# Uncertain volatility

Recently, I have encountered something called "uncertain volatility". Is it a popular concept in QF? Do practitioners use it nowadays? What are its pros and cons compared to e.g more familiar stochastic volatility models?

It is definitely used in practice:

• It affords a tractable way of pricing in a skew that is easier understood
• Avellaneda proves that a derivative priced under any stochastic volatility process that is bounded by (sigma_min, sigma_max) will produce a cheaper price than under UVM
• It is easily implemented into any PDE pricer at no calc time cost

Edit: just to challenge myself on third bullet point. Given how UVM has two vols, if you are using Euler (i.e. conditionally stable, first-order accuracy) you need to use the larger of the vols for the spatial step size to remain stable. This is not ideal for reasons of accuracy.

Rather than move to ADI (unconditionally stable, second-order) which is not simple to implement, i am a strong pusher of ADE (alternate direction explicit) which achieves the same stability and accuracy ADI but with the code- and computation-complexity of two passes of an Euler discretisation. Look up ADE by Daniel Duffy if of interest.

• "It is definitely used in practice" Really? I heard of the model but never heard of a bank that implemented it in front office. – AFK Apr 28 '17 at 23:59
• Implemented it, traded on it and have positions risk managed on it today – James Spencer-Lavan Apr 29 '17 at 6:58
• I disagree with the "definitely used in practice" as well. The model supposes the worst outcome possible and the range $\sigma_{min}$, $\sigma_{max}$ is hardly related to any intuitive range. Also the ADI/ADE comments make no sense for a 1 factor non linear PDE. The remark on the spatial step is not related to the implicit Euler scheme, but to upwinding. – jherek Nov 4 '19 at 13:09

To learn more about these type of volatility models, I suggest you to have a look on this research paper http://math.cims.nyu.edu/faculty/avellane/UVMfirst.pdf. They provide robust heding of volatility derivatives

The model is interesting, but rarely used in practice. One main reason is the choice of the range $$\sigma_{min}, \sigma_{max}$$. As Martini and Jacquier explain in their article The uncertain volatility model,

the price corresponds to the worst-case scenario where the Gamma changes signs exactly when the volatility switches regimes. This will hardly happen for real - even if it could.

The pro is to model the uncertainty of the Black-Scholes volatility directly. For exotics, this will give a much more pessimistic price than the regular Black-Scholes model used with the distinct volatilities $$\sigma_{min}$$ and $$\sigma_{max}$$. Wilmott shows a concrete example in one of his articles. The con is stated above.

• The answer above is incorrect. The model is often used in practice. – James Spencer-Lavan Nov 7 '19 at 11:07
• I provide a reference backing up a major shortcoming of the model. Another shortcoming is that it does not even capture the smile. I have also interacted with many banks and hedge funds, none used that model. I don't see any evidence from @JamesSpencerLavan to back the claim "the model is often used in practice". – jherek Nov 7 '19 at 16:45
• We obviously work in very different fields then. – James Spencer-Lavan Nov 8 '19 at 8:07