We propose Heath-Jarrow-Morton stochastic models for power forward markets with fractional stochastic volatility. There is a focus on curve-based models. In the talk, we motivate such models from a practical viewpoint, and propose a modeling framework which allows for flexibility in describing the forward dynamics marginally for each maturity as well as the dependency structure across maturities. Furthermore, we propose a rough volatility model and discuss its scaling properties.

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