Jean-Paul Décamps

Investment timing and learning externalities

Abstract We study a duopoly model of investment, in which each player learns about the quality of a common value project by observing some public background information, and possibly the experience of his rival. Investment costs are private information, and the background signal takes the form of a Poisson process conditional on the quality of the project being low. The resulting attrition game has a unique, symmetric equilibrium, which depends on initial public beliefs. We determine the impact of changes in the cost and signal distributions on investment timing, and how equilibrium is affected when a first-mover advantage is introduced.

Investment Timing Under Incomplete Information

We study the decision of when to invest in a project whose value is perfectly observable but driven by a parameter that is unknown to the decision maker ex ante. This problem is equivalent to an optimal stopping problem for a bivariate Markov process. Using filtering and martingale techniques, we show that the optimal investment region is characterized by a continuous and nondecreasing boundary in the value-belief state space. This generates path-dependency in the optimal investment strategy. We further show that the decision maker always benefits from an uncertain drift relative to an average drift situation and that the value of the option to invest is not globally increasing with respect to the volatility of the value process.

Optimal Dividend Policy and Growth Option

We analyse the interaction between the dividend policy and the decision on investment in a growth opportunity of a liquidity constrained firm. This leads us to study a mixed singular control/optimal stopping problem for a diffusion that we solve quasi-explicitly by establishing a connection with an optimal stopping problem. We characterize situations where it is optimal to postpone the distribution of dividends in order to invest at a subsequent date in the growth opportunity. We show that uncertainty and liquidity shocks have an ambiguous effect on the investment decision.

Short Sales Constraints, Liquidity and Price Discovery: an Empirical Analysis on the Paris Bourse

In the Paris Bourse some stocks are traded on a spot basis, while others are traded on a monthly settlement basis. The latter are likely to be less subject to leverage and short sales constraints. We empirically analyze the consequences of this difference on the order flow and the return process. Consistent with the theoretical analysis of Diamond and Verrechia (1987), we find that market sell orders are less frequent on the spot market than on the monthly settlement market (although not very significantly) and that the spot market reflects good news (significantly) faster than bad news.

Rethinking Dynamic Capital Structure models with Roll-Over Debt

Dynamic capital structure models with roll-over debt rely on widely accepted arguments that have never been formalized. This paper clarifies the literature and provides a rigorous formulation of the equity holders’ decision problem within a game theory framework. We spell out the linkage between default policies in a rational expectations equilibrium and optimal stopping theory. We prove that there exists a unique equilibrium in constant barrier strategies, which coincides with that derived in the literature. Furthermore, that equilibrium is the unique equilibrium when the firm loses all its value at default time. Whether the result holds when there is a recovery at default remains a conjecture.

A variational approach for pricing options and corporate bonds

SummaryWe show that option prices can always be obtained as the values of simple optimization problems. This easy remark has two consequences: sensitivity analysis is simplified (by applying the envelope theorem) and numerical procedures are improved. We give two examples of applications: options on coupon bonds and corporate bonds.