# Path-dependent volatility

## Julien Guyon on path-dependent volatility models

Three main volatility models have been used so far in the finance industry: constant volatility, local volatility (LV) and stochastic volatility (SV). The first two models are complete: since the asset price is driven by a single Brownian motion, every payoff admits a unique self-financing replicating portfolio consisting of cash and the underlying asset. Therefore, its price is uniquely defined as the initial value of the replicating portfolio, independent