Quantitative Finance

Knuteson, Bruce

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Abstract: We point out a simple equities trading strategy that allows a sufficiently large, market-neutral, quantitative hedge fund to achieve outsized returns while simultaneously contributing significantly to increasing global wealth inequality. Overnight and intraday return distributions in major equity indices in the United States, Canada, France, Germany, and Japan suggest a few such firms have been implementing this strategy successfully for more than twenty-five years.

Bayraktar, Erhan;Dolinsky, Yan;Guo, Jia

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Abstract: In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally, we apply our results to the computation of the minimal expected shortfall (shortfall risk) in the Heston model by building an appropriate lattice approximation.

Flori, Andrea;Lillo, Fabrizio;Pammolli, Fabio;Spelta, Alessandro

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Abstract: By exploiting a bipartite network representation of the relationships between mutual funds and portfolio holdings, we propose an indicator that we derive from the analysis of the network, labelled the Average Commonality Coefficient (ACC), which measures how frequently the assets in the fund portfolio are present in the portfolios of the other funds of the market. This indicator reflects the investment behavior of funds' managers as a function of the popularity of the assets they held. We show that $ACC$ provides useful information to discriminate between funds investing in niche markets and those investing in more popular assets. More importantly, we find that $ACC$ is able to provide indication on the performance of the funds. In particular, we find that funds investing in less popular assets generally outperform those investing in more popular financial instruments, even when correcting for standard factors. Moreover, funds with a low $ACC$ have been less affected by the 2007-08 global financial crisis, likely because less exposed to fire sales spillovers.

Albani, Vinicius;Zubelli, Jorge

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Abstract: We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time and price dependent volatility. Our approach uses a forward Dupire-type partial-integro-differential equations for the option prices to produce a parameter-to-solution map. The ill-posed inverse problem for such map is then solved by means of a Tikhonov-type convex regularization. The proofs of convergence and stability of the algorithm are provided together with numerical examples that substantiate the robustness of the method both for synthetic and real data.

Ferguson, Samuel J.

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Abstract: We model the quantities appearing in Internal Revenue Service (IRS) tax guidance for calculating the health insurance premium tax credit created by the Patient Protection and Affordable Care Act, also called Obamacare. We ask the question of whether there is a procedure, computable by hand, which can calculate the appropriate premium tax credit for any household with self-employment income. We give an example showing that IRS tax guidance, which has had self-employed taxpayers use an iterative fixed point procedure to calculate their premium tax credits since 2014, can lead to a divergent sequence of iterates. As a consequence, IRS guidance does not calculate appropriate premium tax credits for tax returns in certain income intervals, adversely affecting eligible beneficiaries. A bisection procedure for calculating premium tax credits is proposed. We prove that this procedure calculates appropriate premium tax credits for a model of simple tax returns; and apparently, this procedure has already been used to prepare accepted tax returns. We outline the problem of finding a procedure which calculates appropriate premium tax credits for models of general tax returns. While the bisection procedure will work with the tax code in its current configuration, it could fail, in states which have not expanded Medicaid, if a certain deduction were to revert to an earlier form. Future policy objectives might also lead to further problems.

Bińkowski, Mikołaj;Lehalle, Charles-Albert

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Abstract: In this paper we investigate the endogenous information contained in four liquidity variables at a five minutes time scale on equity markets around the world: the traded volume, the bid-ask spread, the volatility and the volume at first limits of the orderbook. In the spirit of Granger causality, we measure the level of information by the level of accuracy of linear autoregressive models. This empirical study is carried out on a dataset of more than 300 stocks from four different markets (US, UK, Japan and Hong Kong) from a period of over five years. We discuss the obtained performances of autoregressive (AR) models on stationarized versions of the variables, focusing on explaining the observed differences between stocks. Since empirical studies are often conducted at this time scale, we believe it is of paramount importance to document endogenous dynamics in a simple framework with no addition of supplemental information. Our study can hence be used as a benchmark to identify exogenous effects. On the other hand, most optimal trading frameworks (like the celebrated Almgren and Chriss one), focus on computing an optimal trading speed at a frequency close to the one we consider. Such frameworks very often take i.i.d. assumptions on liquidity variables; this paper document the auto-correlations emerging from real data, opening the door to new developments in optimal trading.

Eckstein, Stephan;Kupper, Michael;Pohl, Mathias

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Abstract: We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g. the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: Firstly, we derive a dual representation of the considered problem and prove that strong duality holds. Secondly, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real world instance.

Koppl, Roger;Devereaux, Abigail;Herriot, Jim;Kauffman, Stuart

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Abstract: We use a simple combinatorial model of technological change to explain the Industrial Revolution. The Industrial Revolution was a sudden large improvement in technology, which resulted in significant increases in human wealth and life spans. In our model, technological change is combining or modifying earlier goods to produce new goods. The underlying process, which has been the same for at least 200,000 years, was sure to produce a very long period of relatively slow change followed with probability one by a combinatorial explosion and sudden takeoff. Thus, in our model, after many millennia of relative quiescence in wealth and technology, a combinatorial explosion created the sudden takeoff of the Industrial Revolution.

Jelito, Damian;Pitera, Marcin

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Abstract: In this paper we introduce an efficient fat-tail measurement framework that is based on the conditional second moments. We construct a goodness-of-fit statistic that has a direct interpretation and can be used to assess the impact of fat-tails on central data conditional dispersion. Next, we show how to use this framework to construct a powerful normality test. In particular, we compare our methodology to various popular normality tests, including the Jarque--Bera test that is based on third and fourth moments, and show that in many cases our framework outperforms all others, both on simulated and market stock data. Finally, we derive asymptotic distributions for conditional mean and variance estimators, and use this to show asymptotic normality of the proposed test statistic.

Coculescu, Delia;Delbaen, Freddy

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Abstract: We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e. the shareholders.