THE DYNAMICS OF PRIVATE EQUITY FUNDS WHEN DRAWDOWNS, PERFORMANCES AND DISTRIBUTIONS ARE CORRELATED

The dynamics of a private equity fund is split into three components: the drawdowns from the committed capital paid into the fund; the performances of the investments effected by the fund; and the distributions of dividends and investment proceeds taken out of the fund. Three different but correlated diffusion processes model the three components. To keep the model tractable, a standard lognormal process is utilized for the dynamics of the investment performances and two Ornstein–Uhlenbeck processes are utilized for the dynamics of the drawdowns and the distributions. The cases of a standard and a quadratic Ornstein–Uhlenbeck process are successively examined. To complete the modeling framework, a fourth lognormal variable representing the biases and errors in the net asset values reported by the fund is introduced.