# Research articles for the 2021-06-06

Cupid's Invisible Hand: Social Surplus and Identification in Matching Models
Alfred Galichon,Bernard Salanié
arXiv

We investigate a model of one-to-one matching with transferable utility and general unobserved heterogeneity. Under a separability assumption that generalizes Choo and Siow (2006), we first show that the equilibrium matching maximizes a social gain function that trades off exploiting complementarities in observable characteristics and matching on unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint matching surplus and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. We provide efficient algorithms to compute the stable matching and to estimate parametric versions of the model. Finally, we revisit Choo and Siow's empirical application to illustrate the potential of our more general approach.

Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio
Taras Bodnar,Nestor Parolya,Erik Thorsen
arXiv

In this paper, new results in random matrix theory are derived which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage target is determined as the holding portfolio estimated from previous data. The theoretical findings are applied to develop theory for dynamic estimation of the GMV portfolio, where the new estimator of its weights is shrunk to the holding portfolio at each time of reconstruction. Both cases with and without overlapping samples are considered in the paper. The non-overlapping samples corresponds to the case when different data of the asset returns are used to construct the traditional estimator of the GMV portfolio weights and to determine the target portfolio, while the overlapping case allows intersections between the samples. The theoretical results are derived under weak assumptions imposed on the data-generating process. No specific distribution is assumed for the asset returns except from the assumption of finite $4+\varepsilon$, $\varepsilon>0$, moments. Also, the population covariance matrix with unbounded spectrum can be considered. The performance of new trading strategies is investigated via an extensive simulation. Finally, the theoretical findings are implemented in an empirical illustration based on the returns on stocks included in the S\&P 500 index.

Explicit no arbitrage domain for sub-SVIs via reparametrization
Claude Martini,Arianna Mingone
arXiv

The no Butterfly arbitrage domain of Gatheral SVI 5-parameters formula for the volatility smile has been recently described. It requires in general a numerical minimization of 2 functions altogether with a few root finding procedures. We study here the case of some sub-SVIs (all with 3 parameters): the Symmetric SVI, the Vanishing Upward/Downward SVI, and SSVI, for which we provide an explicit domain, with no numerical procedure required.

Forecasting with fractional Brownian motion: a financial perspective
Matthieu Garcin
arXiv

The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the non-Markovian nature of the fBm to forecast future states of the process and make statistical arbitrages. We provide new insights into forecasting an fBm, by proposing theoretical formulas for accuracy metrics relevant to a systematic trader, from the hit ratio to the expected gain and risk of a simple strategy. In addition, we answer some key questions about optimizing trading strategies in the fBm framework: Which lagged increments of the fBm, observed in discrete time, are to be considered? If the predicted increment is close to zero, up to which threshold is it more profitable not to invest? We also propose empirical applications on high-frequency FX rates, as well as on realized volatility series, exploring the rough volatility concept in a forecasting perspective.

Inflation -- who cares? Monetary Policy in Times of Low Attention
Oliver Pfäuti
arXiv

Based on a model of optimal information acquisition, I propose an approach to measure attention to inflation in the data. Applying this approach to US consumers and professional forecasters provides substantial evidence that attention to inflation in the US decreased significantly over the last five decades. Consistent with the theoretical model, attention covaries positively with inflation volatility and persistence. To examine the consequences of limited attention for monetary policy, I augment the standard New Keynesian model with a lower-bound constraint on the nominal interest rate and inflation expectations that are characterized by limited attention. Accounting for the lower bound fundamentally alters the normative implications of declining attention. While lower attention raises welfare absent the lower-bound constraint, it decreases welfare when accounting for the lower bound. In fact, limited attention can lead to inflation-attention traps: prolonged periods of a binding lower bound and low inflation due to slowly-adjusting inflation expectations. To prevent these traps, it is optimal to increase the inflation target as attention declines.

Modeling premiums of non-life insurance companies in India
Kartik Sethi,Siddhartha P. Chakrabarty
arXiv

We undertake an empirical analysis for the premium data of non-life insurance companies operating in India, in the paradigm of fitting the data for the parametric distribution of Lognormal and the extreme value based distributions of Generalized Extreme Value and Generalized Pareto. The best fit to the data for ten companies considered, is obtained for the Generalized Extreme Value distribution.

Price graphs: Utilizing the structural information of financial time series for stock prediction
Junran Wu,Ke Xu,Xueyuan Chen,Shangzhe Li,Jichang Zhao
arXiv

Stock prediction, with the purpose of forecasting the future price trends of stocks, is crucial for maximizing profits from stock investments. While great research efforts have been devoted to exploiting deep neural networks for improved stock prediction, the existing studies still suffer from two major issues. First, the long-range dependencies in time series are not sufficiently captured. Second, the chaotic property of financial time series fundamentally lowers prediction performance. In this study, we propose a novel framework to address both issues regarding stock prediction. Specifically, in terms of transforming time series into complex networks, we convert market price series into graphs. Then, structural information, referring to associations among temporal points and the node weights, is extracted from the mapped graphs to resolve the problems regarding long-range dependencies and the chaotic property. We take graph embeddings to represent the associations among temporal points as the prediction model inputs. Node weights are used as a priori knowledge to enhance the learning of temporal attention. The effectiveness of our proposed framework is validated using real-world stock data, and our approach obtains the best performance among several state-of-the-art benchmarks. Moreover, in the conducted trading simulations, our framework further obtains the highest cumulative profits. Our results supplement the existing applications of complex network methods in the financial realm and provide insightful implications for investment applications regarding decision support in financial markets.

Testing the Goodwin Growth Cycles with Econophysics Approach in 2002-2019 Period in Turkey
Kerim Eser Afşar,Mehmet Özyigit,Yusuf Yüksel,Ümit Akıncı
arXiv

The Turkish economy between 2002-2019 period has been investigated within the econophysical approach. From the individual income data obtained from the Household Budget Survey, the Gompertz-Pareto distribution for each year and Goodwin cycle for the mentioned period have been obtained. For this period, in which thirteen elections were held under the single-party rule, it has been observed that the income distribution fits well with the Gompertz-Pareto distribution which shows the two-class structure of the Turkish economy. The variation of the threshold value $x_t$ (which separates these two classes) as well as Pareto coefficient have been obtained. Besides, Goodwin cycle has been observed within this period, centered at $(u,v)\cong (66.30,83.40)$ and a period of $T=18.30$ years. It has been concluded that these observations are consistent with the economic and social events experienced in the mentioned period.

Time-dependent relations between gaps and returns in a Bitcoin order book
Roberto Mota Navarro,Paulino Monroy Castillero,Francois Leyvraz
arXiv

Several studies have shown that large changes in the returns of an asset are associated with the sized of the gaps present in the order book In general, these associations have been studied without explicitly considering the dynamics of either gaps or returns. Here we present a study of these relationships. Our results suggest that the causal relationship between gaps and returns is limited to instantaneous causation.

Unbiased Optimal Stopping via the MUSE
Zhengqing Zhou,Guanyang Wang,Jose Blanchet,Peter W. Glynn
arXiv

We propose a new unbiased estimator for estimating the utility of the optimal stopping problem. The MUSE, short for `Multilevel Unbiased Stopping Estimator', constructs the unbiased Multilevel Monte Carlo (MLMC) estimator at every stage of the optimal stopping problem in a backward recursive way. In contrast to traditional sequential methods, the MUSE can be implemented in parallel when multiple processors are available. We prove the MUSE has finite variance, finite computational complexity, and achieves $\varepsilon$-accuracy with $O(1/\varepsilon^2)$ computational cost under mild conditions. We demonstrate MUSE empirically in several numerical examples, including an option pricing problem with high-dimensional inputs, which illustrates the use of the MUSE on computer clusters.