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.     

Editors’ note

Portuguese Economic Journal -     

The factor content of regional bilateral trade: The role of technology and demand

The Heckscher–Ohlin–Vanek (HOV) model in its strict form has been strongly rejected by the data. Relaxing some assumptions of the standard HOV model is key to find improvements in its performance. We apply the Davis and Weinstein (2001) methodology to analyse the validity of the HOV model using regions rather than countries. Surprisingly, our results using data for 17 Spanish regions are similar to theirs with international data for OECD countries. Accounting for technological differences improves the predictive capacity of the factor proportions model and including trade costs and geography reduces significantly the missing trade problem. However, relaxing the assumption of factor price equalisation does not improve the performance of the HOV model in a regional setting.     

The case for multi-unit single-run descending-price auctions

We show that a multiple-unit descending-price auction in which the clock is not reset after each sale may be faster and yield more stable prices than an efficient alternative, thus providing sellers a rationale for using it in practice.     

Investigating regional house price convergence in the United States: Evidence from a pair-wise approach

In this paper we examine long-run house price convergence across US states using a novel econometric approach advocated by Pesaran (2007) and Pesaran et al. (2009). Our empirical modelling strategy employs a probabilistic test statistic for convergence based on the percentage of unit root rejections among all state house price differentials. Using a sieve bootstrap procedure, we construct confidence intervals and find evidence in favour of convergence. We also conclude that speed of adjustment towards long-run equilibrium is inversely related to distance.     

The Asian clam Corbicula fluminea in the European freshwater-dependent industry: A latent threat or a friendly enemy?

While the biofouler Corbicula fluminea (Müller, 1774) is known to cause great economic losses in North America, studies reporting the problem in Europe are much scarcer. This paper explores the industrial effects of the species in Portugal, the gateway by which the bivalve entered Europe around 30 years ago. National waterworks, major power stations, cement plants, pulp and paper mills and irrigation systems were surveyed. The industrial impacts of the pest were shown to remain relatively mild; irrigation systems are those that seem to be facing more significant economic losses due to infestation. Possible reasons for the apparent discrepancy between this result and the species dispersal in natural ecosystems are discussed, and recommendations on adequate responses to the latent threat are provided. This study may assist the implementation of integrated pest management policies in countries at risk of invasion or recently invaded, and contribute to an understanding of the species’ progression in industrial environments.     

Idiosyncratic risk and financial policy

In economies subject to uninsurable idiosyncratic risks, competitive equilibrium allocations are constrained inefficient: reallocations of assets support Pareto superior allocations. This is the case even if the asset market for the allocation of aggregate risks is complete.     

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