The shadow of death model revisited with an application to French firms

This article provides an empirical model of the shadow of death in which the exit probability of a firm depends on the firm’s productive performance and the firm’s level of sunk costs, which are viewed as barriers to exit. The shadow of death effect is treated by assuming a relationship between the propensity to exit and both the contemporaneous and lagged values of efficiency and sunk costs. To estimate the unobserved productive efficiency, we use the Ackerberg et al. (2006) estimator extended by the addition of a correction for selection bias. We use an unbalanced sample of approximately 100 000 French firms over the period 1997 to 2002. Our results indicate that the probability of exit is negatively affected by unobserved individual efficiency and the level of sunk costs. The shadow of death effect applies mainly in manufacturing, where both productive efficiency and sunk costs decrease during several years before exit. In service sectors, the exit process seems to occur more suddenly.     

Second order multiscale stochastic volatility asymptotics: stochastic terminal layer analysis and calibration

Multiscale stochastic volatility models have been developed as an efficient way to capture the principal effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book by Fouque et al. (Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives, 2011) analyzes models in which the volatility of the underlying is driven by two diffusions – one fast mean-reverting and one slowly varying – and provides a first order approximation for European option prices and for the implied volatility surface, which is calibrated to market data. Here, we present the full second order asymptotics, which are considerably more complicated due to a terminal layer near the option expiration time. We find that to second order, the implied volatility approximation depends quadratically on log-moneyness, capturing the convexity of the implied volatility curve seen in data. We introduce a new probabilistic approach to the terminal layer analysis needed for the derivation of the second order singular perturbation term, and calibrate to S&P 500 options data.     

Viability of pay-as-you-go systems

When the dependency ratio inactive/active increases to intolerable proportions, the question arises as to how and when pay-as-you-go social security systems can be controlled so as to safeguard a decent way of life to everyone. Between uncertainty linked to wages and the interest rate, and room to manœuvre the age of retirement and the immediate transfer from workers to pensioners, not just any route permits this objective. The set of those which do is here delineated (the viability kernel tube), and the operations at any time necessary to control trajectories so as they remain in this set are identified (the regulation map). Finally, the flexibility necessary to avoid failure, from any state reached by the pay-as-you-go system, is inferred in timing and magnitude.     

Labor market dynamics when effort depends on wage growth comparisons

We present an efficiency wage model in which workers' disutility of effort depends on the level and on the growth rate of their wage relative to an alternative wage. Using data for four countries (US, UK, FR, GY), the implications of the model are examined and are found to be in accordance with the information in the non-stationary data. The restrictions implied by the model dynamics are not rejected by the data and the structural parameters are found to be constant through time. One interesting result is that the workers' disutility of effort depends less on relative wages growth and more on relative wage levels in the US than in the three European countries analyzed. First version received: September 1998 / Final version accepted: November 1999     

Optimal investment with correlated stochastic volatility factors

The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal time with only one random factor can be linearized thanks to a classical distortion transformation. In the present paper, we address the situation with several factors using a perturbation technique around the case where these factors are perfectly correlated reducing the problem to the case with a single factor. Our proposed approximation requires to solve numerically two linear equations in lower dimension instead of a fully nonlinear HJB equation. A rigorous accuracy result is derived by constructing sub- and super-solutions so that their difference is at the desired order of accuracy. We illustrate our result with a particular model for which we have explicit formulas for the approximation. In order to keep the notations as explicit as possible, we treat the case with one stock and two factors and we describe an extension to the case with two stocks and two factors.