Modeling Merger Arbitrage Situations Using Stochastic Processes

Abstract

Merger arbitrage is a speculative investment strategy that, in its simplest form, involves buying shares of a target company in a merger or acquisition, with the intention of capturing the spread between the offer price and the pre-consummation target stock price. Excess returns to merger arbitrage strategies have attracted scores of investors and motivated a body of academic work dedicated to predicting deal outcomes. While the qualitative factors of deal success have been well studied, few attempts have been made to quantitatively model stock prices in transactions. In this paper, through the use of stochastic processes, we present two novel approaches to predicting M&A deal outcomes. In our first approach, we construct, calibrate, and test vari- ous stochastic models that represent target stock price dynamics in completed transactions. In the second approach, we build theoretical generalized random walk models of target stock prices during a merger and present computational approaches to determine success probabil- ity given deal-specific parameters. In both approaches, we draw inferences from a dataset of 2,787 recent M&A transactions and use Monte Carlo methods to estimate predictive power. We demonstrate a roughly 80% success rate across all deal outcome predictions and find a 96% success rate for completed deal predictions. Diverging from past merger arbitrage literature, we extend traditional stochastic models to allow returns from fat-tailed distribu- tions, and demonstrate their superiority to classical Gaussian models in modeling short-term returns during transactions.