Data Analysis for Firm Valuation: Stochastic Modeling of Casino Hold Percentages Using Random Walk and ARIMA

Abstract

This paper presents a stochastic approach to partial firm valuation by analyzing casino hold percentages using Random Walk and ARMA(1,1) models. We establish a mathematical framework that models future cash flows as influenced by current values and random disturbances, enabling us to derive variance formulas for discounted cash flows. By treating casino hold percentages as stochastic variables, we apply the Discounted Cash Flow (DCF) method to evaluate the enterprise value of a casino table under both autocorrelated and non-autocorrelated scenarios. Our findings highlight the critical impact of temporal dependencies on risk assessments, illustrating how ARMA models improve accuracy in variance estimation. To demonstrate the practical application, we analyze monthly hold percentages data from casino games, spanning 2004 to 2024 in Nevada. This research offers valuable insights for financial decision-makers, not only in the gaming industry, emphasizing the importance of considering random fluctuations and advanced modeling techniques in (partial) firm valuation.