Continuous-time Markov chain models to estimate the premium for extended hedge fund lockups

Abstract

A lockup period for investment in a hedge-fund is a time period after making the investment during which an investor cannot freely redeem his investment. Since long lockup periods have recently been imposed, it is important to estimate the premium an investor should expect from extended lockups. For this, Derman et al. (Wilmott J. 1(5-6):263-293, 2009) proposed a parsimonious three-state discrete-time Markov Chain (DTMC) to model the state of a hedge fund, allowing the state to change randomly among the states "good," "sick" and "dead" every year. In this paper, we propose an alternative three-state absorbing continuous-time Markov Chain (CTMC) model, which allows state changes continuously in time instead of yearly. Allowing more dynamic state changes is more realistic, but the CTMC model requires new techniques for parameter fitting. We employ nonlinear programming to solve the new calibration equations. We show that the more realistic CTMC model is a viable alternative to the previous DTMC model for estimating the premium for extended hedge fund lockups.