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### UVM and financial software packages

Posted: **January 31st, 2019, 4:10 pm**

by **berndL**

Are there any commercial or public domain packages shipping the UVM Model (Uncertain Volatility model).

So far i havent seen one. I wonder if this is a sign of unpopularity. Or just verndors think there is no buisiness case for this model as project leaders dont like the relative complexity of the model (non linear -> must be explained to everyone which might be hard. simple black model is easier to sell)

### Re: UVM and financial software packages

Posted: **January 31st, 2019, 7:07 pm**

by **FaridMoussaoui**

I am not aware of such product. The resulting PDE equation from the UVM model is a non-linear Hamilton-Jacobi-Bellman equation. Have a look to this paper:

A computational scheme for uncertain volatility model in option pricing
If you don't have access to the paper, send me a message.

There is a specialised boutique doing volatility analytics called Vola Dynamics. Check with them:

https://www.voladynamics.com/what.html
There is also a project called

Premia by INRIA. I think there is a UVM model there (correct me if I am wrong).

### Re: UVM and financial software packages

Posted: **February 1st, 2019, 10:38 am**

by **Cuchulainn**

There's not much original research from universities in this area it would seem. Why? It presupposes some mathematical sophistication e.g. nonlinear analysis/PDE /ODE etc. Inertia, maybe. Research groups (in general..) in universities tend not to venture outside their 'research silos'

An exception is Paul who has published some work in this area. And Marco Avelleneda.

In EU universities, at least, it's unforunately IMO still business as usual BS PDE and ADI for MSc and PhD student degrees. One of my MSc students did a thesis on 1-factor and 2-factor ADE couple years back .

Where can you find quant developers who understand this stuff?

https://www.wilmott.com/wp-content/uplo ... 18_ade.pdf
Berndl,

The group at Wuppertal are doing good related work AFAIR.

### Re: UVM and financial software packages

Posted: **February 1st, 2019, 11:14 am**

by **Cuchulainn**

Song Wang was a PhD student of John Miller at TCD. He has many papers on nonlinear PDEs and approximations.

### Re: UVM and financial software packages

Posted: **February 3rd, 2019, 9:23 am**

by **berndL**

There's not much original research from universities in this area it would seem. Why? It presupposes some mathematical sophistication e.g. nonlinear analysis/PDE /ODE etc. Inertia, maybe. Research groups (in general..) in universities tend not to venture outside their 'research silos'

An exception is Paul who has published some work in this area. And Marco Avelleneda.

In EU universities, at least, it's unforunately IMO still business as usual BS PDE and ADI for MSc and PhD student degrees. One of my MSc students did a thesis on 1-factor and 2-factor ADE couple years back .

Where can you find quant developers who understand this stuff?

https://www.wilmott.com/wp-content/uplo ... 18_ade.pdf
Berndl,

The group at Wuppertal are doing good related work AFAIR.

Hi Daniel,

you know of implementation of your algorithm in commercial or pd libraries?

i once noticed someone did a master thesis implementing UVM in QuantLib. Up to today at least not in the official QL release though. And a fully fledged model doing portfolio optimization (mixing for example barrier optione, listed options and a delta position in the underlying of the options) seems to be in no library i have seen so far. Ok. Might be i havent seen enough.

I recently came reading across Pauls blog here on the site. I resume it as he started out using a tweaked black model (for transaction cost and discrete hedging for example) then moved on considering the UVM. But finally moved away from it back to the black model world. Leaving the model for risk management purposes. That beeing said i think this sounds like: ok let the risk managers do what they want (as they do it anyway). As long as they not torment traders with uvm worst prices. So this is also not a good basis for spreading the use of uvm.....

### Re: UVM and financial software packages

Posted: **February 3rd, 2019, 9:41 am**

by **Paul**

There's not much original research from universities in this area it would seem. Why? It presupposes some mathematical sophistication e.g. nonlinear analysis/PDE /ODE etc. Inertia, maybe. Research groups (in general..) in universities tend not to venture outside their 'research silos'

An exception is Paul who has published some work in this area. And Marco Avelleneda.

In EU universities, at least, it's unforunately IMO still business as usual BS PDE and ADI for MSc and PhD student degrees. One of my MSc students did a thesis on 1-factor and 2-factor ADE couple years back .

Where can you find quant developers who understand this stuff?

https://www.wilmott.com/wp-content/uplo ... 18_ade.pdf
Berndl,

The group at Wuppertal are doing good related work AFAIR.

Hi Daniel,

you know of implementation of your algorithm in commercial or pd libraries?

i once noticed someone did a master thesis implementing UVM in QuantLib. Up to today at least not in the official QL release though. And a fully fledged model doing portfolio optimization (mixing for example barrier optione, listed options and a delta position in the underlying of the options) seems to be in no library i have seen so far. Ok. Might be i havent seen enough.

I recently came reading across Pauls blog here on the site. I resume it as he started out using a tweaked black model (for transaction cost and discrete hedging for example) then moved on considering the UVM. But finally moved away from it back to the black model world. Leaving the model for risk management purposes. That beeing said i think this sounds like: ok let the risk managers do what they want (as they do it anyway). As long as they not torment traders with uvm worst prices. So this is also not a good basis for spreading the use of uvm.....

1. “Tweaked” suggests starting with something and making small changes. That is wrong. We started from first principles and ended with a non-linear version of BS.

2. We didn’t do much with UVM, that was Avellaneda et al.

3. Since UVM can only be used for exotics we came up with a non-linear model that could be used by both buy and sell sides.

4. An important reason why UVM or any non-linear model is not used is because of numerics. You can’t price or manage contracts one by one, you have to look at portfolios and that is numerically difficult.

5. I expect that there is a simplification to these non-linear models that makes them easier to use and keeps the main features.

6. We don’t think risk managers should do what they want. I have always believed that valuation and risk management should mostly be done at the same level.

7. We then looked at how robust BS is anyway. It turns out that it is very robust as long as you do some hedging and you have a diversified portfolio. The conclusion was that it is probably not necessary to worry too much about your vol model.

### Re: UVM and financial software packages

Posted: **February 3rd, 2019, 9:46 am**

by **berndL**

There's not much original research from universities in this area it would seem. Why? It presupposes some mathematical sophistication e.g. nonlinear analysis/PDE /ODE etc. Inertia, maybe. Research groups (in general..) in universities tend not to venture outside their 'research silos'

An exception is Paul who has published some work in this area. And Marco Avelleneda.

In EU universities, at least, it's unforunately IMO still business as usual BS PDE and ADI for MSc and PhD student degrees. One of my MSc students did a thesis on 1-factor and 2-factor ADE couple years back .

Where can you find quant developers who understand this stuff?

https://www.wilmott.com/wp-content/uplo ... 18_ade.pdf
Berndl,

The group at Wuppertal are doing good related work AFAIR.

Hi Daniel,

you know of implementation of your algorithm in commercial or pd libraries?

i once noticed someone did a master thesis implementing UVM in QuantLib. Up to today at least not in the official QL release though. And a fully fledged model doing portfolio optimization (mixing for example barrier optione, listed options and a delta position in the underlying of the options) seems to be in no library i have seen so far. Ok. Might be i havent seen enough.

I recently came reading across Pauls blog here on the site. I resume it as he started out using a tweaked black model (for transaction cost and discrete hedging for example) then moved on considering the UVM. But finally moved away from it back to the black model world. Leaving the model for risk management purposes. That beeing said i think this sounds like: ok let the risk managers do what they want (as they do it anyway). As long as they not torment traders with uvm worst prices. So this is also not a good basis for spreading the use of uvm.....

1. “Tweaked” suggests starting with something and making small changes. That is wrong. We started from first principles and ended with a non-linear version of BS.

2. We didn’t do much with UVM, that was Avellaneda et al.

3. Since UVM can only be used for exotics we came up with a non-linear model that could be used by both buy and sell sides.

4. An important reason why UVM or any non-linear model is not used is because of numerics. You can’t price or manage contracts one by one, you have to look at portfolios and that is numerically difficult.

5. I expect that there is a simplification to these non-linear models that makes them easier to use and keeps the main features.

6. We don’t think risk managers should do what they want. I have always believed that valuation and risk management should mostly be done at the same level.

7. We then looked at how robust BS is anyway. It turns out that it is very robust as long as you do some hedging and you have a diversified portfolio. The conclusion was that it is probably not necessary to worry too much about your vol model.

Hi Paul,

sorry for misinterpreting you then. This was not my intention

### Re: UVM and financial software packages

Posted: **February 3rd, 2019, 9:53 am**

by **Paul**

It’s probably a dead end to work directly on numerics for the UVM pde. I would think it better to do something asymptotic first, maybe small spread between low and high vol, or short expirations. See where that leads.

### Re: UVM and financial software packages

Posted: **February 3rd, 2019, 11:59 am**

by **Cuchulainn**

It’s probably a dead end to work directly on numerics for the UVM pde. I would think it better to do something asymptotic first, maybe small spread between low and high vol, or short expirations. See where that leads.

Who will step up to the plate?

Berndl,

I am not aware of any commercial packages. I can send the MSc thesis you. At the time we did notice a scarcity of baseline cases and mathematical theory.

### Re: UVM and financial software packages

Posted: **February 3rd, 2019, 12:45 pm**

by **FaridMoussaoui**

The are huge fields where HJB equations arise: optimal control theory, free boundary problems, level set methods...

### Re: UVM and financial software packages

Posted: **February 3rd, 2019, 2:53 pm**

by **Cuchulainn**

The are huge fields where HJB equations arise: optimal control theory, free boundary problems, level set methods...

Bensoussan, Lions, Aubin, Temam, Osher et al?

Not undergrad nor MFE.

### Re: UVM and financial software packages

Posted: **February 3rd, 2019, 4:51 pm**

by **FaridMoussaoui**

The are huge fields where HJB equations arise: optimal control theory, free boundary problems, level set methods...

Bensoussan, Lions, Aubin, Temam, Osher et al?

Yes.

### Re: UVM and financial software packages

Posted: **February 3rd, 2019, 5:02 pm**

by **Paul**

My guess is that valuing a portfolio of thousands of derivatives in thousands of dimensions with additional nonlinearities and hedged with thousands of other contracts and then optimized over those hedging contracts is going to be, er, offputting to most bankers. Especially since all they have to do to become rich is turn up.