Spectral Methods and Pricing Options on Private Equity

Abstract

Over the past several years, researchers in economics and finance have used spectral methods to determine the structure of the stochastic discount factor. In this paper, we show that spectral methods can also be used to value an option on private equity. We show that the volatility of the equity is uniquely determined by the specification of a risk-neutral stochastic process for dividend yields along with the solution of a Sturm Liouville problem.