Discrete Time Wishart Term Structure Models
(with C. Gourieroux)
Journal of Economic Dynamics and Control , 35(6), 2011, pp. 815-824
Abstract: This paper reveals that the class of Affine Term Structure Models (ATSMs) introduced by Duffie and Kan (1996) is larger than previously considered in the literature. In the framework of risk factors following a Wishart autoregressive process, we define the Wishart Term Structure Model (WTSM) as an extension of a subclass of Quadratic Term Structure Models (QTSMs), derive simple parameter restrictions that ensure positive bond yields at all maturities, and observe that the usual constraint on affine processes requiring that the volatility matrix be diagonal up to a path independent linear invertible transformation can be considerably relaxed.
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Derivative Pricing with Wishart Multivariate Stochastic Volatility
(with C. Gourieroux)
Journal of Business and Economic Statistics , 28(3), 2010, pp. 438-451
Abstract: This paper deals with the pricing of derivatives written on several underlying assets or factors satisfying a multivariate model with Wishart stochastic volatility matrix. This multivariate stochastic volatility model leads to a closed-form solution for the conditional Laplace transform, and quasi-explicit solutions for derivative prices written on more than one asset or underlying factor. Two examples are presented: (i) a multiasset extension of the stochastic volatility model introduced by Heston (1993), and (ii) a model for credit risk analysis that extends the model of Merton (1974) to a framework with stochastic firm liability, stochastic volatility, and several firms. A bivariate version of the stochastic volatility model is estimated using stock prices and moment conditions derived from the joint unconditional Laplace transform of the stock returns.
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The Wishart Autoregressive Process of Multivariate Stochastic Volatility
(with C. Gourieroux and J. Jasiak)
Journal of Econometrics , 150(2), 2010, pp. 167-181
Abstract: The Wishart Autoregressive (WAR) process is a dynamic model for time series of multivariate stochastic volatility. The WAR naturally accommodates the positivity and symmetry of volatility matrices and provides closed-form non-linear forecasts. The estimation of the WAR is straightforward, as it relies on standard methods such as the Method of Moments and Maximum Likelihood. For illustration, the WAR is applied to a sequence of intraday realized volatility-covolatility matrices from the Toronto Stock Market (TSX).
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