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The Laplace transform of the integrated Volterra Wishart process

Eduardo Abi Jaber
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Eduardo Abi Jaber: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 UFR27 - Université Paris 1 Panthéon-Sorbonne - UFR Mathématiques & Informatique - UP1 - Université Paris 1 Panthéon-Sorbonne

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional Laplace transform of general Gaussian processes in terms of Fredholm's determinant and resolvent. Furthermore , we link the characteristic exponents to a system of non-standard infinite dimensional matrix Riccati equations. This leads to a second representation of the Laplace transform for a special case of convolution kernel. In practice, we show that both representations can be approximated by either closed form solutions of conventional Wishart distributions or finite dimensional matrix Riccati equations stemming from conventional linear-quadratic models. This allows fast pricing in a variety of highly flexible models, ranging from bond pricing in quadratic short rate models with rich autocorrelation structures, long range dependence and possible default risk, to pricing basket options with covariance risk in multivariate rough volatility models.

Keywords: Wishart processes; Gaussian processes; Fredholm's determinant; quadratic short rate models; rough volatility models (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-rmg
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-02367200v3
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Published in Mathematical Finance, Wiley, In press

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-02367200

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