Continuous Time Wishart Process for Stochastic Risk

DOI10.1080/07474930600713234zbMath1105.62104OpenAlexW2007895608MaRDI QIDQ5485103

Christian Gouriéroux

Publication date: 28 August 2006

Published in: Econometric Reviews (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07474930600713234

zbMATH Keywords

stochastic volatilityOrnstein-Uhlenbeck processRiccati equationcredit riskquadratic term structureconditional Laplace transform

Mathematics Subject Classification ID

Applications of statistics to actuarial sciences and financial mathematics (62P05) Markov processes: estimation; hidden Markov models (62M05) Signal detection and filtering (aspects of stochastic processes) (60G35) Credit risk (91G40)

Related Items

Long-Term Optimal Investment in Matrix Valued Factor Models ⋮ Risk-sensitive asset management in a Wishart-autoregressive factor model with jumps ⋮ MULTIVARIATE ECOGARCH PROCESSES ⋮ The Wishart autoregressive process of multivariate stochastic volatility ⋮ The structure of dynamic correlations in multivariate stochastic volatility models ⋮ On the calibration of fractional two-factor stochastic volatility model with non-Lipschitz diffusions ⋮ On non-negative modeling with CARMA processes ⋮ Valuation of asset and volatility derivatives using decoupled time-changed Lévy processes ⋮ The Explicit Laplace Transform for the Wishart Process ⋮ Stochastic covariance and dimension reduction in the pricing of basket options ⋮ Multi-variate stochastic volatility modelling using Wishart autoregressive processes ⋮ High-dimensional limits of eigenvalue distributions for general Wishart process ⋮ Pricing multi-asset American option under Heston-CIR diffusion model with jumps ⋮ A stochastic volatility factor model of heston type. Statistical properties and estimation ⋮ Multivariate COGARCH(1, 1) processes ⋮ Closed-Form Pricing of Two-Asset Barrier Options with Stochastic Covariance ⋮ A PARSIMONIOUS MULTI-ASSET HESTON MODEL: CALIBRATION AND DERIVATIVE PRICING ⋮ American option pricing under double Heston stochastic volatility model: simulation and strong convergence analysis ⋮ Fourier inversion formulas for multiple-asset option pricing ⋮ Estimating the Wishart affine stochastic correlation model using the empirical characteristic function ⋮ LOST IN CONTAGION? BUILDING A LIQUIDATION INDEX FROM COVARIANCE DYNAMICS ⋮ Option pricing under two-factor stochastic volatility jump-diffusion model ⋮ Two asset-barrier option under stochastic volatility ⋮ On the existence and uniqueness of the solution to the double Heston model equation and valuing lookback option ⋮ Algorithm 963 ⋮ Transform formulae for linear functionals of affine processes and their bridges on positive semidefinite matrices ⋮ Stochastic volatility and stochastic leverage ⋮ Quadratic stochastic intensity and prospective mortality tables ⋮ VIX VERSUS VXX: A JOINT ANALYTICAL FRAMEWORK ⋮ European option pricing under Wishart processes ⋮ The multivariate mixture dynamics model: shifted dynamics and correlation skew ⋮ Pricing of mountain range derivatives under a principal component stochastic volatility model ⋮ Mean-variance portfolio selection with correlation risk ⋮ Fractional Wishart processes and \(\varepsilon\)-fractional Wishart processes with applications ⋮ Discrete time Wishart term structure models ⋮ Long-term yield in an affine HJM framework on \(S_{d}^{+}\) ⋮ BILINEAR TERM STRUCTURE MODEL ⋮ Mean-variance asset-liability management with asset correlation risk and insurance liabilities ⋮ Efficient pricing and hedging under the double Heston stochastic volatility jump-diffusion model ⋮ Long-Time Large Deviations for the Multiasset Wishart Stochastic Volatility Model and Option Pricing ⋮ Modeling the Variance Risk Premium of Equity Indices: The Role of Dependence and Contagion ⋮ DOMAIN RESTRICTIONS ON INTEREST RATES IMPLIED BY NO ARBITRAGE ⋮ Recent advances on eigenvalues of matrix-valued stochastic processes ⋮ Multivariate Stochastic Volatility: A Review ⋮ The log-asset dynamic with Euler-Maruyama scheme under Wishart processes ⋮ Geometric Asian options pricing under the double Heston stochastic volatility model with stochastic interest rate ⋮ A fractionally integrated Wishart stochastic volatility model ⋮ Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing ⋮ Order estimates for the exact Lugannani-Rice expansion

Cites Work

• Unnamed Item
• The Wishart autoregressive process of multivariate stochastic volatility
• Bayesian analysis of stochastic volatility models with fat-tails and correlated errors
• A generalized dynamic conditional correlation model for portfolio risk evaluation
• ARCH modeling in finance. A review of the theory and empirical evidence
• Estimating equations based on eigenfunctions for a discretely observed diffusion process
• Affine processes and applications in finance
• A test for constant correlations in a multivariate GARCH model
• GENERALIZATION OF GMM TO A CONTINUUM OF MOMENT CONDITIONS
• A Theory of the Term Structure of Interest Rates
• An efficiency result for the empirical characteristic function in stationary time-series models
• SOLVABLE AFFINE TERM STRUCTURE MODELS
• A Canonical Representation for the Noncentral Wishart Distribution Useful for Simulation
• A YIELD‐FACTOR MODEL OF INTEREST RATES
• Multivariate Stochastic Variance Models
• Volatility and Links between National Stock Markets
• Transform Analysis and Asset Pricing for Affine Jump-diffusions
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Derivative Pricing With Wishart Multivariate Stochastic Volatility
• Factor Multivariate Stochastic Volatility via Wishart Processes
• AUTOMATED INFERENCE AND LEARNING IN MODELING FINANCIAL VOLATILITY
• Some Extensions of the Wishart Distribution
• Estimation of affine asset pricing models using the empirical characteristic function