Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case
By Christa Cuchiero, Josef Teichmann. 2018
82 citations recorded by the source corpus.
We consider stochastic (partial) differential equations appearing as Markovian lifts of affine Volterra processes with jumps from the point of view of the generalized Feller property which was introduced in, e.g., Dörsek and Teichmann (A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651 ). In particular, we provide new existence, uniqueness and approximation results for Markovian lifts of affine rough volatility models of general jump diffusion type. We demonstrate that in this Markovian light the theory of stochastic Volterra processes becomes almost classical.
Subfields: Finance, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/55119196661f9687a3ce00aab5e98890f53149e5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
- Eduardo Abi Jaber
- Christa Cuchiero
- Mathieu Rosenbaum
- Paul Jusselin
- Martin Larsson
- Sergio Pulido
- Jim Gatheral
- Sara Svaluto‐Ferro
In Molecular Biology
- Paul Jusselin
- Eduardo Abi Jaber
- Sergio Pulido
- Martin Larsson
- Jim Gatheral
- Christa Cuchiero
- Sara Svaluto‐Ferro
- Guido Gazzani
Citations in the corpus
- Joint calibration to SPX and VIX options with signature‐based models (2023, methodology): “See Cuchiero et al. (2022a) for a direct proof using the definition of Stratonovich integrals. Let us recall also the universal approximation theorem of linear functions of the signature in the context of continuous semimartingales as stated in Cuchiero et al. (2022a). We refer to Cuchiero and Mölle”
- A weak solution theory for stochastic Volterra equations of convolution type (2019, methodology): “Yet another approach is to use projections of Markovian solutions to certain degenerate stochastic partial differential equations (Abi Jaber and El Euch, 2019a; Benth, Detering and Kruehner, 2019; Cuchiero and Teichmann, 2020, 2019; Mytnik and Salisbury, 2015).”
- Affine forward variance models (2018, unknown): “For such models, Cuchiero and Teichmann [6] also derive (infinite-dimensional) Riccati PDEs and an abstract affine transform formula similar to equation (2.4) below.”
- The Quadratic Rough Heston Model and the Joint S&P 500/VIX Smile Calibration Problem (2020, background): “In addition derivatives hedging is fully understood as shown in [15, 16], see also [1, 9].”