  Local Stochastic Volatility (LSV) models have been used for pricing and
hedging derivatives positions for over twenty years. An enormous body of
literature covers analytical and numerical techniques for calibrating the model
to market data. However, the literature misses a potent approach commonly used
in physics and works with absolute (dimensional) variables rather than with
relative (non-dimensional) ones. While model parameters defined in absolute
terms are counter-intuitive for trading desks and tend to be heavily
time-dependent, relative parameters are intuitive and stable, making it easy to
steer the model adequately and consistently with its Profit and Loss (PnL)
explanation power. We propose a specification that first explores historical
data and uses physically well-defined relative quantities to design the model.
We then develop an efficient hybrid method to price derivatives under this
specification. We also show how our method can be used for robust scenario
generation purposes - an important risk management task vital for buy-side
firms.\footnote{The authors would like to thank Prof. Marcos Lopez de Prado and
Dr. Vincent Davy Zoonekynd for valuable comments.}
