Although market is busy today working on the bullet LCDS contract to remove the cancellation feature from syndicated secured loan derivatives, in their current form LCDSs and LCDX tranches are still exposed to the cancellation risk. Until recently, in lack of proper modelling framework, market practitioners neglected the cancellation risk and they priced and hedged these products as simple CDSs and CDO tranches. However, cancellation risk does matter! Especially in the current market situation. As we show here, it is more than important to take into account the cancellation risk while marking-to-market and hedging syndicated secured loan derivatives. For this purpose, we present here an easy and robust way to model the cancellation.

Keywords: cancellation risk, bullet LCDS, LCDX, tranche pricing, marking-to-market, hedging, one-factor models, base correlation, Lévy copulas, stochastic recovery.

This is the research plan I submitted to the doctoral committee at KUL.

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In this paper, we develop and experiment an intensity based multi-factor model, which incorporates the joint modelling of default, prepayment and recovery risks. In this way, the model provides a link between the credit default swap (CDS) and the loan-only credit default swap (LCDS) markets. The purpose of this paper is to analyse the relationship of the CDS and LCDS markets, and find stochastic risk factors that can explain the joint puzzle of CDS and LCDS spreads. The developed model is simple and analytically tractable, but it is able to capture the most often mentioned characteristics of the markets, namely there is negative correlation between the default and prepayment intensities and also there is positive correlation between the default intensity and the loss given default.

Keywords: CDS, credit default swap, LCDS, loan-only credit default swap, pricing, valuation, credit derivatives, credit risk, default risk, prepayment risk, recovery risk, correlated default and prepayment intensities, stochastic recovery rate, continuous time modelling, affine processes, multivariate Ornstein-Uhlenbeck process, Riccati ODE.

In this paper, with my promotor Wim Schoutens, we introduce a new robust model for modelling and pricing LCDX tranches. We extend the generic one-factor model of [1], which was developed for modelling and pricing of a synthetic CDO of CDSs, to a model for tranched portfolio of loan-only CDSs (LCDSs). The essential difference is that now also the possibility of prepayments is built in. As a main advantage, the proposed model allows to trade LCDX tranches expressed in base correlations.

Keywords: LCDX tranches, LCDS, loan-only credit default swap, credit risk, credit derivatives, one-factor model, base correlations, tranche pricing, recursive formula, Lévy processes, default risk, prepayment risk, alpha-stable process, variance gamma process.

This paper presents different numerical quadratures to calculate Lévy base correlation that was specified in details in Garcia et al (2007). The different numerical quadratures described here are alternatives to the Gauss-Laguerre quadrature proposed by Garcia et al (2007) in case when the shifted gamma model is used.

One might observe, that deepening in the recent credit crises, the increasing risk averseness caused higher base correlations implied to the synthetic CDO tranche quotes available on the market. However, as the base correlations were climbing up, some market practitioners noticed that the earlier used Gauss-Laguerre quadrature may fail to calculate the unconditional joint default probabilities precisely enough. This remark gave me the intention to test different techniques on the integration problem.

In this paper, at first I review the integration problem related to the calculation of Lévy base correlation. I show how the semi-infinite-part integration can be altered to finite-part integration. In the following section I present different numerical quadratures to solve either the finite-part or the infinite-part integration problem. At the end, I compare these quadratures by precision, robustness and performance.

Garcia, J., Goossens, S., Masol, V. and Schoutens, W. (2007) Lévy Base Correlation. Technical Report 07-04, Section of Statistics, K.U. Leuven. Available at http://www.defaultrisk.com.

Master thesis for my risk management program, 2005.

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