Quantitative Finance

We generalize the classic Shiller cyclically adjusted price-earnings ratio (CAPE) used for prediction of future total returns of the American stock market. We split total returns into three components: earnings growth, dividend yield, and valuation change. The first two components are fundamental, the third is speculative. We treat earnings growth as exogenous. Combining the other two components gives us a new valuation measure, which fits autoregression of order 1 with Gaussian innovations, centered at 4.6%. Therefore, long-term total returns equals long-term earnings growth plus 4.6%. We compare this new valuation measure with CAPE. We confirm the classic rule: a retiree should invest in stocks and withdraw 4% of initial wealth after adjusting for inflation, this will preserve wealth and establish retirement income.

In recent years, machine learning and deep learning have become popular methods for financial data analysis, including financial textual data, numerical data, and graphical data. This paper proposes to use sentiment analysis to extract useful information from multiple textual data sources and a blending ensemble deep learning model to predict future stock movement. The blending ensemble model contains two levels. The first level contains two Recurrent Neural Networks (RNNs), one Long-Short Term Memory network (LSTM) and one Gated Recurrent Units network (GRU), followed by a fully connected neural network as the second level model. The RNNs, LSTM, and GRU models can effectively capture the time-series events in the input data, and the fully connected neural network is used to ensemble several individual prediction results to further improve the prediction accuracy. The purpose of this work is to explain our design philosophy and show that ensemble deep learning technologies can truly predict future stock price trends more effectively and can better assist investors in making the right investment decision than other traditional methods.

We consider in this paper some structured financial products, known as reverse convertible notes, that resulted in substantial losses to certain buyers of these notes in recent years. We shall focus on specific reverse convertible notes known as "Autocallable Optimization Securities with Contingent Protection Linked to the S\&P 500 Financial Index," because these notes are representative of the broad spectrum of reverse convertibles notes. Therefore, the analysis provided in this paper is applicable to many other reverse convertible notes. We begin by describing the notes in detail and identifying potential areas of confusion in the pricing supplement to the prospectus for the notes. We deduce two possible interpretations of the payment procedure for the notes and apply the Law of Total Expectation to develop a probabilistic analysis for each interpretation. We also determine the corresponding expected net payments to note-holders under various scenarios for the financial markets and show that, under a broad range of scenarios, note-holders were likely to suffer substantial losses. As a consequence, we infer that the prospectus is sufficiently complex that financial advisers generally lacked the mathematical knowledge and expertise to understand the prospectus completely. Therefore, financial advisers who recommended purchases of the notes did not have the knowledge and expertise that is required by a fiduciary relationship, hence were unable to exercise fiduciary duty, and ultimately misguided their clients. We conclude that these reverse convertibles notes were designed by financial institutions to insure themselves, against significant declines in the equities markets, at the expense of note-holders.

We demonstrate that the tail dependence should always be taken into account as a proxy for systematic risk of loss for investments. We provide the clear statistical evidence of that the structure of investment portfolios on a regulated market should be adjusted to the price of gold. Our finding suggests that the active bartering of oil for goods would prevent collapsing the national market facing international sanctions.

A wide variety of deep reinforcement learning (DRL) models have recently been proposed to learn profitable investment strategies. The rules learned by these models outperform the previous strategies specially in high frequency trading environments. However, it is shown that the quality of the extracted features from a long-term sequence of raw prices of the instruments greatly affects the performance of the trading rules learned by these models. Employing a neural encoder-decoder structure to extract informative features from complex input time-series has proved very effective in other popular tasks like neural machine translation and video captioning in which the models face a similar problem. The encoder-decoder framework extracts highly informative features from a long sequence of prices along with learning how to generate outputs based on the extracted features. In this paper, a novel end-to-end model based on the neural encoder-decoder framework combined with DRL is proposed to learn single instrument trading strategies from a long sequence of raw prices of the instrument. The proposed model consists of an encoder which is a neural structure responsible for learning informative features from the input sequence, and a decoder which is a DRL model responsible for learning profitable strategies based on the features extracted by the encoder. The parameters of the encoder and the decoder structures are learned jointly, which enables the encoder to extract features fitted to the task of the decoder DRL. In addition, the effects of different structures for the encoder and various forms of the input sequences on the performance of the learned strategies are investigated. Experimental results showed that the proposed model outperforms other state-of-the-art models in highly dynamic environments.

We studied the volatility and cross-sectional return dispersion effect of S&P Health Care Sector under the covid-19 epidemic. We innovatively used the Google index to proxy the impact of the epidemic and modeled the volatility. We also studied the influencing factors of the log-return of S&P Energy Sector and S&P Health Care Sector. We found that volatility is significantly affected by both the epidemic and cross-sectional return dispersion, and the coefficients in front of them are all positive, which means that the herding behaviour did not exist and as the cross-sectional return dispersion increases and the epidemic becomes more severe, the volatility of stock returns is also increasing. We also found that the epidemic has a significant negative impact on the return of the energy sector, and finally we provided our suggestions to investors.

Prediction of future movement of stock prices has been a subject matter of many research work. There is a gamut of literature of technical analysis of stock prices where the objective is to identify patterns in stock price movements and derive profit from it. Improving the prediction accuracy remains the single most challenge in this area of research. We propose a hybrid approach for stock price movement prediction using machine learning, deep learning, and natural language processing. We select the NIFTY 50 index values of the National Stock Exchange of India, and collect its daily price movement over a period of three years (2015 to 2017). Based on the data of 2015 to 2017, we build various predictive models using machine learning, and then use those models to predict the closing value of NIFTY 50 for the period January 2018 till June 2019 with a prediction horizon of one week. For predicting the price movement patterns, we use a number of classification techniques, while for predicting the actual closing price of the stock, various regression models have been used. We also build a Long and Short-Term Memory - based deep learning network for predicting the closing price of the stocks and compare the prediction accuracies of the machine learning models with the LSTM model. We further augment the predictive model by integrating a sentiment analysis module on twitter data to correlate the public sentiment of stock prices with the market sentiment. This has been done using twitter sentiment and previous week closing values to predict stock price movement for the next week. We tested our proposed scheme using a cross validation method based on Self Organizing Fuzzy Neural Networks and found extremely interesting results.

Stock return predictability is an important research theme as it reflects our economic and social organization, and significant efforts are made to explain the dynamism therein. Statistics of strong explanative power, called "factor" have been proposed to summarize the essence of predictive stock returns. Although machine learning methods are increasingly popular in stock return prediction, an inference of the stock returns is highly elusive, and still most investors, if partly, rely on their intuition to build a better decision making. The challenge here is to make an investment strategy that is consistent over a reasonably long period, with the minimum human decision on the entire process. To this end, we propose a new stock return prediction framework that we call Ranked Information Coefficient Neural Network (RIC-NN). RIC-NN is a deep learning approach and includes the following three novel ideas: (1) nonlinear multi-factor approach, (2) stopping criteria with ranked information coefficient (rank IC), and (3) deep transfer learning among multiple regions. Experimental comparison with the stocks in the Morgan Stanley Capital International (MSCI) indices shows that RIC-NN outperforms not only off-the-shelf machine learning methods but also the average return of major equity investment funds in the last fourteen years.

This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window averaged sample estimate of the second order cumulant spectrum to build a test statistic with an asymptotic complex standard normal distribution. We derive the test statistic, study the properties of the test and demonstrate its application using 137Cs gamma ray decay data. Future areas of research include testing for strict stationarity of graph signals, with applications in learning convolutional neural networks on graphs, denoising, and inpainting.

We propose and investigate two model classes for forward power price dynamics, based on continuous branching processes with immigration, and on Hawkes processes with exponential kernel, respectively. The models proposed exhibit jumps clustering features. Models of this kind have been already proposed for the spot price dynamics, but the main purpose of the present work is to investigate the performances of such models in describing the forward dynamics. We adopt a Heath-Jarrow-Morton approach in order to capture the whole forward curve evolution. By examining daily data in the French power market, we perform a goodness-of-fit test and we present our conclusions about the adequacy of these models in describing the forward prices evolution.