We present a model of worldwide crisis contagion based on the Google matrix analysis of the world trade network obtained from the UN Comtrade database. The fraction of bankrupted countries exhibits an \textit{on-off} phase transition governed by a bankruptcy threshold $\kappa$ related to the trade balance of the countries. For $\kappa>\kappa_c$, the contagion is circumscribed to less than 10\% of the countries, whereas, for $\kappa<\kappa_c$, the crisis is global with about 90\% of the countries going to bankruptcy. We measure the total cost of the crisis during the contagion process. In addition to providing contagion scenarios, our model allows to probe the structural trading dependencies between countries. For different networks extracted from the world trade exchanges of the last two decades, the global crisis comes from the Western world. In particular, the source of the global crisis is systematically the Old Continent and The Americas (mainly US and Mexico). Besides the economy of Australia, those of Asian countries, such as China, India, Indonesia, Malaysia and Thailand, are the last to fall during the contagion. Also, the four BRIC are among the most robust countries to the world trade crisis.

Stock price prediction has been an important research theme both academically and practically. Various methods to predict stock prices have been studied until now. The feature that explains the stock price by a cross-section analysis is called a "factor" in the field of finance. Many empirical studies in finance have identified which stocks having features in the cross-section relatively increase and which decrease in terms of price. Recently, stock price prediction methods using machine learning, especially deep learning, have been proposed since the relationship between these factors and stock prices is complex and non-linear. However, there are no practical examples for actual investment management. In this paper, therefore, we present a cross-sectional daily stock price prediction framework using deep learning for actual investment management. For example, we build a portfolio with information available at the time of market closing and invest at the time of market opening the next day. We perform empirical analysis in the Japanese stock market and confirm the profitability of our framework.

We develop a methodology for detecting asset bubbles using a neural network. We rely on the theory of local martingales in continuous-time and use a deep network to estimate the diffusion coefficient of the price process more accurately than the current estimator, obtaining an improved detection of bubbles. We show the outperformance of our algorithm over the existing statistical method in a laboratory created with simulated data. We then apply the network classification to real data and build a zero net exposure trading strategy that exploits the risky arbitrage emanating from the presence of bubbles in the US equity market from 2006 to 2008. The profitability of the strategy provides an estimation of the economical magnitude of bubbles as well as support for the theoretical assumptions relied on.

We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market with multiple traded assets whose marginal risk-neutral distributions are known, and assume that several derivatives written on these assets are traded simultaneously. In this setting, there is a bijection between the existence of an equivalent martingale measure and the existence of a copula that couples these marginals. Using this bijection and recent results on improved Fr\'echet-Hoeffding bounds in the presence of additional information, we derive sufficient conditions for the absence of arbitrage and formulate an optimization problem for the detection of a possible arbitrage opportunity. This problem can be solved efficiently using numerical optimization routines. The most interesting practical outcome is the following: we can construct a financial market where each multi-asset derivative is traded within its own no-arbitrage interval, and yet when considered together an arbitrage opportunity may arise.

The present paper originated from a problem in Financial Mathematics concerned with calculating the value of a European call option based on multiple assets each following the binomial model. The model led to an interesting family of polytopes $P(b)$ associated with the power-set $\mathcal{L} = \wp\{1,\dots,m\}$ and parameterized by $b \in \mathbb{R}^m$, each of which is a collection of probability density function on $\mathcal{L}$. For each non-empty $P(b)$ there results a family of probability measures on $\mathcal{L}^n$ and, given a function $F \colon \mathcal{L}^n \to \mathbb{R}$, our goal is to find among these probability measures one which maximises (resp. minimises) the expectation of $F$. In this paper we identify a family of such functions $F$, all of whose expectations are maximised (resp. minimised under some conditions) by the same {\em product} probability measure defined by a distinguished vertex of $P(b)$ called the supervertex (resp. the subvertex). The pay-offs of European call options belong to this family of functions.

In recent years cryptocurrency trading has captured the attention of practitioners and academics. The volume of the exchange with standard currencies has known a dramatic increasing of late. This paper addresses to the need of models describing a bitcoin-US dollar exchange dynamic and their use to evaluate European option having bitcoin as underlying asset.

The St. Petersburg Paradox was proposed before two centuries. In the paper we proposed a new pricing theory with several rules to solve the paradox and state that the fair pricing should be judged by buyer and seller independently. The pricing theory we proposed can be applied to financial market to solve the confusion with fat tails.

We revisit and demonstrate the Epps effect using two well-known non-parametric covariance estimators; the Malliavin and Mancino (MM), and Hayashi and Yoshida (HY) estimators. We show the existence of the Epps effect in the top 10 stocks from the Johannesburg Stock Exchange (JSE) by various methods of aggregating Trade and Quote (TAQ) data. Concretely, we compare calendar time sampling with two volume time sampling methods: asset intrinsic volume time averaging, and volume time averaging synchronised in volume time across assets relative to the least and most liquid asset clocks. We reaffirm the argument made in much of the literature that the MM estimator is more representative of trade time reality because it does not over-estimate short-term correlations in an asynchronous event driven world. We confirm well known market phenomenology with the aim of providing some standardised R based simulation tools.

Comovement of economic activity across sectors and countries is a defining feature of business cycles. However, standard models that attribute comovement to propagation of exogenous shocks struggle to generate a level of comovement that is as high as in the data. In this paper, we consider models that produce business cycles endogenously, through some form of non-linear dynamics---limit cycles or chaos. These models generate stronger comovement, because they combine shock propagation with synchronization of endogenous dynamics. In particular, we study a demand-driven model in which business cycles emerge from strategic complementarities across sectors in different countries, synchronizing their oscillations through input-output linkages. We first use a combination of analytical methods and extensive numerical simulations to establish a number of theoretical results. We show that the importance that sectors or countries have in setting the common frequency of oscillations depends on their eigenvector centrality in the input-output network, and we develop an eigendecomposition that explores the interplay between non-linear dynamics, shock propagation and network structure. We then calibrate our model to data on 27 sectors and 17 countries, showing that synchronization indeed produces stronger comovement, giving more flexibility to match the data.

Optimal asset allocation is a key topic in modern finance theory. To realize the optimal asset allocation on investor's risk aversion, various portfolio construction methods have been proposed. Recently, the applications of machine learning are rapidly growing in the area of finance. In this article, we propose the Student's $t$-process latent variable model (TPLVM) to describe non-Gaussian fluctuations of financial timeseries by lower dimensional latent variables. Subsequently, we apply the TPLVM to minimum-variance portfolio as an alternative of existing nonlinear factor models. To test the performance of the proposed portfolio, we construct minimum-variance portfolios of global stock market indices based on the TPLVM or Gaussian process latent variable model. By comparing these portfolios, we confirm the proposed portfolio outperforms that of the existing Gaussian process latent variable model.

Nowadays, machine learning methods have been widely used in stock prediction. Traditional approaches assume an identical data distribution, under which a learned model on the training data is fixed and applied directly in the test data. Although such assumption has made traditional machine learning techniques succeed in many real-world tasks, the highly dynamic nature of the stock market invalidates the strict assumption in stock prediction. To address this challenge, we propose the second-order identical distribution assumption, where the data distribution is assumed to be fluctuating over time with certain patterns. Based on such assumption, we develop a second-order learning paradigm with multi-scale patterns. Extensive experiments on real-world Chinese stock data demonstrate the effectiveness of our second-order learning paradigm in stock prediction.