Kalman Filter vs Alternative Modeling Techniques and Applied Investment Strategies

This thesis examines the efficacy of alternative modeling techniques to predict stock market returns modeled with time-varying coefficients with the goal of developing and implementing a trading strategy that yields excess returns. First, we determine the modeling technique with the smallest forecast error using historical predictors: the differenced dividend-price ratio, lagged S&P 500 returns, and the change in implied volatility. The candidate modeling techniques include both constant and recursive ordinary least squares (OLS) regression methods and diverges from previous return forecast literature with the comparison of a state-space model (SSM) cast as a VAR(1) process to each OLS technique. The state-space model is found to be the superior modeling technique with the smallest RMSE 3.76% and greatest out-of-sample of 2.62% using delta VIX as the forecasting variable. Second, we demonstrate economic significance, using 1) monthly stock return forecasts in a market timing strategy, and 2) daily price forecasts in a simulated live pairs trading strategy taking into account implementation shortfall. In both trading strategies, the state-space model Kalman filter significantly outperforms the alternative OLS modeling techniques with an annualized total return of 21.64% in the market timing strategy and an annualized total return of 13.21% unlevered in the pairs trading strategy

Is News Sentiment More Than Just Noise?

Big Data analytics has recently fostered significant research on the influence of news sentiment in finance. This paper thus examines the effect of news sentiment on crude oil prices for different investor types according to the noise trader approach. The noise trader approach assumes the presence of informed and uninformed investors. Informed investors possess a perfect information horizon, whereas uninformed investors trade upon noise signals, such as sentiment. Methodologically, we decompose the crude oil price with a Kalman filter into a Kalman-smoothed, fundamental price component and a noise residual. We then regress news sentiment on both decomposed oil price components. Our findings suggest that news sentiment not only has a significant positive effect on the noise residual (as suggested by the noise trader approach), but also on the fundamental price. Thus, we find empirical evidence contradicting the noise trader model, which assumes that only uninformed investors trade on sentiment

Robust estimation of statistical temporal networks for financial time series modeling: theoretical formulation and temporal patterns typology

Although the idea of using Neural Networks technology for Financial Time Series prediction is an old one, the abundance and availability of stock-price data, including high-frequency (intra-minute) data has given an additional impetus to this fledgling field of study. Nevertheless, the study and applications have focused on the hedge-funds and brokerage operations of investments banks and very little academic attention has been devoted to the day-trading activity aiming at the accumulation of short-term incremental gains – still considered as a retail activity, similar to betting. The purpose of this research is precisely to investigate the possibility to use the sound time series smoothing techniques of feedforward Neural Networks along with elementary but powerful Classification Neural Networks techniques to produce a decision-aid system for intraday trading decisions. The basic design of the study consisted in presenting a new typology of intraday patterns and apply it to the 126 trading days of the first half of 2020 for the SP500 index, using intraday, minute-by-minute prices. While applying this methodology generated questions for further research, the major finding of this study was that when a price trend was soundly established during the first half of a trading day session, more often than not (in 57 cases versus 31) the trend continued till the end of the trading day. This result, which translates into the possibility for the trader to engage in short-term profitable trades, is non-trivial, though needs more past data to be consolidated. Further research into the conditions prevailing in other markets, before a trading day begins, could also prove useful

Stochastic control, numerical methods, and machine learning in finance and insurance

We consider three problems motivated by mathematical and computational finance which utilize forward-backward stochastic differential equations (FBSDEs) and other techniques from stochastic control. Firstly, we review the case of post-retirement annuitization with labor income in framework of optimal stochastic control and optimal stopping. We apply the martingale approach to a Cobb–Douglas type utility maximization problem. We have proved the theoretical existence and uniqueness of an optimal solution. Several analyses are made based on the simulations for the optimal stopping choice and strategies. Secondly, We review the convolution method in backward stochastic differential equations (BSDEs) framework and study the application of convolution method to Heston model. We provide an easy representation of the Heston characteristic function that avoids the discontinuities caused by branch rotations in the logarithm of complex functions and is able to be applied in calibration. We proposed two convolution schemes to the Heston model and provide the error analysis that shows the error orders of discretization and truncation. We review two error control methods and improve the accuracy on the boundaries. Numerical results comparing to a Fourier method and an integration method is provided. Thirdly, we review the forecasting problem in bond markets. Our data include both U.S. Treasuries and coupon bonds from twelve corporate issuers. We apply the arbitrage-free model in predicting the yields and the prices of coupon bonds in a sequential model with the Kalman filter, the extended Kalman filter and the particle filter. We implement the arbitrage penalty and obtain the optimal dynamic parameterization using deep neural networks. The purpose of the prediction is to examine the effect of arbitrage penalty and the forecasting performance on different time horizons. Our result shows that the arbitrage-free penalty has improving performance on short time period but downgrading performance on long time period. We provide analysis on the prediction errors, the distribution of errors, and the average excess return. The predicted bond prices shows the prediction errors have non-Gaussian distribution, excess kurtosis, and fat tails. Future works will be from two aspects, refine the importance sampling by non-parametric distribution and refine the term structure model with jump process and credit risk

Noise Trader Behavior - A Disaggregated Approach to Understanding News Reception in Financial Markets

Financial disclosures serve as primary intermediaries between companies and investors. However, investors have different information processing skills and might easily be misled by noisy signals that lack a deeper meaning. In financial markets, this is formalized by the noise trader theory, which groups investors into two categories: (a) informed investors assumed to form rational decisions and (b) noise traders forming beliefs partly based on non-fundamental noise signals and news sentiment. Yet, little is known about how these groups actually interpret textual information in financial statements and how the resulting stock market reaction differs. This work extends previous research by unraveling the role of word choice and semantic orientation in financial disclosures for both investor types. For this purpose, we use Kalman filtering to decompose the stock market reaction following the publication of U.S. regulated Form 8-K filings into a fundamental price component and a noise residual. We then use LASSO regression to identify the statistically relevant words for informed investors and noise traders. According to our results, each investor type assigns significantly different interpretations and degrees of importance to individual words and documents. Keywords: Noise trader theory, Information processing, Decision-making, Financial markets, News sentiment, Kalman filte

Estimation of Hidden Markov Models and Their Applications in Finance

Movements of financial variables exhibit extreme fluctuations during periods of economic crisis and times of market uncertainty. They are also affected by institutional policies and intervention of regulatory authorities. These structural changes driving prices and other economic indicators can be captured reasonably by models featuring regime-switching capabilities. Hidden Markov models (HMM) modulating the model parameters to incorporate such regime-switching dynamics have been put forward in recent years, but many of them could still be further improved. In this research, we aim to address some of the inadequacies of previous regime-switching models in terms of their capacity to provide better forecasts and efficiency in estimating parameters. New models are developed, and their corresponding filtering results are obtained and tested on financial data sets. The contributions of this research work include the following: (i) Recursive filtering algorithms are constructed for a regime-switching financial model consistent with no-arbitrage pricing. An application to the filtering and forecasting of futures prices under a multivariate set-up is presented. (ii) The modelling of risk due to market and funding liquidity is considered by capturing the joint dynamics of three time series (Treasury-Eurodollar spread, VIX and S\&P 500 spread-derived metric), which mirror liquidity levels in the financial markets. HMM filters under a multi-regime mean- reverting model are established. (iii) Kalman filtering techniques and the change of reference probability-based filtering methods are integrated to obtain hybrid algorithms. A pairs trading investment strategy is supported by the combined power of both HMM and Kalman filters. It is shown that an investor is able to benefit from the proposed interplay of the two filtering methods. (iv) A zero-delay HMM is devised for the evolution of multivariate foreign exchange rate data under a high-frequency trading environment. Recursive filters for quantities that are functions of a Markov chain are derived, which in turn provide optimal parameter estimates. (v) An algorithm is designed for the efficient calculation of the joint probability function for the occupation time in a Markov-modulated model for asset returns under a general number of economic regimes. The algorithm is constructed with accessible implementation and practical considerations in mind

On Explainable Deep Learning for Macroeconomic Forecasting and Finance

Deep Learning (DL) has gained momentum in recent years due to its incredible generalisation performance achieved across many learning tasks. Nevertheless, practitioners and academics have sometime been reluctant to apply these models because perceived as black boxes. This is particularly problematic in Economics and Finance. The objective of this thesis is to develop interpretable DL models and explainable DL tools with a focus on macroeconomic and financial applications. In doing so we highlight connections between such models and the standard economic ones. The first part of this work introduces a new class of interpretable models called Deep Dynamic Factor Models. The study merges the DL literature on autoencoders with that of the Econometrics on Dynamic Factor Models. Empirical validations of the approach are carried out both on synthetic and on real-time macroeconomic data. Part two of the work analyses feature attribution methods and Shapley values among explainability tools that are used to additively decompose model predictions. One of their limitations is highlighted, given that it is necessary to define a baseline that represents the missingness of a feature. A solution to the problem is proposed and compared against the ones currently in use both on simulated data and in the financial context of credit card default. We show that the proposed baseline is the only one that accounts for the specific use of the model. The final part of the work discusses the use of DL techniques for dynamic asset allocation. Using US market data, a comparison in recursive out-of-sample among different machine learning, economic-financial and hybrid models, including the one introduced in the first part of the work, is performed. Finally, a nonlinear factor-based portfolio performance attribution via the use of Shapley values and the baseline proposed in part two of the work is presented

Nonparametric Bayes dynamic modeling of relational data

Symmetric binary matrices representing relations among entities are commonly collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being in inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimensionality in characterizing the binary matrix through a lower-dimensional latent space representation, with the latent coordinates evolving in continuous time via Gaussian processes. By using a logistic mapping function from the probability matrix space to the latent relational space, we obtain a flexible and computational tractable formulation. Employing P\`olya-Gamma data augmentation, an efficient Gibbs sampler is developed for posterior computation, with the dimension of the latent space automatically inferred. We provide some theoretical results on flexibility of the model, and illustrate performance via simulation experiments. We also consider an application to co-movements in world financial markets