This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To capture the multiscale volatility of the financial market, our model adds a fast scale factor to the well-known Heston volatility and we derive approximate analytic pricing formulas for the options under the model. The analytic tractability can greatly improve the efficiency of calibration compared to fitting procedures with the finite difference method or Monte Carlo simulation. Our experiment using options data from 2016 to 2018 shows that the model reduces the errors on the training sets of the SPX and VIX options by 9.9% and 13.2%, respectively, and decreases the errors on the test sets of the SPX and VIX options by 13.0\% and 16.5\%, respectively, compared to the single-scale model of Heston. The error reduction is possible because the additional factor reflects short-term impacts on the market, which is difficult to achieve with only one factor. It highlights the necessity of modeling multiscale volatility.

Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when DL is used for financial time series forecasting tasks, where the non-stationary and multimodal nature of the data pose significant challenges and severely affect the performance of DL models. In this work, a simple, yet effective, neural layer, that is capable of adaptively normalizing the input time series, while taking into account the distribution of the data, is proposed. The proposed layer is trained in an end-to-end fashion using back-propagation and leads to significant performance improvements compared to other evaluated normalization schemes. The proposed method differs from traditional normalization methods since it learns how to perform normalization for a given task instead of using a fixed normalization scheme. At the same time, it can be directly applied to any new time series without requiring re-training. The effectiveness of the proposed method is demonstrated using a large-scale limit order book dataset, as well as a load forecasting dataset.

We investigate state-dependent effects of fiscal multipliers and allow for endogenous sample splitting to determine whether the US economy is in a slack state. When the endogenized slack state is estimated as the period of the unemployment rate higher than about 12 percent, the estimated cumulative multipliers are significantly larger during slack periods than non-slack periods and are above unity. We also examine the possibility of time-varying regimes of slackness and find that our empirical results are robust under a more flexible framework. Our estimation results points out the importance of the heterogenous effects of fiscal policy.

We develop a dynamic version of the SSVI parameterisation for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the constraint that the total implied variance needs to be null at the maturity of the option, we show that no model--in our setting--allows for such behaviour. This naturally gives rise to the concept of implied volatility bubbles, whereby trading in an arbitrage-free way is only possible during part of the life of the contract, but not all the way until expiry.

In the following paper, we analyse the ID$_3$-Price in the German Intraday Continuous electricity market using an econometric time series model. A multivariate approach is conducted for hourly and quarter-hourly products separately. We estimate the model using lasso and elastic net techniques and perform an out-of-sample, very short-term forecasting study. The model's performance is compared with benchmark models and is discussed in detail. Forecasting results provide new insights to the German Intraday Continuous electricity market regarding its efficiency and to the ID$_3$-Price behaviour.

Sustainable development is a worldwide recognized social and political goal, discussed in both academic and political discourse and with much research on the topic related to sustainable development in higher education. Since mental models are formed more effectively at school age, we propose a new way of thinking that will help achieve this goal. This paper was written in the context of Russia, where the topic of sustainable development in education is poorly developed. The authors used the classical methodology of the case analysis. The analysis and interpretation of the results were conducted in the framework of the institutional theory. Presented is the case of Ural Federal University, which has been working for several years on the creation of a device for the purification of industrial sewer water in the framework of an initiative student group. Schoolchildren recently joined the program, and such projects have been called university-to-school projects. Successful solutions of inventive tasks contribute to the formation of mental models. This case has been analyzed in terms of institutionalism, and the authors argue for the primacy of mental institutions over normative ones during sustainable society construction. This case study is the first to analyze a partnership between a Federal University and local schools regarding sustainable education and proposes a new way of thinking.

We introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). The ES currently receives much attention through its introduction into the Basel III Accords, which stipulate its use as the primary market risk measure for the international banking regulation. We utilize joint loss functions for the pair ES and Value at Risk to set up three ES encompassing test variants. The tests are built on misspecification robust asymptotic theory and we verify the finite sample properties of the tests in an extensive simulation study. We use the encompassing tests to illustrate the potential of forecast combination methods for different financial assets.

Portfolio optimization emerged with the seminal paper of Markowitz (1952). The original mean-variance framework is appealing because it is very efficient from a computational point of view. However, it also has one well-established failing since it can lead to portfolios that are not optimal from a financial point of view. Nevertheless, very few models have succeeded in providing a real alternative solution to the Markowitz model. The main reason lies in the fact that most academic portfolio optimization models are intractable in real life although they present solid theoretical properties. By intractable we mean that they can be implemented for an investment universe with a small number of assets using a lot of computational resources and skills, but they are unable to manage a universe with dozens or hundreds of assets. However, the emergence and the rapid development of robo-advisors means that we need to rethink portfolio optimization and go beyond the traditional mean-variance optimization approach. Another industry has faced similar issues concerning large-scale optimization problems. Machine learning has long been associated with linear and logistic regression models. Again, the reason was the inability of optimization algorithms to solve high-dimensional industrial problems. Nevertheless, the end of the 1990s marked an important turning point with the development and the rediscovery of several methods that have since produced impressive results. The goal of this paper is to show how portfolio allocation can benefit from the development of these large-scale optimization algorithms. Not all of these algorithms are useful in our case, but four of them are essential when solving complex portfolio optimization problems. These four algorithms are the coordinate descent, the alternating direction method of multipliers, the proximal gradient method and the Dykstra's algorithm.

Will a large economy be stable? Building on Robert May's original argument for large ecosystems, we conjecture that evolutionary and behavioural forces conspire to drive the economy towards marginal stability. We study networks of firms in which inputs for production are not easily substitutable, as in several real-world supply chains. Relying on results from Random Matrix Theory, we argue that such networks generically become dysfunctional when their size increases, when the heterogeneity between firms becomes too strong or when substitutability of their production inputs is reduced. At marginal stability and for large heterogeneities, we find that the distribution of firm sizes develops a power-law tail, as observed empirically. Crises can be triggered by small idiosyncratic shocks, which lead to "avalanches" of defaults characterized by a power-law distribution of total output losses. This scenario would naturally explain the well-known "small shocks, large business cycles" puzzle, as anticipated long ago by Bak, Chen, Scheinkman and Woodford.

We define the concept of good trade execution and we construct explicit adapted good trade execution strategies in the framework of linear temporary market impact. Good trade execution strategies are dynamic, in the sense that they react to the actual realisation of the traded asset price path over the trading period; this is paramount in volatile regimes, where price trajectories can considerably deviate from their expected value. Remarkably however, the implementation of our strategies does not require the full specification of an SDE evolution for the traded asset price, making them robust across different models. Moreover, rather than minimising the expected trading cost, good trade execution strategies minimise trading costs in a pathwise sense, a point of view not yet considered in the literature. The mathematical apparatus for such a pathwise minimisation hinges on certain random Young differential equations that correspond to the Euler-Lagrange equations of the classical Calculus of Variations. These Young differential equations characterise our good trade execution strategies in terms of an initial value problem that allows for easy implementations.

This paper studies the bail-out optimal dividend problem with regime switching under the constraint that the cumulative dividend strategy is absolutely continuous. We confirm the optimality of the regime-modulated refraction-reflection strategy when the underlying risk model follows a general spectrally negative Markov additive process. To verify the conjecture of a barrier type optimal control, we first introduce and study an auxiliary problem with the final payoff at an exponential terminal time and characterize the optimal threshold explicitly using fluctuation identities of the refracted-reflected Levy process. Second, we transform the problem with regime-switching into an equivalent local optimization problem with a final payoff up to the first regime switching time. The refraction-reflection strategy with regime-modulated thresholds can be shown as optimal by using results in the first step and some fixed point arguments for auxiliary recursive iterations.

Recent technology advances have enabled firms to flexibly process and analyze sophisticated employee performance data at a reduced and yet significant cost. We develop a theory of optimal incentive contracting where the monitoring technology that governs the above procedure is part of the designer's strategic planning. In otherwise standard principal-agent models with moral hazard, we allow the principal to partition agents' performance data into any finite categories and to pay for the amount of information that the output signal carries. Through analysis of the trade-off between giving incentives to agents and saving the monitoring cost, we obtain characterizations of optimal monitoring technologies such as information aggregation, strict MLRP, likelihood ratio-convex performance classification, group evaluation in response to rising monitoring costs, and assessing multiple task performances according to agents' endogenous tendencies to shirk. We examine the implications of these results for workforce management and firms' internal organizations.

In this paper, we derive the price of a European call option of an asset following a normal process assuming stochastic volatility. The volatility is assumed to follow the Cox Ingersoll Ross (CIR) process. We then use the fast Fourier transform (FFT) to evaluate the option price given we know the characteristic function of the return analytically. We compare the results of fast Fourier transform with the Monte Carlo simulation results of our process. Further, we present a numerical example to understand the normal implied volatility of the model.

Sectoral production is modeled by cascading binary compounding processes. The sequence of processes is discovered in a self-similar hierarchical structure stylized in the economy-wide networks of production. All nesting substitution elasticities and Hicks neutral productivity growths are measured in order that the general equilibrium feedbacks between all sectoral unit cost functions reenact the transformation of networks observed as a set of two temporally distant input-output coefficient matrices. This system of unit cost functions is examined as to how idiosyncratic sectoral productivity shocks propagate into aggregate macroeconomic fluctuations in light of potential networks transformation. Also, we study how sectoral productivity increments propagate into dynamical general equilibrium allowing networks transformation and ultimately gain social benefits.

This paper introduces novel backtests for the risk measure Expected Shortfall (ES) following the testing idea of Mincer and Zarnowitz (1969). Estimating a regression framework for the ES stand-alone is infeasible, and thus, our tests are based on a joint regression for the Value at Risk and the ES, which allows for different test specifications. These ES backtests are the first which solely backtest the ES in the sense that they only require ES forecasts as input parameters. As the tests are potentially subject to model misspecification, we provide asymptotic theory under misspecification for the underlying joint regression. We find that employing a misspecification robust covariance estimator substantially improves the tests' performance. We compare our backtests to existing approaches and find that our tests outperform the competitors throughout all considered simulations. In an empirical illustration, we apply our backtests to ES forecasts for 200 stocks of the S&P 500 index.

We study the system of heterogeneous interbank lending and borrowing based on the relative average of log-capitalization given by the linear combination of the average within groups and the ensemble average and describe the evolution of log-capitalization by a system of coupled diffusions. The model incorporates a game feature with homogeneity within groups and heterogeneity between groups where banks search for the optimal lending or borrowing strategies through minimizing the heterogeneous linear quadratic costs in order to avoid to approach the default barrier. Due to the complicity of the lending and borrowing system, the closed-loop Nash equilibria and the open-loop Nash equilibria are both driven by the coupled Riccati equations. The existence of the equilibria in the two-group case where the number of banks are sufficiently large is guaranteed by the solvability for the coupled Riccati equations as the number of banks goes to infinity in each group. The equilibria are consisted of the mean-reverting term identical to the one group game and the group average owing to heterogeneity. In addition, the corresponding heterogeneous mean filed game with the arbitrary number of groups is also discussed. The existence of the $\epsilon$-Nash equilibrium in the general $d$ heterogeneous groups is also verified. Finally, in the financial implication, we observe the Nash equilibria governed by the mean-reverting term and the linear combination of the ensemble averages of individual groups and study the influence of the relative parameters on the liquidity rate through the numerical analysis.

We compare performance of US stocks based on their size (market capitalization). We regress alpha and beta over size and other factors for individual stocks in Standard & Poor 500, and for randomly generated portfolios. In addition, we compare exchange-traded funds (ETFs) consisting of large-, mid- and small-cap stocks, including international ETFs. Conclusions: Size and market exposure (beta) are inversely related (strong evidence for ETFs and portfolios, weaker evidence for individual stocks).

In this paper we formulate a regression problem to predict realized volatility by using option price data and enhance VIX-styled volatility indices' predictability and liquidity. We test algorithms including regularized regression and machine learning methods such as Feedforward Neural Networks (FNN) on S&P 500 Index and its option data. By conducting a time series validation we find that both Ridge regression and FNN can improve volatility indexing with higher prediction performance and fewer options required. The best approach found is to predict the difference between the realized volatility and the VIX-styled index's prediction rather than to predict the realized volatility directly, representing a successful combination of human learning and machine learning. We also discuss suitability of different regression algorithms for volatility indexing and applications of our findings.

The paper uses diffusion models to understand the main determinants of diffusion of solar photovoltaic panels (SPP) worldwide, focusing on the role of public incentives. We applied the generalized Bass model (GBM) to adoption data of 26 countries between 1992-2016. The SPP market appears as a frail and complicate one, lacking public media support. Even the major shocks in adoption curves, following state incentive implemented after 2006, failed to go beyond short-term effects and therefore were unable to provide sustained momentum to the market. This suggests that further barriers to adoption should be removed.