MODELING PRIVATE EQUITY FUNDS AND PRIVATE EQUITY COLLATERALISED FUND OBLIGATIONS

Etienne de Malherbe
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Etienne de Malherbe: Rabobank International (Rabobank International is a trading name used by Coöperatieve Centrale Raiffeisen–Boerenleenbank B.A. which is regulated by the FSA for the conduct of investment business in the United Kingdom.), Thames Court, 1 Queenhithe, London EC4V 3RL, United Kingdom

International Journal of Theoretical and Applied Finance (IJTAF), 2004, vol. 07, issue 03, 193-230

Abstract: The recent development of the securitisation of funds of private equity funds poses the question of the individual and joint modelling of the underlying funds. Private equity funds are different from other managed funds because of their particular bounded life cycle: when the fund starts, the investment partners make an initial capital commitment, the fund managers gradually draw down the committed capital into investments, returns and proceeds are distributed as the investments are realised and the fund is eventually liquidated as the final investment horizon is reached. Modelling private equity funds therefore requires three stages: the modelling of the commitment drawdowns, the modelling of the investment value and the modelling of the return repayments. A standard lognormal process is utilised for the dynamics of the investment value. Squared Bessel processes are utilised for the dynamics of the rates of drawdowns and repayments.Résumé: Le récent développement de la titrisation de fonds de fonds de placements privés pose la question de la modélisation individuelle et jointe des fonds sous-jacents. Les fonds de placements privés sont différents des autres sociétés d'investissement à cause de leur cycle de vie particulier et limité: au démarrage du fonds, les associés s'engagent sur un apport initial en capital; puis les gérants du fonds opèrent des tirages progressifs sur le capital apporté pour procéder à des investissements; les revenus et les profits sont distribués à mesure que les investissements sont réalisés; enfin, le fonds est liquidé lorsque l'horizon d'investissement est atteint. La modélisation d'un fonds doit donc se faire en trois étapes: la modélisation des tirages sur l'apport en capital, la modélisation de la valeur des investissements et enfin la modélisation des paiements et remboursements des dividendes et retours sur investissements. Un processus lognormal standard est utilisé pour la dynamique de la valeur des investissements. Des processus de Bessel carré sont utilisés pour la dynamique des taux de tirage et de remboursement.

Keywords: Private equity fund; fund of funds; collateralised fund obligation (CFO); Cox–Ingersoll–Ross (CIR) process; squared Bessel process; Fonds de placements privés; fonds de fonds; fonds commun de fonds (FCF); processus de Cox-Ingersoll-Ross (CIR); processus de Bessel carré (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024904002359

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