Copulas. We study the model risk of multivariate risk models in a comprehensive empirical study on Copula-GARCH models used for forecasting Value-at-Risk and Expected Shortfall. To determine whether model risk inherent in the forecasting of portfolio risk is caused by the candidate marginal or copula models, we analyze different groups of models in which we fix either the marginals, the copula, or neither. Model risk is economically significant, is especially high during periods of crisis, and is almost completely due to the choice of the copula. We then propose the use of the model confidence set procedure to narrow down the set of available models and reduce model risk for Copula-GARCH risk models. Our proposed approach leads to a significant improvement in the mean absolute deviation of one day ahead forecasts by our various candidate risk models.
We mine the leaked history of trades on Mt. Gox, the dominant Bitcoin exchange from 2011 to early 2014, to detect the triangular arbitrage activity conducted within the platform. The availability of user identifiers per trade allows us to focus on the historical record of 440 investors, detected as arbitrageurs, and consequently to describe their trading behavior. We begin by showing that a considerable difference appears between arbitrageurs when indicators of their expertise are taken into account. In particular, we distinguish between those who conducted arbitrage in a single or in multiple markets: using this element as a proxy for trade ability, we find that arbitrage actions performed by expert users are on average non-profitable when transaction costs are accounted for, while skilled investors conduct arbitrage at a positive and statistically significant premium. Next, we show that specific trading strategies, such as splitting orders or conducting arbitrage non aggressively, are further indicators of expertise that increase the profitability of arbitrage. Most importantly, we exploit within-user (across hours and markets) variation and document that expert users make profits on arbitrage by reacting quickly to plausible exogenous variations on the official exchange rates. We present further evidence that such differences are chiefly due to a better ability of the latter in incorporating information, both on the transactions costs and on the exchange rates volatility, eventually resulting in a better timing choice at small time scale intervals. Our results support the hypothesis that arbitrageurs are few and sophisticated users.
The outcome of a foregone alternative is not always learnt. We incorporate this observation into a model of regret, supposing that the ex-post information available depends on choice. We show that a more informative ex-post environment is never desirable for a regret averse individual. We then suppose that there are multiple regret averse individuals where the ex-post information available depends on own choice and the choices of others. This implies that what appears to be a series of isolated decision problems is in fact a behavioural game with multiple equilibria. We experimentally test the model and find support for our theory.
In recent years a large literature on deep learning based methods for the numerical solution partial differential equations has emerged; results for integro-differential equations on the other hand are scarce. In this paper we study deep neural network algorithms for solving linear and semilinear parabolic partial integro-differential equations with boundary conditions in high dimension. To show the viability of our approach we discuss several case studies from insurance and finance.