Affine Processes on Positive Semidefinite Matrices

By Christa Cuchiero, Damir Filipovi'c, Eberhard Mayerhofer, Josef Teichmann. 2009

165 citations recorded by the source corpus.

This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/aa7174aa701311351e4f1448dc779403c25684a3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Christa Cuchiero
2. Eduardo Abi Jaber
3. Martin Larsson
4. Sergio Pulido
5. Josef Teichmann
6. Omar El Euch

In Management Science and Operations Research

1. Eduardo Abi Jaber
2. Josef Teichmann

Citations in the corpus

• Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case (2018, background): “[14, 8, 9], since unbounded test functions can be considered.”
• Affine Volterra processes (2017, background): “…case, existence and uniqueness is often approached by first fixing a state space E of interest, and then studying conditions on (a, b) under which existence and uniqueness can be proved; see e.g. Duffie et al. (2003); Cuchiero et al. (2011); Spreij and Veerman (2012); Larsson and Krühner (2017).”
• Density Approximations for Multivariate Affine Jump-Diffusion Processes (2011, unknown): “…from Aı̈t-Sahalia (2008).3 A specialization on affine models is not a severe limitation, since virtually any continuous-time multivariate application is based on affine models.4 This includes Wishart processes Bru (1991) and even general affine matrixvalued processes (Cuchiero et al., 2010a).”
• Riding on the smiles (2011, unknown): “…is quite disappointing if we reason from a calibration perspective. ySee also Gauthier and Possamai (2009b) for another approximation and Gauthier and Possamai (2009a), Cuchiero et al. (2010) and Mayerhofer et al. (2010) for theoretical and numerical aspects of the Wishart and related processes.”
• On strong solutions for positive definite jump diffusions (2009, unknown): “17 84 v5 [ m at h. PR ] 5 M ay 2 01 1 Moreover, we consider stochastic differential equations where the diffusion coefficient is given by the α-th positive semidefinite power of the process itself with 0.5 α 1 and obtain existence conditions for them.”
• General closed-form basket option pricing bounds (2016, unknown): “Furthermore, we assume α ≥ n − 1, see Cuchiero et al. (2011).”