Research articles for the 2019-11-10

An analysis of Uniswap markets
Guillermo Angeris,Hsien-Tang Kao,Rei Chiang,Charlie Noyes,Tarun Chitra

Uniswap---and other constant product markets---appear to work well in practice despite their simplicity. In this paper, we give a simple formal analysis of constant product markets and their generalizations, showing that, under some common conditions, these markets must closely track the reference market price. We also show that Uniswap satisfies many other desirable properties and numerically demonstrate, via a large-scale agent-based simulation, that Uniswap is stable under a wide range of market conditions.

Carry and Time-Series Momentum: A Match Made in Heaven
Molyboga, Marat,Qian, Junkai,He, Chaohua
This paper introduces a novel approach to combining time-series momentum and carry trade by conditioning trading signals of time-series momentum on the sign of the basis, a key input for carry trade. We find that this new technique applied to four major asset classes improves the Sharpe ratio of time-series momentum by approximately 0.17 net of fees. The improvement in performance is greater during recessions and, therefore, conditioning time-series momentum signals on the sign of the basis improves performance when it matters the most. Thus, the new approach has practical importance for investors and asset managers who attempt to improve their long-term performance without increasing downside risk during periods of market turbulence.

Critical slowing down associated with critical transition and risk of collapse in cryptocurrency
Chengyi Tu,Paolo DOdorico,Samir Suweis

The year 2017 saw the rise and fall of the crypto-currency market, followed by high variability in the price of all crypto-currencies. In this work, we study the abrupt transition in crypto-currency residuals, which is associated with the critical transition (the phenomenon of critical slowing down) or the stochastic transition phenomena. We find that, regardless of the specific crypto-currency or rolling window size, the autocorrelation always fluctuates around a high value, while the standard deviation increases monotonically. Therefore, while the autocorrelation does not display signals of critical slowing down, the standard deviation can be used to anticipate critical or stochastic transitions. In particular, we have detected two sudden jumps in the standard deviation, in the second quarter of 2017 and at the beginning of 2018, which could have served as early warning signals of two majors price collapses that have happened in the following periods. We finally propose a mean-field phenomenological model for the price of crypto-currency to show how the use of the standard deviation of the residuals is a better leading indicator of the collapse in price than the time series' autocorrelation. Our findings represent a first step towards a better diagnostic of the risk of critical transition in the price and/or volume of crypto-currencies.

Discovering Fundamental Value
Dudley, Evan,Khan, Saad,Phelps, Luke,Riordan, Ryan
Using machine learning methods we identify the fundamental value and noise components of quarterly stock prices. We show that 28% of stock price variation is attributable to noise, and that 40% of noise is attributable to mutual fund trading. We find spikes in noise around the dot-com bubble, the 2008 financial crisis, and the European sovereign-debt crisis. Noise is higher for small firms and firms with high R&D expenditures. In an application of our methodology, we show that corporate managers do not have private information about future changes in fundamental value nor can they identify noise in prices.

Dual Representation of Expectile based Expected Shortfall and Its Properties
Samuel Drapeau,Mekonnen Tadese

The expectile can be considered as a generalization of quantile. While expected shortfall is a quantile based risk measure, we study its counterpart -- the expectile based expected shortfall -- where expectile takes the place of quantile. We provide its dual representation in terms of Bochner integral. Among other properties, we show that it is bounded from below in terms of convex combinations of expected shortfalls, and also from above by the smallest law invariant, coherent and comonotonic risk measure, for which we give the explicit formulation of the corresponding distortion function. As a benchmark to the industry standard expected shortfall we further provide its comparative asymptotic behavior in terms of extreme value distributions. Based on these results, we finally compute explicitly the expectile based expected shortfall for some selected class of distributions.

How Inheritance Law Affects Family Firm Performance: Evidence from a Natural Experiment
Gam, Yong Kyu,Kang, Min Jung,Park, Junho,Shin, Hojong
We argue that changes in the inheritance system affect the incentives toward sibling rivalry among descendants, thereby having a material impact on family firm performance. Using South Korea’s 1991 inheritance law reform that stipulates the equal distribution of a deceased person’s property to the descendants, we find that performance and operating growth rate in family firms show a significant enhancement compared to those of non-family firms. Moreover, the positive effects are greater for family firms that undertake a business succession with multiple sons and married daughters. Overall, our results suggest that changing to equal bequests of inheritance brings positive effect on firm value by providing better-aligned incentives to heirs in family firms. We conclude our paper by discussing implications of our findings for current generations in family firms.

Inference for Volatility Functionals of Multivariate It\^o Semimartingales Observed with Jump and Noise
Richard Y. Chen

This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and jumps. Second-order expansion reveals explicit biases and a pathway to bias correction. Estimators based on this framework achieve the optimal convergence rate. A class of stable central limit theorems are attained with estimable asymptotic covariance matrices. This paper form a basis for infill asymptotic results of, for example, the realized Laplace transform, the realized principal component analysis, the continuous-time linear regression, and the generalized method of integrated moments, hence helps to extend the application scopes to more frequently sampled noisy data.

Infinite dimensional polynomial processes
Christa Cuchiero,Sara Svaluto-Ferro

We introduce polynomial processes taking values in an arbitrary Banach space $B$ via their infinitesimal generator $L$ and the associated martingale problem. We obtain two representations of the (conditional) moments in terms of solutions of a system of ODEs on the truncated tensor algebra of dual respectively bidual spaces. We illustrate how the well-known moment formulas for finite dimensional or probability-measure valued polynomial processes can be deduced in this general framework. As an application we consider polynomial forward variance curve models which appear in particular as Markovian lifts of (rough) Bergomi-type volatility models. Moreover, we show that the signature process of a $d$-dimensional Brownian motion is polynomial and derive its expected value via the polynomial approach.

Liquidity Provision: Normal Times vs Crashes
Jagannathan, Ravi,Pelizzon, Loriana,Schaumburg, Ernst,Getmansky Sherman, Mila,Yuferova, Darya
We study the role of various trader types in providing liquidity in spot and futures markets based on data from the National Stock Exchange of India for a single large stock. During normal times, short-term traders who carry little inventory overnight are the primary liquidity providers in both spot and futures markets. We have two crashes in our sample, both originated in the spot market and spilled into the futures market. Mutual funds had to move in before price recovery took place in both markets. Market stability may require the presence of well-capitalized standby liquidity providers for recovery from crashes.

Modelling information flows by Meyer-$\sigma$-fields in the singular stochastic control problem of irreversible investment
Peter Bank,David Besslich

In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows when about the exogenous shocks and how and when she can act on this information. We propose to use Meyer-$\sigma$-fields as a flexible tool to model information flow in such situations. The possibilities of this approach are illustrated first in a very simple linear stochastic control problem and then in a fairly general formulation for the singular stochastic control problem of irreversible investment with inventory risk. For the latter, we illustrate in a first case study how different signals on exogenous jumps lead to different optimal controls, interpolating between the predictable and the optional case in a systematic manner.

Multiple yield curve modelling with CBI processes
Claudio Fontana,Alessandro Gnoatto,Guillaume Szulda

We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). Exploiting the self-exciting behavior of CBI jump processes, this approach can reproduce the relevant empirical features of spreads between different interbank rates. We provide a complete analytical framework, including a detailed study of discounted exponential moments of CBI processes. The proposed framework yields explicit valuation formulae for all linear interest rate derivatives as well as semi-closed formulae for nonlinear derivatives via Fourier techniques and quantization. We show that a simple specification of the model can be successfully calibrated to market data.

Pricing Variance Swaps on Time-Changed Markov Processes
Peter Carr,Roger Lee,Matthew Lorig

We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process, provided that the payoff function $G$ of the European contract satisfies an ordinary integro-differential equation, which depends only on the dynamics of the Markov process, not on the clock. We present examples of Markov processes where the function $G$ that prices the variance swap can be computed explicitly. In general, the solutions $G$ are not contained in the logarithmic family previously obtained in the special case where the Markov process is a L\'evy process.

Random concave functions
Peter Baxendale,Ting-Kam Leonard Wong

Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave functions on the unit simplex measure the concentration of capital, and their gradient maps define novel investment strategies. The gradient maps may also be regarded as optimal transport maps on the simplex. In this paper we construct and study probability measures supported on spaces of concave functions. These measures may serve as prior distributions in Bayesian statistics and Cover's universal portfolio, and induce distribution-valued random variables via optimal transport. The random concave functions are constructed on the unit simplex by taking a suitably scaled (mollified, or soft) minimum of random hyperplanes. Depending on the regime of the parameters, we show that as the number of hyperplanes tends to infinity there are several possible limiting behaviors. In particular, there is a transition from a deterministic almost sure limit to a non-trivial limiting distribution that can be characterized using convex duality and Poisson point processes.

Robust Mathematical Formulation of Agent-Based Computational Economic Market Models
Maximilian Beikirch,Simon Cramer,Martin Frank,Philipp Otte,Emma Pabich,Torsten Trimborn

In science and especially in the economic literature, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects of numerical modeling for two agent-based computational economic market models: the Levy-Levy-Solomon model and the Franke-Westerhoff model. We derive time-continuous formulations of both models and, for the Levy-Levy-Solomon model, we discuss the impact of the time-scaling on the model behavior. For the Franke-Westerhoff model, we proof that a constraint required in the original model is not necessary for stability of the time-continuous model. It is shown that a semi-implicit discretization of the time-continuous system preserves this unconditional stability. In addition, this semi-implicit discretization can be computed at cost comparable to the original model.

КОНТРОЛИРУЮЩЕЕ ЛИЦО Ð"ЛЯ ЦЕЛИ СОÐ'ЕРШЕНИЯ СÐ"ЕЛОК С ЗАИНТЕРЕСОÐ'АННОСТЬЮ (Controller for the Purpose of Making Transactions with Interest)
Glushetskiy, Andrei
Russian Abstract: Ð' статье анализируется конструкция контролирующего лица хозяйственного общества, применяемая для цели совершения сделок с заинтересованностью. Сопоставляются два подхода к определению контролирующих лиц: только по правовым последствиям голосования участника хозяйственного общества на общем собрании участников общества или также по сведениям, содержащимся в реестрах, в которых фиксируется количество акций или размер долей, принадлежащих участникам общества.English Abstract: The article analyses the structure of the supervisory entity of the economic society, used for the purpose of committing transactions with interest. Compares two approaches to defining the controlling persons: only on the legal consequences of a vote of a participant in a business society at a general meeting of shareholders or to the information contained in registers which register the number of shares or amount of shares belonging to the company participants.

КРИТЕРИИ ОЦЕНКИ ОÐ'ЫЧНОЙ ХОЗЯЙСТÐ'ЕННОЙ Ð"ЕЯТЕЛЬНОСТИ (Criteria for the Evaluation of Ordinary Economic Activities)
Glushetskiy, Andrei
Russian Abstract: Преодолевается устойчивый стереотип,согласно которому любая сделка, стоимость которой превышает 25% балансовой стоимости активов общества, является крупной. Ð"аются критерии крупной сделки. Показаны новые подходы к определению обычной хозяйственной деятельности, предусмотренные законами об акционерных обществах и обществах с ограниченной ответственностью. Предлагается методика оценки сделок на предмет их совершения в рамках обычной хозяйственной деятельности.English Abstract: A stable stereotype is overcoming, according to which any transaction, the value of which exceeds 25% of the book value of the company's assets, is large. The criteria for a major transaction are given. The new approaches to the definition of ordinary business activities, provided by the laws on joint-stock companies and limited liability companies, are shown. A methodology is proposed for evaluating transactions with a view to making them within the ordinary course of business.

ПОРЯÐ"ОК СОÐ'МЕСТНОÐ"О ОСУЩЕСТÐ'ЛЕНИЯ НЕСКОЛЬКИМИ АКЦИОНЕРАМИ ОПРЕÐ"ЕЛЕННЫХ КОРПОРАТИÐ'НЫХ ПРОЦЕÐ"УР (Procedure for Joint Implementation of Separate Corporate Procedures by Several Shareholders)
Glushetskiy, Andrei
Russian Abstract: Аннотация. Рассматривается установленный в нормативном акте Ð'анка России ранее не применявшийся порядок совместного осуществления несколькими акционерами следующих корпоративных процедур:внесение вопроса (вопросов) в повестку дня общего собрания акционеров,выдвижение кандидатов в органы общества для избрания на общем собрании акционеров,предъявление требования о проведении внеочередного общего собрания акционеров. Сопоставляются различные возможные подходы к регулированию таких совместных действий акционеров и различные критерии определения акционеров, действующих совместно.English Abstract: The procedure for joint implementation by several shareholders of the following corporate procedures established by the Bank of Russia normative act is examined: introducing the issue (s) on the agenda of the general meeting of shareholders, nominating candidates to the company’s bodies for election at a general meeting of shareholders, presenting requirements for an extraordinary general meeting shareholders. Various possible approaches to regulating such joint actions of shareholders are compared with various criteria for determining shareholders acting together.