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.
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