Path-dependent volatility
So far, path-dependent volatility models have drawn little attention compared with local volatility and stochastic volatility models. In this article, Julien Guyon shows they combine benefits from both and can also capture prominent historical patterns of volatility
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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
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