Optimal Dividend Policy And Stock Prices

We model a corporation dividend as an exchange option on stochastic cash flow and capital budge. Then we solve optimal dividend policy problem completely based on the dividend model under the assumption that the cash reservoir of a corporation follows a mean reverting process from empirical evidence and economic arguments. Our optimal dividend controls depend on explicitly with the cash flow and the capital budget of the corporation, and maximizes the HARA utility performance. We specify the unique optimal dividend control for the cash flow and the capital budge. Multiplicity or absence of optimal dividend policies are given. The stock price of the corporation is studied in terms of our stochastic dividend model. We find an explicit relation among the volatility of the stock price, the volatility of the cash flow and the volatility of the capital budget. The ex-dividend stock price is positively proportional to the stochastic cash flow and the probability of the dividend delta with respect to the cash flow, and negatively proportional to the capital budget and the probability of the dividend delta with respect to the capital budget. Hence, our approach provides another passage through which countercyclical volatility of the stock price can arise from the countercyclical cash flow and capital budget directly.