Markovian structure of the Volterra Heston model
By Eduardo Abi Jaber, Omar El Euch. Statistics and Probability Letters, 2018
67 citations recorded by the source corpus.
We characterize the Markovian and affine structure of the Volterra Heston model in terms of an infinite-dimensional adjusted forward process and specify its state space. More precisely, we show that it satisfies a stochastic partial differential equation and displays an exponentially-affine characteristic functional. As an application, we deduce an existence and uniqueness result for a Banach-space valued square-root process and provide its state space. This leads to another representation of the Volterra Heston model together with its Fourier-Laplace transform in terms of this possibly infinite system of affine diffusions.
Subfields: Computer Networks and Communications, Finance, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e2883db506ccfd55bdb882681d750977da55391f
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In Computer Networks and Communications
In Finance
In Statistical and Nonlinear Physics
Citations in the corpus
- Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case (2018, background): “fy : E → [0, 1];λ 7→ exp(〈y, λ〉) (4.”
- A weak solution theory for stochastic Volterra equations of convolution type (2019, background): “This type of equation appears in multiple applications, for example turbulence (Barndorff-Nielsen and Schmiegel, 2008), energy markets (Barndorff-Nielsen et al., 2013), and rough volatility modeling in finance (El Euch and Rosenbaum, 2019; Gatheral et al., 2018). In the latter context the kernel is ”