The problem of option pricing is treated using the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be mean‐reverting. Assuming that only discrete past stock information is available, an interacting particle stochastic filtering algorithm due to Del Moral et al. (Del Moral et al., 2001 Del Moral, P. , Jacod, J. and Protter, P. 2001. The Monte‐Carlo method for filtering with discrete time observations.. Probability Theory and Related Fields, 120: 346–368. [Crossref], [Web of Science ®] [Google Scholar] ) is adapted to estimate the SV, and a quadrinomial tree is constructed which samples volatilities from the SV filter's empirical measure approximation at time 0. Proofs of convergence of the tree to continuous‐time SV models are provided. Classical arbitrage‐free option pricing is performed on the tree, and provides answers that are close to market prices of options on the SP500 or on blue‐chip stocks. Results obtained here are compared with those from non‐random volatility models, and from models which continue to estimate volatility after time 0. It is shown precisely how to calibrate the incomplete market, choosing a specific martingale measure, by using a benchmark option.

In 2012, Securities and Exchange Commission (SEC) mandated all corporate filings for any company doing business in the U.S. be entered into the electronic data gathering, analysis, and retrieval (EDGAR) system. In this work, we are investigating ways to analyze the data available through the EDGAR database. This may serve portfolio managers (pension funds, mutual funds, insurance, and hedge funds) to get automated insights into companies they invest in, to better manage their portfolios. The analysis is based on artificial neural networks applied to the data. In particular, one of the most popular machine learning methods, the convolutional neural network (CNN) architecture, originally developed to interpret and classify images, is now being used to interpret financial data. This work investigates the best way to input data collected from the SEC filings into a CNN architecture. We incorporate accounting principles and mathematical methods into the design of three image encoding methods. Specifically, two methods are derived from accounting principles (sequential arrangement, category chunk arrangement) and one is using a purely mathematical technique [the Hilbert vector arrangement (HVA)]. In this work, we analyze fundamental financial data as well as financial ratio data and study companies from the financial, healthcare, and information technology sectors in the United States. We find that using imaging techniques to input data for CNN works better for financial ratio data but is not significantly better than simply using the 1-D input directly for fundamental data. We do not find the HVA technique to be significantly better than other imaging techniques.

In this research, we develop a set of new measures to evaluate the data flow in the U.S. equity exchanges using Level I order book data. The quantities we develop and use to summarize trading activity are as follows: the activity‐weighted spread and the activity‐weighted return. We study the distribution of these two quantities and observe that there are significant changes in their behavior when equity markets are impacted by an external event. We focus the study on three exchanges: New York Stock Exchange (NYS), NASDAQ InterMarket (THM), and NYSE Arca (PSE) since they exhibit the largest impact to the proposed measures. We also study two different financial events which happened suddenly without any prior warning. These events are as follows: May 6, 2010, the “Flash Crash,” and April 23, 2013, the “Hoax tweet” event. Based on the results we obtain, the order flow dynamic is disturbed during these rare events. We quantify this change by measuring the number of detected “anomalies” for each exchange and equity studied. We believe the methodology we propose may be capable of detecting a potential unforecasted event as it is impacting the equity markets.

Accurate prediction of storm surge is a difficult problem. Most forecast systems produce multiple possible forecasts depending on the variability in weather conditions, possible temperature levels, winds, etc. Ensemble modeling techniques have been developed with the stated purpose of obtaining the best forecast (in some specific sense) from the individual forecasts. In this work a statistical methodology of evaluating the performance of multiple ensemble forecasting models is developed. The methodology is applied to predicting storm surge in the New York Harbor area. Data from three hurricane events collected from multiple locations in the New York Bay area are used. The methodology produces three key findings for the particular test data used. First, it is found that even the simplest possible way of creating an ensemble produces results superior to those of any single forecast. Second, for the data used and the events under study the methodology did not interact with any event at any location studied. Third, based on the methodology results for the data studied selecting the best-performing ensemble models for each specific location may be possible.

Exchange-Traded Funds (ETFs) have been widely viewed as a more liquid alternative to mutual funds. Liquidity is an important consideration while analyzing investment opportunities of ETFs. Since liquidity is not directly observable in financial markets, there exist proxies to quantify liquidity in the market. In this study, we consider 25 liquidity measures that are feasible to serve as proxies and maybe calculated using the high frequency data set available. We use a statistical model to examine whether liquidity affects the movement of price. We study this effect to show how liquidity measures impact the components of XLU ETF. We conclude that considering only one liquidity measure in an asset pricing model is not sufficient to capture the dynamics of market liquidity.