pwc-archive/papers-with-abstracts huggingface dataset:
Rough multifactor volatility for SPX and VIX options
Authors: Antoine Jacquier, Aitor Muguruza, Alexandre Pannier
Date: 2021-12-28 00:00:00
Tasks: Gaussian Processes

We provide explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-factor versions. Our general setup encompasses both European options on a stock and VIX options, thereby providing new insights on their joint calibration. The tools used are essentially based on Malliavin calculus for Gaussian processes. We develop a detailed theoretical and numerical analysis of the two-factor rough Bergomi model and provide insights on the interplay between the different parameters for joint SPX-VIX smile calibration.
Pricing and hedging of SOFR derivatives
Authors: Matthew Bickersteth, Yining Ding, Marek Rutkowski
Date: 2021-12-28 00:00:00

The LIBOR has served since the 1970s as a fundamental measure for floating term rates across multiple currencies and maturities. However, in 2017 the Financial Conduct Authority announced the discontinuation of LIBOR from the end of 2021 and the New York Fed declared the Treasury repo financing rate, called the Secured Overnight Financing Rate (SOFR), as a candidate for a new reference rate for interest rate swaps denominated in U.S. dollars. We examine arbitrage-free pricing and hedging of swaps referencing SOFR without and with collateral backing. As hedging instruments, we take SOFR futures and idiosyncratic funding rates for the hedge and margin account. For simplicity, a one-factor model based on Vasicek's equation is used to specify the joint dynamics of several overnight interest rates, including the SOFR and unsecured funding rate.
Regime Switching Entropic Risk Measures on Crude Oil Pricing
Authors: Babacar Seck, Robert J. Elliott
Date: 2021-12-24 00:00:00

This paper introduces a new type of risk measures, namely regime switching entropic risk measures, and study their applicability through simulations. The state of the economy is incorporated into the entropic risk formulation by using a Markov chain. Closed formulae of the risk measure are obtained for futures on crude oil derivatives. The applicability of these new types of risk measures is based on the study of the risk aversion parameter and the convenience yield. The numerical results show a term structure and a mean-reverting behavior of the convenience yield.
Principal agent mean field games in REC markets
Authors: Dena Firoozi, Arvind V Shrivats, Sebastian Jaimungal
Date: 2021-12-22 00:00:00
Tasks: Navigate

Principal agent games are a growing area of research which focuses on the optimal behaviour of a principal and an agent, with the former contracting work from the latter, in return for providing a monetary award. While this field canonically considers a single agent, the situation where multiple agents, or even an infinite amount of agents are contracted by a principal are growing in prominence and pose interesting and realistic problems. Here, agents form a Nash equilibrium among themselves, and a Stackelberg equilibrium between themselves as a collective and the principal. We apply this framework to the problem of implementing Renewable Energy Certificate (REC) markets, where the principal requires regulated firms (power generators) to pay a non-compliance penalty which is inversely proportional to the amount of RECs they have. RECs can be obtained by generating electricity from clean sources or purchasing on the market. The agents react to this penalty and optimize their behaviours to navigate the system at minimum cost. In the agents' model we incorporate market clearing as well as agent heterogeneity. For a given market design, we find the Nash equilibrium among agents using techniques from mean field games. We then use techniques from extended McKean-Vlasov control problems to solve the principal (regulators) problem, who aim to choose the penalty function in such a way that balances environmental and revenue impacts optimally. We find through these techniques that the optimal penalty function is linear in the agents' state, suggesting the optimal emissions regulation market is more akin to a tax or rebate, regardless of the principal's utility function.
Rainbow Options under Bayesian MS-VAR Process
Authors: Battulga Gankhuu
Date: 2021-12-20 00:00:00

This paper presents pricing and hedging methods for rainbow options and lookback options under Bayesian Markov-Switching Vector Autoregressive (MS--VAR) process. Here we assumed that a regime-switching process is generated by a homogeneous Markov process. An advantage of our model is it depends on economic variables and simple as compared with previous existing papers.
Dollar Cost Averaging Returns Estimation
Authors: Hayden Brown
Date: 2021-12-17 00:00:00

Given a geometric Brownian motion wealth process, a log-Normal lower bound is constructed for the returns of a regular investing schedule. The distribution parameters of this bound are computed recursively. For dollar cost averaging (equal amounts in equal time intervals), parameters are computed in closed form. A lump sum (single amount at time 0) investing schedule is described which achieves a terminal wealth distribution that matches the wealth distribution indicated by the lower bound. Results are applied to annual returns of the S&P Composite Index from the last 150 years. Among data analysis results, the probability of negative returns is less than 2.5% when annual dollar cost averaging lasts over 40 years.
Discrete signature and its application to finance
Authors: Takanori Adachi, Yusuke Naritomi
Date: 2021-12-17 00:00:00
Tasks: Time Series, Time Series Analysis

Signatures, one of the key concepts of rough path theory, have recently gained prominence as a means to find appropriate feature sets in machine learning systems. In this paper, in order to compute signatures directly from discrete data without going through the transformation to continuous data, we introduced a discretized version of signatures, called "flat discrete signatures". We showed that the flat discrete signatures can represent the quadratic variation that has a high relevance in financial applications. We also introduced the concept of "discrete signatures" that is a generalization of "flat discrete signatures". This concept is defined to reflect the fact that data closer to the current time is more important than older data, and is expected to be applied to time series analysis. As an application of discrete signatures, we took up a stock market related problem and succeeded in performing a good estimation with fewer data points than before.
Deep Partial Hedging
Authors: Songyan Hou, Thomas Krabichler, Marcus Wunsch
Date: 2021-12-14 00:00:00

Using techniques from deep learning (cf. [B\"uh+19]), we show that neural networks can be trained successfully to replicate the modified payoff functions that were first derived in the context of partial hedging by [FL00]. Not only does this approach better accommodate the realistic setting of hedging in discrete time, it also allows for the inclusion of transaction costs as well as general market dynamics.
Dynamic Portfolio Optimization with Inverse Covariance Clustering
Authors: Yuanrong Wang, Tomaso Aste
Date: 2021-12-31 00:00:00
Tasks: Clustering, Portfolio Optimization

Market conditions change continuously. However, in portfolio's investment strategies, it is hard to account for this intrinsic non-stationarity. In this paper, we propose to address this issue by using the Inverse Covariance Clustering (ICC) method to identify inherent market states and then integrate such states into a dynamic portfolio optimization process. Extensive experiments across three different markets, NASDAQ, FTSE and HS300, over a period of ten years, demonstrate the advantages of our proposed algorithm, termed Inverse Covariance Clustering-Portfolio Optimization (ICC-PO). The core of the ICC-PO methodology concerns the identification and clustering of market states from the analytics of past data and the forecasting of the future market state. It is therefore agnostic to the specific portfolio optimization method of choice. By applying the same portfolio optimization technique on a ICC temporal cluster, instead of the whole train period, we show that one can generate portfolios with substantially higher Sharpe Ratios, which are statistically more robust and resilient with great reductions in maximum loss in extreme situations. This is shown to be consistent across markets, periods, optimization methods and selection of portfolio assets.
Community detection and portfolio optimization
Authors: Longfeng Zhao, Chao Wang, Gang-Jin Wang, H. Eugene Stanley, Lin Chen
Date: 2021-12-26 00:00:00
Tasks: Community Detection, Management, Portfolio Optimization

Community detection methods can be used to explore the structure of complex systems. The well-known modular configurations in complex financial systems indicate the existence of community structures. Here we analyze the community properties of correlation-based networks in worldwide stock markets and use community information to construct portfolios. Portfolios constructed using community detection methods perform well. Our results can be used as new portfolio optimization and risk management tools.
Optimal Portfolio Choice and Stock Centrality for Tail Risk Events
Authors: Christis Katsouris
Date: 2021-12-01 00:00:00

We propose a novel risk matrix to characterize the optimal portfolio choice of an investor with tail concerns. The diagonal of the matrix contains the Value-at-Risk of each asset in the portfolio and the off-diagonal the pairwise Delta-CoVaR measures reflecting tail connections between assets. First, we derive the conditions under which the associated quadratic risk function has a closed-form solution. Second, we examine the relationship between portfolio risk and eigenvector centrality. Third, we show that portfolio risk is not necessarily increasing with respect to stock centrality. Forth, we demonstrate under certain conditions that asset centrality increases the optimal weight allocation of the asset to the portfolio. Overall, our empirical study indicates that a network topology which exhibits low connectivity is outperformed by high connectivity based on a Sharpe ratio test.
An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model
Authors: Edoardo Berton, Lorenzo Mercuri
Date: 2021-12-22 00:00:00

In this study, we propose a new formula for spread option pricing with the dependence of two assets described by a copula function. The advantage of the proposed method is that it requires only the numerical evaluation of a one-dimensional integral. Any univariate stock price process, admitting an affine characteristic function, can be used in our formula to get an efficient numerical procedure for computing spread option prices. In the numerical analysis we present a comparison with Monte Carlo simulation methods to assess the performance of our approach, assuming that the univariate stock price follows three widely applied models: Variance Gamma, Heston's Stochastic Volatility and Affine Heston Nandi GARCH(1,1) model.
Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricing
Authors: Qi Chen, Chao Guo
Date: 2021-12-16 00:00:00

Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem in quantum mechanics; for double-barrier step options, the option price changing process is analogous to a particle moving in a finite symmetric square potential well. Using path integral method, the analytical expressions of pricing kernel and option price could be derived. Numerical results of option price as a function of underlying price, potential and exercise price are shown, which are consistent with the results given by mathematical method.
On the decomposition of an insurer's profits and losses
Authors: Marcus C. Christiansen
Date: 2021-12-21 00:00:00

Current reporting standards for insurers require a decomposition of observed profits and losses in such a way that changes in the insurer's balance sheet can be attributed to specified risk factors. Generating such a decomposition is a nontrivial task because balance sheets generally depend on the risk factors in a non-linear way. This paper starts from an axiomatic perspective on profit and loss decompositions and finds that the axioms necessarily lead to infinitesimal sequential updating (ISU) decompositions, provided that the latter exist and are stable, whereas the current practice is rather to use sequential updating (SU) decompositions. The generality of the axiomatic approach makes the results useful also beyond insurance applications wherever profits and losses shall be additively decomposed in a risk-oriented manner.
Limiting Spectral Distribution of High-dimensional Hayashi-Yoshida Estimator of Integrated Covariance Matrix
Authors: Arnab Chakrabarti, Rituparna Sen
Date: 2022-01-01 00:00:00

In this paper, the estimation of the Integrated Covariance matrix from high-frequency data, for high dimensional stock price process, is considered. The Hayashi-Yoshida covolatility estimator is an improvement over Realized covolatility for asynchronous data and works well in low dimensions. However it becomes inconsistent and unreliable in the high dimensional situation. We study the bulk spectrum of this matrix and establish its connection to the spectrum of the true covariance matrix in the limiting case where the dimension goes to infinity. The results are illustrated with simulation studies in finite, but high, dimensional cases. An application to real data with tick-by-tick data on 50 stocks is presented.
Evolutionary correlation, regime switching, spectral dynamics and optimal trading strategies for cryptocurrencies and equities
Authors: Nick James
Date: 2021-12-31 00:00:00
Tasks: Management, Time Series, Time Series Analysis

This paper uses new and recently established methodologies to study the evolutionary dynamics of the cryptocurrency market, and compares the findings with that of the equity market. We begin by applying random matrix theory and principal components analysis (PCA) to correlation matrices of both collections, highlighting clear differences in the eigenspectra exhibited. We then explore the heterogeneity of both asset classes, studying the time-varying dynamics of underlying sector behaviours, and determine the collective similarity within each collection. We then turn to a study of structural break dynamics and evolutionary power spectra, where we quantify the collective affinity in structural breaks and evolutionary behaviours of underlying sector time series. Finally, we implement two algorithms simulating `portfolio choice' dynamics to compare the effectiveness of stock selection and sector allocation in cryptocurrency portfolios. There, we highlight the importance of both endeavours and comment on noteworthy implications for cryptocurrency portfolio management.
Stationarity analysis of the stock market data and its application to mechanical trading
Authors: Kazuki Kanehira, Norikazu Todoroki
Date: 2021-12-23 00:00:00
Tasks: Stock Price Prediction, Time Series, Time Series Analysis

This study proposes a scheme for stationarity analysis of stock price fluctuations based on KM$_2$O-Langevin theory. Using this scheme, we classify the time-series data of stock price fluctuations into three periods: stationary, non-stationary, and intermediate. We then suggest an example of a low-risk stock trading strategy to demonstrate the usefulness of our scheme by using actual stock index data. Our strategy uses a trend-based indicator, moving averages, for stationary periods and an oscillator-based indicator, psychological lines, for non-stationary periods to make trading decisions. Finally, we confirm that our strategy is a safe trading strategy with small maximum drawdown by back testing on the Nikkei Stock Average. Our study, the first to apply the stationarity analysis of KM$_2$O-Langevin theory to actual mechanical trading, opens up new avenues for stock price prediction.
Denoised Labels for Financial Time-Series Data via Self-Supervised Learning
Authors: Yanqing Ma, Carmine Ventre, Maria Polukarov
Date: 2021-12-19 00:00:00
Tasks: Denoising, image-classification, Image Classification, Self-Supervised Learning, Time Series, Time Series Analysis

The introduction of electronic trading platforms effectively changed the organisation of traditional systemic trading from quote-driven markets into order-driven markets. Its convenience led to an exponentially increasing amount of financial data, which is however hard to use for the prediction of future prices, due to the low signal-to-noise ratio and the non-stationarity of financial time series. Simpler classification tasks -- where the goal is to predict the directions of future price movement -- via supervised learning algorithms, need sufficiently reliable labels to generalise well. Labelling financial data is however less well defined than other domains: did the price go up because of noise or because of signal? The existing labelling methods have limited countermeasures against noise and limited effects in improving learning algorithms. This work takes inspiration from image classification in trading and success in self-supervised learning. We investigate the idea of applying computer vision techniques to financial time-series to reduce the noise exposure and hence generate correct labels. We look at the label generation as the pretext task of a self-supervised learning approach and compare the naive (and noisy) labels, commonly used in the literature, with the labels generated by a denoising autoencoder for the same downstream classification task. Our results show that our denoised labels improve the performances of the downstream learning algorithm, for both small and large datasets. We further show that the signals we obtain can be used to effectively trade with binary strategies. We suggest that with proposed techniques, self-supervised learning constitutes a powerful framework for generating "better" financial labels that are useful for studying the underlying patterns of the market.
On The Quality Of Cryptocurrency Markets: Centralized Versus Decentralized Exchanges
Authors: Andrea Barbon, Angelo Ranaldo
Date: 2021-12-14 00:00:00

We analyze the market quality of centralized crypto exchanges (CEXs) and decentralized blockchain-based venues (DEXs) using a unique and comprehensive dataset. Focusing on two fundamental aspects, transaction costs and deviations from the no-arbitrage condition, we estimate the causal effect of ``gas fees'' on DEX market quality. We show that these fixed costs impose a significant burden on relatively small trades and cause persistent arbitrage deviations. Conversely, DEXs offer more competitive transaction costs for larger trades, offering a more favorable environment for institutional investors. Furthermore, we provide causal evidence that innovations aimed at enhancing the flexibility of liquidity provision in DEX markets lead to sizeable improvements in market quality.
A machine learning analysis of the relationship between some underlying medical conditions and COVID-19 susceptibility
Authors: Mostafa Rezapour, Colin A. Varady
Date: 2021-12-24 00:00:00

For the past couple years, the Coronavirus, commonly known as COVID-19, has significantly affected the daily lives of all citizens residing in the United States by imposing several, fatal health risks that cannot go unnoticed. In response to the growing fear and danger COVID-19 inflicts upon societies in the USA, several vaccines and boosters have been created as a permanent remedy for individuals to take advantage of. In this paper, we investigate the relationship between the COVID-19 vaccines and boosters and the total case count for the Coronavirus across multiple states in the USA. Additionally, this paper discusses the relationship between several, selected underlying health conditions with COVID-19. To discuss these relationships effectively, this paper will utilize statistical tests and machine learning methods for analysis and discussion purposes. Furthermore, this paper reflects upon conclusions made about the relationship between educational attainment, race, and COVID-19 and the possible connections that can be established with underlying health conditions, vaccination rates, and COVID-19 total case and death counts.
Multiple Imputation via Generative Adversarial Network for High-dimensional Blockwise Missing Value Problems
Authors: Zongyu Dai, Zhiqi Bu, Qi Long
Date: 2021-12-21 00:00:00
Tasks: Generative Adversarial Network, Imputation

Missing data are present in most real world problems and need careful handling to preserve the prediction accuracy and statistical consistency in the downstream analysis. As the gold standard of handling missing data, multiple imputation (MI) methods are proposed to account for the imputation uncertainty and provide proper statistical inference. In this work, we propose Multiple Imputation via Generative Adversarial Network (MI-GAN), a deep learning-based (in specific, a GAN-based) multiple imputation method, that can work under missing at random (MAR) mechanism with theoretical support. MI-GAN leverages recent progress in conditional generative adversarial neural works and shows strong performance matching existing state-of-the-art imputation methods on high-dimensional datasets, in terms of imputation error. In particular, MI-GAN significantly outperforms other imputation methods in the sense of statistical inference and computational speed.
Crash Data Augmentation Using Conditional Generative Adversarial Networks (CGAN) for Improving Safety Performance Functions
Authors: Mohammad Zarei, Bruce Hellinga
Date: 2021-12-21 00:00:00
Tasks: Data Augmentation, parameter estimation

In this paper, we present a crash frequency data augmentation method based on Conditional Generative Adversarial Networks to improve crash frequency models. The proposed method is evaluated by comparing the performance of Base SPFs (developed using original data) and Augmented SPFs (developed using original data plus synthesised data) in terms of hotspot identification performance, model prediction accuracy, and dispersion parameter estimation accuracy. The experiments are conducted using simulated and real-world crash data sets. The results indicate that the synthesised crash data by CGAN have the same distribution as the original data and the Augmented SPFs outperforms Base SPFs in almost all aspects especially when the dispersion parameter is low.
Deep Generative Models for Vehicle Speed Trajectories
Authors: Farnaz Behnia, Dominik Karbowski, Vadim Sokolov
Date: 2021-12-14 00:00:00
Tasks: Self-Driving Cars

Generating realistic vehicle speed trajectories is a crucial component in evaluating vehicle fuel economy and in predictive control of self-driving cars. Traditional generative models rely on Markov chain methods and can produce accurate synthetic trajectories but are subject to the curse of dimensionality. They do not allow to include conditional input variables into the generation process. In this paper, we show how extensions to deep generative models allow accurate and scalable generation. Proposed architectures involve recurrent and feed-forward layers and are trained using adversarial techniques. Our models are shown to perform well on generating vehicle trajectories using a model trained on GPS data from Chicago metropolitan area.