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Estimating Option Implied Risk-Neutral Densities using Spline and Hypergeometric Functions

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  • Economics
  • Mathematics

Abstract

[halshs-00408014, v1] Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations GREQAM Groupement de Recherche en Economie Quantitative d'Aix-Marseille - UMR-CNRS 6579 Ecole des Hautes Etudes en Sciences Sociales Universités d'Aix-Marseille II et III Document de Travail n°2009-13 Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations Ruijun BU Ludovic GIET Kaddour HADRI Michel LUBRANO May 2009 ha ls hs -0 04 08 01 4, v er sio n 1 - 1 5 No v 20 09 Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations Ruijun Bu∗ Ludovic Giet† Kaddour Hadri‡ Michel Lubrano§ May 2009 Abstract We propose a new approach for modeling non-linear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of non-linear SDEs that are reducible to Ornstein-Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a non-linear transfor- mation function. The main advantage of this approach is that these SDEs can account for non-linear features, observed in short-term in- terest rate series, while at the same time leading to exact discretisation and closed form likelihood functions. Although a rich set of specifi- cations may be entertained, our exposition focuses on a couple of non- linear constant elasticity volatility (CEV) processes, denoted OU-CEV and CIR-CEV, respectively. These two processes encompass a num- ber of existing models that have closed form likelihood functions. The statistical properties of the two processes are investigated. In order to obtain more flexible functional form over time, we allow the transfor- mation function to be time-varying. Results from our study of US and UK

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