Hybrid & Practical Models
Pure models are clean but limited. Stochastic vol gets the dynamics right but not the smile. Local vol gets the smile right but not the dynamics. These hybrids combine both -- and are what production desks run.
SLV is the industry default for exotics
Ask a quant what model they use for exotic pricing. The answer is almost always stochastic local vol -- local vol combined with a stochastic vol layer.
At a Glance
What they share
Both models combine simpler components to solve problems that pure stochastic vol or pure local vol cannot handle alone. They differ in complexity, inputs, and target use case.
How they relate to each other
Stochastic Local Vol is the production workhorse for exotic pricing. It takes a local vol surface (calibrated to match all vanilla prices exactly) and overlays a stochastic vol process, giving it realistic dynamics for path-dependent products. The cost is calibration complexity -- it requires particle methods or PDE solvers and a full vol surface as input. Vanna-Volga sits at the other end of the spectrum. It constructs a smile from just three FX market quotes (ATM, risk reversal, butterfly) by computing the cost of hedging vanna and volga risk with those three instruments. It is fast, analytic, and widely used on FX desks, but it does not extend naturally to exotic pricing or non-FX markets.
Models in this section:
- Stochastic Local Vol — The production workhorse
- Vanna-Volga Method — 3-quote smile construction