Towards a Stochastic Cash Flow Model for Private Equity Funds

Abstract

A four-factor model is intoduced for modelling the dynamics of a private equity fund. This framework is meant to encompass the main features of a private equity fund: how the capital committed by the investors is progressively drawn by the fund manager into private investments, how the investments perform, how much return is paid back by the fund manager to the investors and, finally, how reliable are the fund intermediary values reported by the manager during the fund lifetime? The resulting model, albeit complex, is still tractable and allows an efficient representation of the dynamics of a private equity fund.

Keywords: Private equity fund, lognormal process, Cox-Ingersoll-Ross (CIR) process, inverse gamma process

JEL Classification: G12, G13, G24