Markovian structure of the Volterra Heston model

We unravel the Markovian structure of the Volterra Heston model. The model belongs to the class of affine Volterra processes as introduced in Abi Jaber, Larsson and Pulido (2017) and nests as special cases the standard Heston... [ view full abstract ]

We unravel the Markovian structure of the Volterra Heston model. The model belongs to the class of affine Volterra processes as introduced in Abi Jaber, Larsson and Pulido (2017) and nests as special cases the standard Heston model and the rough Heston model of El Euch and Rosenbaum (2016) able to capture the roughness of the volatility. We provide two infinite dimensional Markovian representations explaining the affine structure of the Volterra Heston model and leading to new numerical approximation schemes.