LAIDI Y.; PLANCHET F.

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In this paper, we propose to study a method for calibrating Longstaff, Mithal and Neis model (or LMN model) from a CDS (credit derivative swaps) and bonds associated with the same entity as the CDS. This model is used by many insurers. The calculations will use at each observation date a risk-free rate curve generated through Nelson, Siegel and Svensson method from swap rates vs. six-month Euribor. The process will decompose the spread attributed to the reference entity and will especially evaluate the component associated to default risk and the one associated to liquidity risk. The entity will be Deutsch Bank AG. The study will reveal the existence of a negative liquidity component for some corporate bonds and at some cotation dates, which will show that rate swaps indexed on six-month Euribor include an implied spread. Calibration data come from cotations provided by Reuters and the studied period spreads from the 5th January 2009 to the 30th December 2011. The main idea of this paper is that parameters must be determined to ensure the prices from the model represent the best possible prices observed not at a given date, but over a fixed period. The practical implementation of this idea requires the use of a genetic algorithm, which we present here.