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  • Sequential Sampling for CGMY Processes via Decomposition of their Time Changes abstract We present a new and easy-to-implement sequential sampling method for CGMY processes with either finite or infinite variation, exploiting the time change representation of the CGMY model and a decomposition of its time change. We find that the time change can be decomposed into two independent components. While the first component is a finite generalized gamma convolution process whose increments can be sampled by either the exact double CFTP ("coupling from the past") method or an approximation scheme with high speed and accuracy, the second component can easily be made arbitrarily small in the $L^1$ sense. Our approach is appealing in that its approximation errors have a more transparent interpretation than those of existing methods. The proposed method is compared with several widely used methods via simulations of the pricing of European and path-dependent options.
  • On Biased Correlation Estimation abstract In general, underestimation of risk is something which should be avoided as far as possible. Especially in financial asset management, equity risk is typically characterized by the measure of portfolio variance, or indirectly by quantities which are derived from it. Since there is a linear dependency of the variance and the empirical correlation between asset classes, one is compelled to control or to avoid the possibility of underestimating correlation coefficients. In the present approach, we formalize common practice and classify these approaches by computing their probability of underestimation. In addition, we introduce a new estimator which is characterized by having the advantage of a constant and controllable probability of underestimation. We prove that the new estimator is statistically consistent.
  • Explicit expressions for European option pricing under a generalized skew normal distribution abstract Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative distribution function of the univariate skew normal and the bivariate standard normal distributions. Some special cases are investigated in a greater detail. To carry out the sensitivity of the option price to the skew parameters, numerical methods are applied. Some concluding remarks and further works are given. The results obtained are extensions of the results provided by [4].
  • A risk measure that optimally balances capital determination errors abstract In this paper, we propose a risk measurement approach that minimizes the expectation of sum between costs from capital determination overestimation and underestimation. We develop results that guarantee the existence of a solution, indicate properties that our risk measure fulfills, and characterize the resulting minimum cost as a deviation measure. We generalize this approach to a robust framework, where the minimization is over a supremum of expectations, based on a convex set of probability measures. We relate this robust approach with the dual representation of coherent risk measures. In a numerical example, we illustrate our approach for simulated and real financial data. Results indicate our approach leads to more parsimonious capital requirement determinations and reduces the mentioned costs.
  • Stock Prediction: a method based on extraction of news features and recurrent neural networks abstract This paper proposed a method for stock prediction. In terms of feature extraction, we extract the features of stock-related news besides stock prices. We first select some seed words based on experience which are the symbols of good news and bad news. Then we propose an optimization method and calculate the positive polar of all words. After that, we construct the features of news based on the positive polar of their words. In consideration of sequential stock prices and continuous news effects, we propose a recurrent neural network model to help predict stock prices. Compared to SVM classifier with price features, we find our proposed method has an over 5% improvement on stock prediction accuracy in experiments.
  • Spurious memory in non-equilibrium stochastic models of imitative behavior abstract The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example of Markov processes with spurious memory is stochastic process driven by a non-linear stochastic differential equation (SDE). This example is at odds with models built using fractional Brownian motion (fBm). We analyze differences between these two cases seeking to establish possible empirical tests of the origin of the observed long-range memory. We investigate probability density functions (PDFs) of burst and inter-burst duration in numerically obtained time series and compare with the results of fBm. Our analysis confirms that the characteristic feature of the processes described by a one-dimensional SDE is the power-law exponent $3/2$ of the burst or inter-burst duration PDF. This property of stochastic processes might be used to detect spurious memory in various non-equilibrium systems, where observed macroscopic behavior can be derived from the imitative interactions of agents.
  • Agent Inspired Trading Using Recurrent Reinforcement Learning and LSTM Neural Networks abstract With the breakthrough of computational power and deep neural networks, many areas that we haven't explore with various techniques that was researched rigorously in past is feasible. In this paper, we will walk through possible concepts to achieve robo-like trading or advising. In order to accomplish similar level of performance and generality, like a human trader, our agents learn for themselves to create successful strategies that lead to the human-level long-term rewards. The learning model is implemented in Long Short Term Memory (LSTM) recurrent structures with Reinforcement Learning or Evolution Strategies acting as agents The robustness and feasibility of the system is verified on GBPUSD trading.
  • An Alternative Estimation of a Time-Varying Parameter Model abstract A non-Bayesian, generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven very efficient because, unlike conventional methods, it does not require the Kalman filtering and smoothing procedures, but yields a smoothed estimate that is identical to the Kalman-smoothed estimate. Unlike the maximum likelihood estimator, the possibility of the pile-up problem is shown to be small. In addition, this approach enables us to possibly deal with stochastic volatility models and models with a time-dependent variance-covariance matrix.
  • Nash equilibria for game contingent claims with utility-based hedging abstract Game contingent claims (GCCs) generalize American contingent claims by allowing the writer to recall the option as long as it is not exercised, at the price of paying some penalty. In incomplete markets, an appealing approach is to analyze GCCs like their European and American counterparts by solving option holder's and writer's optimal investment problems in the underlying securities. By this, partial hedging opportunities are taken into account. We extend results in the literature by solving the stochastic game corresponding to GCCs with both continuous time stopping and trading. Namely, we construct Nash equilibria by rewriting the game as a non-zero-sum stopping game in which players compare payoffs in terms of their exponential utility indifference values. As a by-product, we also obtain an existence result for the optimal exercise time of an American claim under utility indifference valuation by relating it to the corresponding nonlinear Snell envelope.
  • Extended Gini-type measures of risk and variability abstract The main of this paper is to introduce a family of risk measures which generalizes the Gini-type measures of risk and variability, by taking into consideration the psychological behavior. Our risk measures family is coherent and catches variability with respect to the decision-maker attitude towards risk.
  • Optimal Trade Execution Under Endogenous Pressure to Liquidate: Theory and Numerical Solutions abstract We study optimal liquidation of a trading position (so-called block order or meta-order) in a market with a linear temporary price impact (Kyle, 1985). We endogenize the pressure to liquidate by introducing a downward drift in the unaffected asset price while simultaneously ruling out short sales. In this setting the liquidation time horizon becomes a stopping time determined endogenously, as part of the optimal strategy. We find that the optimal liquidation strategy is consistent with the square-root law which states that the average price impact per share is proportional to the square root of the size of the meta-order (Bershova and Rakhlin, 2013; Farmer et al., 2013; Donier et al., 2015; T\'oth et al., 2016).
    Mathematically, the Hamilton-Jacobi-Bellman equation of our optimization leads to a severely singular and numerically unstable ordinary differential equation initial value problem. We provide careful analysis of related singular mixed boundary value problems and devise a numerically stable computation strategy by re-introducing time dimension into an otherwise time-homogeneous task.
  • Lagrange regularisation approach to compare nested data sets and determine objectively financial bubbles' inceptions abstract Inspired by the question of identifying the start time $\tau$ of financial bubbles, we address the calibration of time series in which the inception of the latest regime of interest is unknown. By taking into account the tendency of a given model to overfit data, we introduce the Lagrange regularisation of the normalised sum of the squared residuals, $\chi^{2}_{np}(\Phi)$, to endogenously detect the optimal fitting window size := $w^* \in [\tau:\bar{t}_2]$ that should be used for calibration purposes for a fixed pseudo present time $\bar{t}_2$. The performance of the Lagrange regularisation of $\chi^{2}_{np}(\Phi)$ defined as $\chi^{2}_{\lambda (\Phi)}$ is exemplified on a simple Linear Regression problem with a change point and compared against the Residual Sum of Squares (RSS) := $\chi^{2}(\Phi)$ and RSS/(N-p):= $\chi^{2}_{np}(\Phi)$, where $N$ is the sample size and p is the number of degrees of freedom. Applied to synthetic models of financial bubbles with a well-defined transition regime and to a number of financial time series (US S\&P500, Brazil IBovespa and China SSEC Indices), the Lagrange regularisation of $\chi^{2}_{\lambda}(\Phi)$ is found to provide well-defined reasonable determinations of the starting times for major bubbles such as the bubbles ending with the 1987 Black-Monday, the 2008 Sub-prime crisis and minor speculative bubbles on other Indexes, without any further exogenous information. It thus allows one to endogenise the determination of the beginning time of bubbles, a problem that had not received previously a systematic objective solution.
  • Geopolitical Model of Investment Project Implementation abstract Two geopolitical actors implement a geopolitical project that involves transportaion and storage of some commodities. They interact with each other through a transport network. The network consists of several interconnected vertices. Some of the vetrices are trading hubs, storage spaces, production hubs and goods buyers. Actors wish to satify the demand of buyers and recieve the highest possible profit subject to compromise solution principle. A numerical example is given.
  • Hybrid marked point processes: characterisation, existence and uniqueness abstract We introduce the class of hybrid marked point processes, which incorporate a state process that interacts with past-dependent events. For example, like in a Hawkes process, events can exhibit self- or cross-excitation effects, but these effects can now also depend on the state process. Events of type A will precipitate events of type B only when they move the state process to some critical region, say. In parallel, as each event occurs, the state process transitions to a new value according to transition probabilities that vary with the event type. We prove that such dynamics are equivalent to an intensity process of a specific product form. Our main result addresses the existence of non-explosive marked point processes with given intensities by studying a well-known Poisson-driven SDE (via Poisson embedding). The existing strong existence and uniqueness results rely on a Lipschitz condition that the intensity of a hybrid marked point process may fail to satisfy. This motivates us to propose a natural pathwise construction that instead requires only sublinear behaviour of the intensity. Using a domination argument, we are able to verify that this construction yields indeed a solution. As we restrict ourselves to non-explosive marked point processes, we also manage to prove uniqueness without any specific assumptions on the intensity.
  • Ether: Bitcoin's competitor or ally? abstract Although Bitcoin has long been dominant in the crypto scene, it is certainly not alone. Ether is another cryptocurrency related project that has attracted an intensive attention because of its additional features. This study seeks to test whether these cryptocurrencies differ in terms of their volatile and speculative behaviors, hedge, safe haven and risk diversification properties. Using different econometric techniques, we show that a) Bitcoin and Ether are volatile and relatively more responsive to bad news, but the volatility of Ether is more persistent than that of Bitcoin; b) for both cryptocurrencies, the exuberance and the collapse of bubbles were identified, but Bitcoin appears more speculative than Ether; c) there is negative and significant correlation between Bitcoin/Ether and other assets (S\&P500 stocks, US bonds, oil), which would indicate that digital currencies can hedge against the price movements of these assets; d) there is negative tail independence between Bitcoin/Ether and other financial assets, implying that these cryptocurrencies exhibit the function of a weak safe haven; and e) The inclusion of Bitcoin/ Ether in a portfolio improve its efficiency in terms of higher reward-to-risk ratios. But investors who hold diversified portfolios made of stocks or bonds and Ether may face losses over bearish regime. In such situation, stock and bond investors may take a short position on Bitcoin.
  • Equilibrium Liquidity Premia abstract We study equilibrium returns in a continuous-time model where heterogeneous mean-variance investors trade subject to quadratic transaction costs. The unique equilibrium is characterized by a system of coupled but linear forward-backward stochastic differential equations. Explicit solutions obtain in a number of concrete settings. The corresponding liquidity premia compared to the frictionless case are mean reverting; they are positive if the more risk-averse agents are net sellers or if the asset supply expands over time.
  • Contagious disruptions and complexity traps in economic development abstract Poor economies not only produce less; they typically produce things that involve fewer inputs and fewer intermediate steps. Yet the supply chains of poor countries face more frequent disruptions---delivery failures, faulty parts, delays, power outages, theft, government failures---that systematically thwart the production process. To understand how these disruptions affect economic development, we model an evolving input--output network in which disruptions spread contagiously among optimizing agents. The key finding is that a poverty trap can emerge: agents adapt to frequent disruptions by producing simpler, less valuable goods, yet disruptions persist. Growing out of poverty requires that agents invest in buffers to disruptions. These buffers rise and then fall as the economy produces more complex goods, a prediction consistent with global patterns of input inventories. Large jumps in economic complexity can backfire. This result suggests why "big push" policies can fail, and it underscores the importance of reliability and of gradual increases in technological complexity.
  • Measuring the Knowledge Intensity of Economies with an Improved Measure of Economic Complexity abstract How much knowledge is there in an economy? In recent years, data on the mix of products that countries export has been used to construct measures of economic complexity that estimate the knowledge available in an economy and predict future economic growth. Here we introduce a new metric of economic complexity (ECI+) that measures the total exports of an economy corrected by how difficult it is to export each product. We use data from 1973 to 2013 to compare the ability of ECI+, the Economic Complexity Index (ECI), and Fitness complexity, to predict future economic growth using 5, 10, and 20-year panels in a pooled OLS, a random effects model, and a fixed effects model. We find that ECI+ outperforms ECI and Fitness in its ability to predict economic growth and in the consistency of its estimators across most econometric specifications. We then combine ECI+ with measures of physical capital, human capital, and institutions, to select a robust model of economic growth and test the robustness of ECI+. We find that the ability of ECI+ to predict growth is robust to these controls, and also, that human capital, political stability, and control of corruption, are positively associated with future economic growth, and initial level of income, is negatively associated with growth, in agreement with the traditional growth literature. Finally, we use ECI+ to generate economic growth predictions for the next 20 years and compare these predictions with the ones obtained using ECI and Fitness. These findings improve the methods available to estimate the knowledge intensity of economies using exports data and confirm the economic relevance of export structures.
  • Statistical properties and multifractality of Bitcoin abstract Using 1-min high frequency returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed and kurtosis largely deviates from the Gaussian expectation. Although with large time scales, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at small time scales and becomes consistent with zero at large time scales. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models and find no evidence of volatility asymmetry. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are also investigated and it is confirmed that both temporal correlation and the fat-tailed distribution contribute to the multifractality, and the degree of multifractality for the time correlation is stronger than that for the fat-tailed distribution.
  • Breadth Momentum and Vigilant Asset Allocation (VAA): Winning More by Losing Less
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