Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models

In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black–Scholes dynamics. The proposed techniques, called GPR Tree (GRP-Tree) and GPR Exact Integration (GPR-EI), are both based on Machine Learning, exploited together with binomial trees or with a closed form formula for integration. Moreover, these two methods solve the backward dynamic programing problem considering a Bermudan approximation of the American option. On the exercise dates, the value of the option is first computed as the maximum between the exercise value and the continuation value and then approximated by means of Gaussian Process Regression. The two methods mainly differ in the approach used to compute the continuation value: a single step of the binomial tree or integration according to the probability density of the process. Numerical results show that these two methods are accurate and reliable in handling American options on very large baskets of assets. Moreover we also consider the rough Bergomi model, which provides stochastic volatility with memory. Despite that this model is only bidimensional, the whole history of the process impacts on the price, and how to handle all this information is not obvious at all. To this aim, we present how to adapt the GPR-Tree and GPR-EI methods and we focus on pricing American options in this non-Markovian framework.     

Cooperative conversion and communalization: Closely observed interactions between the material and the mental

Various authors, including Elinor Ostrom, have shown that the legal form of a cooperative has many of the characteristics of a Common. Here we focus on cooperative conversion, through which conventional enterprises become labor‐managed firms (LMFs), viewing it dynamically as a communalization process. These processes are addressed in the light of a field survey carried out in France, looking at six firms involved in cooperative conversion. The changes entailed are two‐dimensional, both material and mental. This is visible, for example, when finding the capital to mount an LMF: members of the workforce must draw on their own funds; they must also believe in the project. Through our empirical observations we highlight the obstacles in the way of forming an LMF. In particular participants must undertake a work of negotiation hinging on stakes marked by the two, largely inseparable dimensions. Ultimately we query the ethic brought into play in the collective action of constituting a Common. Specifically, individuals must contribute to a collective action underpinned by principles of self‐governance, or commoning, the rock on which the Common rests. A key finding of our study is to demonstrate that a Common can only be successfully created if the constituent processes are consistent with the overall goal. In other words the manner in which we travel is inseparable from our final destination; otherwise we shall surely lose our way.     

Gaussian process regression for pricing variable annuities with stochastic volatility and interest rate

Decisions in Economics and Finance - In this paper, we investigate value and Greeks computation of a guaranteed minimum withdrawal benefit (GMWB) variable annuity, when both stochastic volatility...     

Duality for pathwise superhedging in continuous time

Finance and Stochastics - We provide a model-free pricing–hedging duality in continuous time. For a frictionless market consisting of $d$  risky assets with continuous price...     

A GENERALIZED OLIGOPOLY MODEL WITH CONJECTURAL VARIATIONS

This paper considers a generalization of the Stackelberg model to cover a T‐stage framework with several leaders and followers who compete on quantities. Assuming a linear demand function and constant marginal costs, we introduce constant conjectural variations in order to capture various structures of competition. First, we characterize the equilibrium market outcome. Second, we study the influence of conjectures on welfare. We notably propose a welfare comparison for six symmetric equilibria. Third, we consider convergence analysis, and we also show that the competitive equilibrium is a consistent oligopoly equilibrium.     

Conjectural variations, symmetric equilibria and economic policy

In this paper, we consider conjectural variations in a simple static general equilibrium model under oligopolistic competition. The modeling of conjectures captures the role played by beliefs in a micro-founded model. So, the economy may have three kinds of symmetric general equilibria. Furthermore, these equilibria can be Pareto-ranked by the conjectural variation parameter. Finally, we consider the implementation of a tax on the strategic behaviors in case of balanced-budget rule. The comparative statics illustrates the idea according to which the effectiveness of the multiplier mechanism to mitigate the market distortions depends on the symmetric equilibrium considered. Therefore, the effect of the tax on the prices and economic activity depends on the degree of market power which is conjectured by the agents.     

The British aluminium industry, 1945-80s: chronicles of a death foretold?

The paper aims to give an overview of the evolution of the British aluminium industry after 1945. Its objective is to analyse the national character of the sector's evolution over the post-war period. The case seems to illustrate the so-called British economic 'failure' often quoted by economic historians writing about the period (Jones, 1997). Nevertheless, geographical, financial, managerial and cultural factors are crucial to understanding Britain's inability to sustain a domestically owned aluminium industry.     

Participatory determinants of innovation and their impact on plantain production systems in Cameroon

Current statistics question the capacity of food-crop production to meet the challenges of food security in Central Africa. However, for local food crops like plantain, the potential for improving productivity is very high. In response to this challenge, after identification of the most serious constraints, an interdisciplinary team used participatory research and action-research tools to try and speed up the adoption of technical innovation by farmers. The project began in 1990 in South-West Province and subsequently expanded to include 100 plantain producers and 60 extension technicians in the Central and Southern Provinces of Cameroon. The approach used produced satisfactory results as far as the adoption and dissemination of methods of multiplication and cleaning of planting material were concerned but there was resistance to new cropping practices involving intercrops and crop rotation. The project resulted in major technical changes in plantain production systems in Cameroon that not only increased productivity and food security but also reduced deforestation showing that sustainable intensification is possible in sub-Saharan Africa.     

Debt contracts with ex-ante and ex-post asymmetric information: an example

Summary. We consider a simple model of lending and borrowing combining two informational problems: adverse selection and costly state verification. Our analysis highlights the interaction between these two informational problems. We notably show that the higher the monitoring cost, the less discriminating the optimal menu of contracts is.Received: 24 September 2004, Revised: 5 April 2005, JEL Classification Numbers: C7, D8, G3.L. Renou: Correspondence toWe thank Anne Villamil for insightful comments.