A Separating Equilibrium for Stock Repurchase Programs via PUT Options: Transforming a Mathematical Proof into Visual Form

Abstract

We develop a mathematical proof demonstrating that only financially-strong firms will sell put options on their own stock, but financially-weak firms will not. The sale of options on a company’s own stock exposes the buyer to default risk of the issuer, which additionally complicates the payoff structure of the put option. This signaling equilibrium is unique because it allows producing a non-costly signal of quality. Instead, the signal allows a cash inflow to the signaling firm. We next develop a graphical presentation of the mathematical proof showing the separating equilibrium. We then show how presenting visually the separating equilibrium before presenting the mathematical proof aids in understanding. We provide some empirical evidence that the combination of three very difficult concepts, put options, separating equilibria, and issuer default risk can be grasped more easily when a mathematical proof can be presented in graphical form prior to a mathematical proof.