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Modeling Private Equity Funds And Private Equity Collateralised Fund Obligations

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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)

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.

Suggested Citation

  • Etienne de Malherbe, 2004. "Modeling Private Equity Funds And Private Equity Collateralised Fund Obligations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 193-230.
    • Handle: RePEc:wsi:ijtafx:v:07:y:2004:i:03:n:s0219024904002359
    DOI: 10.1142/S0219024904002359
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    References listed on IDEAS

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    1. Darrel Duffie & Damir Filipović & Walter Schachermayer, 2002. "Affine Processes and Application in Finance," NBER Technical Working Papers 0281, National Bureau of Economic Research, Inc.
    2. Ola Elerian, 1998. "A note on the existence of a closed form conditional transition density for the Milstein scheme," Economics Series Working Papers 1998-W18, University of Oxford, Department of Economics.
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    Cited by:

    1. de Zwart, G.J. & Frieser, B. & van Dijk, D.J.C., 2007. "A Recommitment Strategy for Long Term Private Equity Fund Investors," ERIM Report Series Research in Management ERS-2007-097-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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