This paper presents a novel adaptive-filter approach for predicting assets on the stock markets. Concepts are introduced here, which allow understanding this method and computing of the corresponding forecast. This approach is applied, as an example, through the prediction over the actual valuation of the PETR3 shares (Petrobras ON) traded in the Brazilian Stock Market. The first-rate choices of the window length and the number of filter coefficient are evaluated. This is done by observing the correlation between the predictor signal and the actual course performed by the market in terms of both the window prevision length and filter coefficient values. It is shown that such adaptive predictors furnish, on the average, very substantial profit on the invested amount.

There has been considerable public debate about whether the economic impact of the current COVID19 restrictions are worth the costs. Although the potential impact of COVID19 has been modelled extensively, very few numbers have been presented in the discussions about potential economic impacts. For a good answer to the question - will the restrictions cause as much harm as COVID19? - credible evidence-based estimates are required, rather than simply rhetoric. Here we provide some preliminary estimates to compare the impact of the current restrictions against the direct impact of the virus. Since most countries are currently taking an approach that reduces the number of COVID19 deaths, the estimates we provide for deaths from COVID19 are deliberately taken from the low end of the estimates of the infection fatality rate, while estimates for deaths from an economic recession are deliberately computed from double the high end of confidence interval for severe economic recessions. This ensures that an adequate challenge to the status quo of the current restrictions is provided. Our analysis shows that strict restrictions to eradicate the virus are likely to lead to at least eight times fewer total deaths than an immediate return to work scenario.

We investigate whether sophisticated volatility estimation improves the out-of-sample performance of mean-variance portfolio strategies relative to the na\"{\i}ve 1/N strategy. The portfolio strategies rely solely upon second moments. Using a diverse group of econometric and portfolio models across multiple datasets, we show that a majority of models achieve significantly higher Sharpe ratios and lower portfolio volatility relative to the na\"{\i}ve rule, even after controlling for turnover costs. Our results suggest that there are benefits to employing more sophisticated econometric models than the sample covariance matrix, and that mean-variance strategies often outperform the na\"{\i}ve portfolio across multiple datasets and assessment criteria.

Differential machine learning (ML) extends supervised learning, with models trained on examples of not only inputs and labels, but also differentials of labels to inputs.

Differential ML is applicable in all situations where high quality first order derivatives wrt training inputs are available. In the context of financial Derivatives risk management, pathwise differentials are efficiently computed with automatic adjoint differentiation (AAD). Differential ML, combined with AAD, provides extremely effective pricing and risk approximations. We can produce fast pricing analytics in models too complex for closed form solutions, extract the risk factors of complex transactions and trading books, and effectively compute risk management metrics like reports across a large number of scenarios, backtesting and simulation of hedge strategies, or capital regulations.

The article focuses on differential deep learning (DL), arguably the strongest application. Standard DL trains neural networks (NN) on punctual examples, whereas differential DL teaches them the shape of the target function, resulting in vastly improved performance, illustrated with a number of numerical examples, both idealized and real world. In the online appendices, we apply differential learning to other ML models, like classic regression or principal component analysis (PCA), with equally remarkable results.

This paper is meant to be read in conjunction with its companion GitHub repo https://github.com/differential-machine-learning, where we posted a TensorFlow implementation, tested on Google Colab, along with examples from the article and additional ones. We also posted appendices covering many practical implementation details not covered in the paper, mathematical proofs, application to ML models besides neural networks and extensions necessary for a reliable implementation in production.

We propose a novel framework of estimating systemic risk measures and risk allocations based on Markov chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo (MC) methods often provide inefficient estimates due to the rare-event character of the crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments.

We analyze recently proposed mortgage contracts which aim to eliminate selective borrower default when the loan balance exceeds the house price (the "underwater" effect). We show that contracts which automatically reduce the outstanding balance in the event of local house price decline remove the default incentive, but may induce prepayment in low price states. However, low state prepayments vanish if borrower utility from home ownership, or outside options such as rental costs, are too high. We also show that capital gain sharing features, through prepayment penalties in high house price states, are ineffective, as they virtually eliminate prepayment in such states. For typical foreclosure costs, we find that contracts with automatic balance adjustments become preferable to the traditional fixed rate mortgage at contract rate spreads of approximately 50-100 basis points, depending on how far prices must fall before adjustments are made. Furthermore, these spreads rapidly decrease with the borrower utility from home ownership. Our results are obtained using American options pricing methods, in a model with diffusive home prices, and either diffusive or constant interest rates. We determine the contract, default and prepayment option values with optimal decision rules. We provide explicit solutions in the perpetual case with constant interest rates; and numerically compute the prepayment and default boundaries in the general case.

We propose a novel estimation procedure for scale-by-scale lead-lag relationships of financial assets observed at high-frequency in a non-synchronous manner. The proposed estimation procedure does not require any interpolation processing of original datasets and is applicable to those with highest time resolution available. Consistency of the proposed estimators is shown under the continuous-time framework that has been developed in our previous work Hayashi and Koike (2018). An empirical application to a quote dataset of the NASDAQ-100 assets identifies two types of lead-lag relationships at different time scales.

We fully characterize the absence of Butterfly arbitrage in the SVI formula for implied total variance proposed by Gatheral in 2004. The main ingredient is an intermediary characterization of the necessary condition for no arbitrage obtained for any model by Fukasawa in 2012 that the inverse functions of the -d1 and -d2 of the Black-Scholes formula, viewed as functions of the log-forward moneyness, should be increasing. A natural rescaling of the SVI parameters and a meticulous analysis of the Durrleman condition allow then to obtain simple range conditions on the parameters. This leads to a straightforward implementation of a least-squares calibration algorithm on the no arbitrage domain, which yields an excellent fit on the market data we used for our tests, with the guarantee to yield smiles with no Butterfly arbitrage.

Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In addition, it helps with the parsimonious construction of correlation matrices of large dimensions. However, complications arise in the presence of "unbalanced data", that is, when (expected) magnitude of observations over a single triangle, or between triangles, can vary substantially. Specifically, if a single common shock is applied to all of these cells, it can contribute insignificantly to the larger values and/or swamp the smaller ones, unless careful adjustments are made. This problem is further complicated in applications involving negative claim amounts. In this paper, we address this problem in the loss reserving context using a common shock Tweedie approach for unbalanced data. We show that the solution not only provides a much better balance of the common shock proportions relative to the unbalanced data, but it is also parsimonious. Finally, the common shock Tweedie model also provides distributional tractability.

To contain the pandemic of coronavirus (COVID-19) in Mainland China, the authorities have put in place a series of measures, including quarantines, social distancing, and travel restrictions. While these strategies have effectively dealt with the critical situations of outbreaks, the combination of the pandemic and mobility controls has slowed China's economic growth, resulting in the first quarterly decline of Gross Domestic Product (GDP) since GDP began to be calculated, in 1992. To characterize the potential shrinkage of the domestic economy, from the perspective of mobility, we propose two new economic indicators: the New Venues Created (NVC) and the Volumes of Visits to Venue (V^3), as the complementary measures to domestic investments and consumption activities, using the data of Baidu Maps. The historical records of these two indicators demonstrated strong correlations with the past figures of Chinese GDP, while the status quo has dramatically changed this year, due to the pandemic. We hereby presented a quantitative analysis to project the impact of the pandemic on economies, using the recent trends of NVC and V^3. We found that the most affected sectors would be travel-dependent businesses, such as hotels, educational institutes, and public transportation, while the sectors that are mandatory to human life, such as workplaces, residential areas, restaurants, and shopping sites, have been recovering rapidly. Analysis at the provincial level showed that the self-sufficient and self-sustainable economic regions, with internal supplies, production, and consumption, have recovered faster than those regions relying on global supply chains.

The Social Cost of Carbon (SCC) is estimated by integrated assessment models and is widely used by government agencies to value the climate impacts of rulemakings, however, the core discussion around SCC so far was focused on validity of obtained numerical estimates and related uncertainties while largely neglecting a deeper discussion of the SCC applicability limits stemming from the calculation method. This work provides a conceptual mathematical background and the economic interpretation that is behind the SCC calculation in the three widely used integrated assessment models. Policy makers need to be aware of the difference between the commonly implied and the actual meaning of SCC that substantially limits its applicability in practice. The presented results call for a critical revision of the SCC concept and the SCC calculation methods in integrated assessment models.

Using a large dataset of research seminars held at US economics departments in 2018, I explore the factors that determine who is invited to present at a research seminar and whether the invitation is accepted. I find that high-quality scholars have a higher probability of being invited than low-quality scholars, and researchers are more likely to accept an invitation if it is issued by a top economics department. The probability of being invited increases with the size of the host department. Young and low-quality scholars have a higher probability of accepting an invitation. The distance between the host department and invited scholar reduces the probability of being invited and accepting the invitation. Female scholars do not have a lower probability of being invited to give a research seminar than men.