Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications
研究有限责任企业家如何通过现金储备、债务和股权融资，并分析离散时间最优契约向连续时间收敛的过程及其对股票价格、波动率和杠杆率的资产定价含义。
An entrepreneur with limited liability needs to finance an infinite horizon investment project. An agency problem arises because she can divert operating cash flows before reporting them to the financiers. We first study the optimal contract in discrete time. This contract can be implemented by cash reserves, debt, and equity. The latter is split between the financiers and the entrepreneur and pays dividends when retained earnings reach a threshold. To provide appropriate incentives to the entrepreneur, the firm is downsized when it runs short of cash. We then study the continuous-time limit of the model. We prove the convergence of the discrete-time value functions and optimal contracts. Our analysis yields rich implications for the dynamics of security prices. Stock prices follow a diffusion reflected at the dividend barrier and absorbed at 0. Their volatility, as well as the leverage ratio of the firm, increase after bad performance. Stock prices and book-to-market ratios are in a non-monotonic relationship. A more severe agency problem entails lower price-earning ratios and firm liquidity and higher default risk.