The Log Private Company Valuation Model

TL;DR

This paper introduces a novel valuation model for private companies based on the dynamic Gordon growth model, providing closed-form pricing and hedging formulas for European options and life insurance products, along with estimation methods.

Contribution

It develops the first closed-form valuation and hedging formulas for private companies using a log-based model and introduces ML estimators and EM algorithm for parameter estimation.

Findings

Closed-form formulas for private company options and insurance products.

Maximum Likelihood estimators and EM algorithm for model parameters.

Enhanced valuation methods for private companies.

Abstract

For a public company, pricing and hedging models of options and equity--linked life insurance products have been sufficiently developed. However, for a private company, because of unobserved prices, pricing and hedging models of the European options and life insurance products are in their early stages of development. For this reason, this paper introduces a log private company valuation model, which is based on the dynamic Gordon growth model. In this paper, we obtain closed--form pricing and hedging formulas of the European options and equity--linked life insurance products for private companies. Also, the paper provides Maximum Likelihood (ML) estimators of our model, Expectation Maximization (EM) algorithm, and valuation formula for private companies.