Uncertain Volatility

This project is based on two papers: one describing how to model implied volatility
directly instead of modelling first the instantaneous volatility as a stochastic
process and then obtaining the process of implied volatilities, and the other paper is
a purely mathematical finance paper describing the foundations of the theory of
uncertain volatilities. The goal is to combine these two papers and see how the
former paper can be transformed into the language of the latter.
Ref:
Mete Soner, Quasi-sure stochastic analysis through aggregation.
Liuren Wu, Peter Carr, A New Framework for Analyzing Volatility Risk and
Premium Across Option Strikes and Expiries