machine learning and uncertain volatility model?

[deeds]

@ronin - would suggest there is likely arbitrage...maybe not in the way discussed here

- saw Bruno Dupire last night talking about available arbitrage in parameter space...an old idea he was recapping, maybe with new examples (probably to fill a slot in the very pleasant monthly bloomberg quant series in NY)

- at a high level

- since market participants use the same models, reparameterization from date to date leaves convexity on the table

- very roughly, analytical procedure is to draw convex hull around skew region to allow hyperplane separation of profit and loss regions and identify a point that always ends up in profit (am trying to get the slides)

- demonstrated in several products and models, including SABR, Heston...in addition, one of the illustrations was that both sticky strike and sticky delta have this vulnerability

- very pleasant...will share reference when/if i find, if any interest

[ronin]

@deeds,



Definitely - would love to see that.



The problem with these regions that always end up in profit is that you never get the opportunity to trade them...!



But I'd be interested in having a look.

[Strange]

@ronin

"But in all seriousness: if you don't know which way your exposures lie, should you really be trading it?"

It's less about exposures being unknown and more about exposures changing with time/underlying which is hard to deal with. For example, take a simple cliquet - you have the local caps (long vol) and a global floor (short vol) but depending on your path, level of vol and slope of the skew one can dominate the other. The usual approach is to overhedge some of the parameters of the structure itself (e.g. moving the cap or the floor against you). UVM seem to offer a nice alternative to the overhedge approach.



PS. after tinkering with it, I decided against using it, it's just too unstable.

[ronin]

I'm wondering if that is such a great example.



The buyer is long low strike vols, short high strike vols. The strikes reset so he doesn't know exactly what strikes he is long and short at any point, but he knows he is long low strikes and short high strikes.



Ergo, he bumps the skew down. It marks down low strikes that he is long, at least relatively to the higher strikes that he is short. The position is marked conservatively.



I'm racking my brain trying to think of a payout where you would genuinely have no idea where you are long and where you are short. Some sort of cliquet-resetting range accrual? Nope - that's a simple smile bump. Lookbacks? Nope, that's just like the cliquet. Passport options? Nope - the details are hazy, but the overal exposure is clear.



And we already deep in the territory where you wouldn't be using simple conditional vol scenarios anyway.



Just don't see it.

[Strange]

The local cap is being reset periodically, thus creating pockets of long convexity after each reset. On the other hand, the global floor is with respect to the value of the portfolio. The uncertainty of the exposure comes from that path dependency. Take, for example, a very plausible scenario where you are resetting into your local cap but the whole portfolio is already at the global floor. It's not clear what convexity profile this position presents, it's going to depend on many things (e.g. time to maturity).



There is a bunch of other structures (like some fairly common autocallbles) where the value of the barrier exposure changes with time and spot, making them very hard to track. When managing a book of these, usually people overhedge the barriers one way, check the value of the overhedges on regular basis and change the direction of the overhedge when the value flips.



FWIW, none of these structures are managed using UVM. I am simply illustrating that in plenty of cases you do not know which way the exposures lie and up doing various tricks to deal with that problem.



This all aside, people use UVM for mostly-vanilla call spreads on illiquid names. These are a byproduct of the convertible bond issuance and are pretty long dated (3-6 years). Because of long maturity and some mismatch in expiration, it's hard to know if you are simply dealing with a skew position or is it going to be a pure convexity position at some point. So for a name that shows no visible spot/vol correlation, it's much easier to come up with max and min vol levels and back out the sk10 number to quote.

[ronin]

I think we are talking cross purposes here. The skew exposure in your cliqet example doesn't flip, so you don't need some on-the-fly adjustment. Same thing with autocallables.



And where the exposure does flip, like corridors, that just tells you that your primary exposure is smile rather than skew.



I am happy to concur with call spreads locally reducing to just gamma before expiry.



So is that basically it - vanilla call spreads? OK. I guess...

[Strange]

Darn, I was not expressing my thoughts clearly and we ended up in the weeds.



1.What is the general the idea behind UVM?



(a) in absence of magical hedges and MtM, your "actual" risk is gamma

(b) at inception sign of convexity exposure is uncertain due to path dependency

(c) so you overhedge long gamma by managing it at low vol

(d) and overhedge short gamma by managing it at high vol

(e) the cost of these overhedges is discounted to today and included in price



That thought process makes it sort of a reasonable universal model. However, it does make some implicit assumptions:



(a) you are in position to dictate pricing to you can manage your position conservatively

(b) you are living in the world where you do not really trust the existing vol market and can avoid marking to market



Of course, both assumptions are usually false, thus limiting the usefulness of the model.



2. Why/when is pricing and managing on UVM is better than making explicit vol and skew bumps?



(a) UVM is a conservative model for managing uncertain convexity exposure (see above)

(b) even in vanilla options, a combination of vanna and theta can quickly flip your convexity exposure

(d) you can imagine simple cases when pricing with both conservative vol and skew will end with unpleasant management path



Imagine that you are selling a vanilla 5 year 100/150 call spread (let's keep it simple):

(a) you think the fair vol is 75 (stock's been realizing anywhere between 50 and 100 vols)

(b) at inception, your exposure is long vega and short skew

(d) you price it with bumped-down vol (let's say 50) and conservative skew (let's say sk10=3.5, if you can get away with it)

(e) a volatile selloff ensues, you end up short vol and managing the position at bumped-down vol - you mark vols up and take a loss

(f) UVM would have forced you to manage the initial position at high vol since it's short gamma



Does it make sense now?

[nikol]

jeez.



Just one though/idea:



Can't you formulate this whole thing in terms of HJB-equation with switching vol up-down threshold used for hedging?



If I imagine this process correctly, it resembles me Stoikov-Avellaneda MM-formulation.. (Avellaneda again is not for nothing, I guess)

[ronin]

Yeah. This is beginning to sound a bit like that story about NASA spending millions on a space pen, and the Russians using a pencil.



Which, by the way, isn't true - https://www.scientificamerican.com/article/fact-or-fiction-nasa-spen/



But still.



Yes, you could hedge a call spread with some massively over-engineered contraption like this. Or, you could just book each leg with the appropriate vol bump.



Up to you, really.

[willis]

How do you know the appropriate vol? Or more basic, what delta to run?



[edit] in response to ronin's response -



"Yes, you could hedge a call spread with some massively over-engineered contraption like this. Or, you could just book each leg with the appropriate vol bump."