Fast calibration of the LIBOR Market Model with Stochastic Volatility based on analytical gradient

Hervé Andres (), Pierre-Edouard Arrouy (), Paul Bonnefoy (), Alexandre Boumezoued and Sophian Mehalla
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Hervé Andres: Recherche et Développement, Milliman Paris - Milliman France
Pierre-Edouard Arrouy: Recherche et Développement, Milliman Paris - Milliman France
Paul Bonnefoy: Recherche et Développement, Milliman Paris - Milliman France
Alexandre Boumezoued: Recherche et Développement, Milliman Paris - Milliman France
Sophian Mehalla: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique, Recherche et Développement, Milliman Paris - Milliman France

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Abstract: We propose to take advantage of the common knowledge of the characteristic function of the swap rate process as modelled in the LIBOR Market Model with Stochastic Volatility and Displaced Diffusion (DDSVLMM) to derive analytical expressions of the gradient of swaptions prices with respect to the model parameters. We use this result to derive an efficient calibration method for the DDSVLMM using gradient-based optimization algorithms. Our study relies on and extends the work by (Cui et al., 2017) that developed the analytical gradient for fast calibration of the Heston model, based on an alternative formulation of the Heston moment generating function proposed by (del Baño et al., 2010). Our main conclusion is that the analytical gradient-based calibration is highly competitive for the DDSVLMM, as it significantly limits the number of steps in the optimization algorithm while improving its accuracy. The efficiency of this novel approach is compared to classical standard optimization procedures.

Keywords: LIBOR Market Model; Stochastic Volatility; Displaced Diffusion; Swaptions pricing; Affine processes; Optimization algorithms (search for similar items in EconPapers)
Date: 2020-06-19
New Economics Papers: this item is included in nep-ore
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