A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS

We present here the quantization method which is well-adapted for the pricing and hedging of American options on a basket of assets. Its purpose is to compute a large number of conditional expectations by projection of the diffusion on optimal grids designed to minimize the (square mean) projection error ( Graf and Luschgy 2000 ). An algorithm to compute such grids is described. We provide results concerning the orders of the approximation with respect to the regularity of the payoff function and the global size of the grids. Numerical tests are performed in dimensions 2, 4, 5, 6, 10 with American style exchange options. They show that theoretical orders are probably pessimistic.     

Economic and Social Security: The Role of the EU

This lecture addresses the issue of growing inequality of labour incomes in the EU. In this lecture, it is observed that through higher unemployment at downward rigid wages, the market position of low-skilled workers has deteriorated over the past quarter-century in Western Europe and that European countries have failed to develop an efficient instrument of income insurance on behalf of low-skilled workers. Wage subsidies are such an instrument. Furthermore, it is argued that labour market integration in an economic union like the EU entails externalities, resulting in underprovision of insurance and that coordination or matching grants could overcome this second inefficiency. On these empirical and theoretical grounds, this article proposes the organisation at EU level of a scheme of matching grants for low-skilled labour, whereby a share of national wage subsidies to low-skilled labour would be financed by the EU under suitable funding.     

An empirical model of the multi‐unit,sequential, clock auction

We construct a model of participation and bidding at multi‐unit, sequential, clock auctions when bidders have multi‐unit demand. We describe conditions sufficient to characterize a symmetric, perfect‐Bayesian equilibrium and then demonstrate that this equilibrium induces an efficient allocation. We propose an algorithm, based on the generalized Vickrey auction, to calculate the expected winning bid for each unit sold. This algorithm allows us to construct a simulation‐based estimator of the parameters for both the participation process and the distribution of latent valuations. We apply our method to data from 37 multi‐lot, sequential, English auctions of export permits for timber held in Russia. Copyright © 2006 John Wiley & Sons, Ltd.     

Private monitoring,collusion, and the timing of information

When a principal's monitoring information is private (nonverifiable), the agent should be concerned that the principal could misrepresent the information to reduce the agent's wage or collect a monetary penalty. Restoring credibility may lead to an extreme waste of resources—the so‐called burning of money. A more realistic and efficient outcome is feasible when the private information arrives in time to rescale the agent's effort. Rescaling is more effective than pure monetary penalties because effort has different values to different parties whereas money is equally valuable to all parties. Furthermore, when rescaling is feasible, private monitoring is more efficient than public monitoring subject to collusion because nonmonetary penalties are ineffective to deter collusion.     

Long-Term Yield Rates for Actuarial Valuations

Consider the problem of valuing a life insurance or annuity on a person aged 20. The valuation formula requires that we know the prices of pure-discount bonds with maturities of up to 100 years. This article investigates the problem of estimating the yield rate for a pure-discount bond that matures in 100 years. It is shown how to estimate this yield rate with parametric and nonparametric models on the price of U.S. Treasury strips. Moreover, confidence intervals on these rates are constructed with bootstrap methods.     

Taxes,female labour supply and household income: differences between the Netherlands and the Federal Republic of Germany

The article investigates the effect of taxes and social premiums on female labour supply and household income. A comparison is made between labour supply and household income between the Netherlands and the Federal Republic of Germany in 1992. A discrete choice model for labour supply is used in which taxes and social premiums are implicitly incorporated. As male labour supply is highly inelastic an individual, male chauvinist model is used. The estimated models are used to simulate the effect of the differences in the tax and social premium system on the differences in labour supply and income between both countries. The results indicate that labour force participation is higher the more individualized the system. The German system leads to a lower tax burden compared to the Dutch system. It is concluded that differences in the tax and social premium system between both countries have hardly any influence on the differences in the inequality of net household labour income. There is evidence that the German system leads to a slightly more unequal distribution of household income. It is also concluded that although the tax and social premium system does influence labour supply and income, it can be doubted whether these effects are substantial.     

Grazing Games: Sharing Common Property Resources with Complex Dynamics

Grasslands used for domestic livestock are often the common property of several owners and are typically characterized by complex ecosystem dynamics. We account for both these aspects by modeling the problem as a differential game where each farmer maximizes profits, given the dynamics of livestock and grass interaction. We compare the first best outcome obtained when farmers cooperate with that for non-cooperative farmers. By accounting for grassland dynamics, we challenge conventional results from the common pool literature. Although we do identify situations where the standard result holds—a tragedy of the commons unless farmers cooperate—we also find examples where a tragedy is exacerbated due to ecosystem dynamics as well as cases where a non-cooperative regime under-exploits the grassland compared to the first best outcome.