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math.PR2023★ 1 cited
Path-dependent PDEs for volatility derivatives
Alexandre Pannier
We regard options on VIX and Realised Variance as solutions to path-dependent partial differential equations (PDEs) in a continuous stochastic volatility model. The modeling assump…
math.PR2023★ 6 cited
Rough volatility, path-dependent PDEs and weak rates of convergence
Ofelia Bonesini, Antoine Jacquier, Alexandre Pannier
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-depende…