing trading books still are still like that. And these are definitely path dependent.

"There is a SIX am?" -- Arthur

frolloos


Total Posts: 99
Joined: Dec 2007
 
Posted: 2020-01-16 19:22
Yes, it is a big step. Some exotics then :) I think forward starts, timer options, barriers are perhaps manageable, but there is another in addition to the callables you mentioned for which I currently have no clue at all how to simplify without losing too much accuracy: American options. If someone solves that we can all go home and drink beer.

And thNks for wanting to read the paper but you might want to wait until I have updated it with the derivation of the improved hedge ratio and also some more numerical results.

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

Strange


Total Posts: 1620
Joined: Jun 2004
 
Posted: 2020-01-17 05:02

I thought we are talking about flow exotics here. I.e. index vol desks have dedicated traders who only trade non-standard vol products and stuff like vanilla barriers. In some places it falls in the hands of index vol traders instead and it would be combined with the vix and variance books. Maturities are short and the products are fairly standardized. As a result markets for these things are highly efficient and EV is very thin (e.g. conditional var trades as tight as vanilla variance). Having ran a book like that, I would always err on the side of dedicated models/approximations and optimizing each product separately.

It's a very different business from proper exotics which mostly involves structured notes, long-dated products with hard-to-value risks. These products are much more complex and require a generic model that can be flexibly fit all kinds of payoffs. However, the amount of juice in these products is also much higher.

"In Russia, every CDS ends in bullet payment"

ronin


Total Posts: 527
Joined: May 2006
 
Posted: 2020-01-17 21:33
That explains everything. I did trade actual exotics, but I never traded vol derivatives. So to me this was all "wait, what?"

I absolutely agree with dedicated models for that sort of book. Like you woldn't use American SLV Monte Carlo to manage a book of vanillas, you wouldn't use it here either.

"There is a SIX am?" -- Arthur

frolloos


Total Posts: 99
Joined: Dec 2007
 
Posted: 2020-01-18 08:05
Btw, @ronin: sent you the paper per email with updates and numerical experiments. Will be online @arXiv on Monday anyway.

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

ronin


Total Posts: 527
Joined: May 2006
 
Posted: 2020-01-18 23:14
Got it, thnx. Will look through.

"There is a SIX am?" -- Arthur
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