Multiscale Stochastic Volatility Models
Multiscale stochastic volatility models were first introduced by JeanPierre Fouque, George Papanicolaou and Ronnie Sircar around 1999. At that time, the model assumed that only one fast timescale governed the evolution of the stochastic volatility of a financial asset. The most recent version of the model assumes two timescales, one slow and one fast when compared to the usual maturities of derivatives on the given asset.
Such models lead to a firstorder approximation of derivatives prices. This approximation is composed by the leadingorder term given by the BlackScholes price with the averaged effective volatility and the firstorder correction only involves Greeks of this leadingterm.
In terms of implied volatility, this perturbation analysis translates into an affine approximation in the logmoneyness to maturity ratio (LMMR). Subsequently, this leads to a simple calibration procedure of the group market parameters, that are also used to compute the firstorder approximation of the price of exotic derivatives.
My research contributions in this topic are:

perturbation analysis to price of derivatives on futures using an inversion argument. Differently from previous methods, this leads to a simple calibration procedure and drops some unnecessary smoothness assumptions.

application of Functional Itô Calculus to perturbation analysis of pathdependent derivatives.