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NuclearPhysicist


Total Posts: 4
Joined: Nov 2019
 
Posted: 2019-11-18 12:23
Hello,

Does it makes sense to calibrate a LSV or SV model only to the vanilla smile only?

Thanks

nikol


Total Posts: 850
Joined: Jun 2005
 
Posted: 2019-11-18 14:10
Look at your question from different angle (due to duality between probability space and stochastic path).
Two things you look to:
-marginal forward distribution (european option smile)
-transition (conditional) probabilities (americal option smile and term structure of any smile)

Answer is, yes, it does make sense. The main question remains which products you want to price using those calibrations. Their path dependence is key.

NuclearPhysicist


Total Posts: 4
Joined: Nov 2019
 
Posted: 2019-11-19 08:43
I do find it nonsensical to calibrate them to the vanilla smile. Yet, I read people use as a backup a calibration to a term structure of implied vol.

Unless you can exhibit static or pseudo-static hedge of the exotic, I would say it does not make sense.
As you said, the vanilla smile only contains only the marginal distributions, and we know that if we know the densities of a process X at 2 dates T_1

NuclearPhysicist


Total Posts: 4
Joined: Nov 2019
 
Posted: 2019-11-19 08:49
I do find it nonsensical to calibrate them to the vanilla smile. Yet, I read people use as a backup a calibration to a term structure of implied vol.

Unless you can exhibit static or pseudo-static hedge of the exotic, I would say it does not make sense.
As you said, the vanilla smile only contains only the marginal distributions, and we know that if we know the densities of a process X at 2 dates
, it does not constraint much the conditional probability of X at T_2 knowing X at T_1.

nikol


Total Posts: 850
Joined: Jun 2005
 
Posted: 2019-11-19 11:49
what else do you have?

Counter-example: SABR is classic SV model but fits well to european smile.

In your question you did not mention whether your product is 1) "exotic" with 2) path dependence or not. Hence, pose questions correctly.

PS. you have button "Edit", dont make multiple posts.

ronin


Total Posts: 512
Joined: May 2006
 
Posted: 2019-11-19 12:01
@np,

I think you probably misunderstand the concept of calibration in finance.

All calibration does is making you consistent with the current prices of your hedging instruments. Nothing more, nothing less. It isn't some guide into the inner workings of finance.

You don't calibrate to exotic instruments because they are not sufficiently liquid to be used as hedging instruments. For many underlyings even a vanilla options surface is some voodoo thing with no basis in objective reality - and you want to calibrate to exotics.

Exotics are only of interest to make sure you aren't giving free money away. Other than that, they are at best a guidance, and at worst irrelevant.

Do you know how an actual trading desk prices risks they can't hedge?

"Put at least ten points for this one."
"Isn't that too expensive?"
"Who cares. If the client wants to pay it, good. If somebody else beats us to it, even better."


"There is a SIX am?" -- Arthur

Strange


Total Posts: 1597
Joined: Jun 2004
 
Posted: 2019-11-19 14:16
As per usual, I'll contradict @ronin here :)

It really depends on what you are trying to do. If your primary goal is to price/hedge products where stoch vol exposure is minor, you're mostly going to care about matching your vanillas. If you are dealing with instruments where vol of vol exposure is primary and there is a market, you have to spend some (or most) time trying to match that market and back out the parameters.

I.e. if you are dealing with light SPX exotics, you probably don't care much about matching options on VIX (and less liquid but commonly traded capped/uncapped variance spreads and var/vol spreads). If you are looking at knock-in-forward variance, you definitely want a model that at least somewhat matches the vol of vol markets.

Also, in some markets more "exotic" products are more liquid than vanillas and the tail starts wagging the dog.

"In Russia, every CDS ends in bullet payment"

ronin


Total Posts: 512
Joined: May 2006
 
Posted: 2019-11-20 12:56
> As per usual, I'll contradict @ronin here :)

Man - if we ever do agree on something, the phorum will definitely go nuclear...


"There is a SIX am?" -- Arthur

NuclearPhysicist


Total Posts: 4
Joined: Nov 2019
 
Posted: 2019-11-20 14:01
Apologies for the double message and thank you guy for your responses.

Are there products usable to calibrate spot/vol covariance?

@Strange: When you talk about exotic products being more liquid than vanillas, do you mean korean market or are there other?

ronin


Total Posts: 512
Joined: May 2006
 
Posted: 2019-11-20 21:27
> Are there products usable to calibrate spot/vol covariance?

Depends on what you mean.

In sv, the covariance matrix calibrates to the vanilla surface. Var of spot is level, var of var is smile, spot vol covar is skew.

But that's presumably not what you mean.

In slv, the covariances drive the stickiness of the surface. Sticky spot, sticky strike, sticky delta etc.

What exotic prices, and how many of them, would you need to be able to tell how much of your surface dynamics is sticky strike, and how much is sticky delta?

"There is a SIX am?" -- Arthur
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