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...     

Rich Nations, Poor Nations: How Much Can Multiple Equilibria Explain?

This paper asks whether the income gap between rich and poor nations can be explained by multiple equilibria. We explore the quantitative implications of a simple two-sector general equilibrium model that gives rise to multiplicity, and calibrate the model for 127 countries. Under the assumptions of the model, around a quarter of the world’s economies are found to be in a low output equilibrium. We also find that, since the output gains associated with an equilibrium switch are sizeable, the model can explain between 15 and 25% of the variation in the logarithm of GDP per worker across countries.     

Standards,learning, and growth in Britain, 1901–2009

This article considers the model of voluntary, consensus based standardization as developed through the British Standards Institution (BSI) and its contribution to learning and productivity growth. It discusses the significant role played by professional engineers in the model's introduction, its extension at home, and its imitation overseas. It is argued that by 1931 the BSI catalogue of standards represented a considerable stock of codified knowledge whose growth reflected underlying aggregate technological opportunities, assisting in their transformation into technological advance. To help validate this claim, a measure of the size of the BSI catalogue of standards is incorporated into an econometric model of aggregate productivity growth in Britain. Findings show that the growth of the standards catalogue is associated with a substantial proportion of labour productivity growth over the period 1931–2009. Estimates relating to the short‐run dynamics involved are consistent with the idea that there are causal linkages running from standards to growth. When interpreting these findings, it is argued that the overall weight of historical evidence points to standardization—coordinated through the BSI—as providing an important path of learning for the British economy over the period considered.     

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.     

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.     

The geography of output volatility

This paper examines the structural determinants of output volatility in developing countries, and especially the roles of geography and institutions. We investigate the volatility effects of market access, climate variability, the geographic predisposition to trade, and various measures of institutional quality. We find an especially important role for market access: remote countries are more likely to have undiversified exports and to experience greater volatility in output growth. Our results are based on Bayesian methods that allow us to address formally the problem of model uncertainty and to examine robustness across a wide range of specifications.     

Growth Regressions and What the Textbooks Don't Tell You

The paper discusses three econometric problems that are rarely given adequate discussion in textbooks: model uncertainty, parameter heterogeneity, and outliers. Leamer's extreme bounds analysis can be adapted to address all three problems simultaneously. Two examples are presented based on an influential cross-country growth paper by Levine and Renelt ( American Economic Review , vol. 82, 1992, pp. 942-63).     

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...     

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.