pwc-archive/papers-with-abstracts huggingface dataset:
Tax systems for sustainable economic development
Authors: N. S. Gonchar
Date: 2024-10-01 00:00:00

A complete description of taxation systems that ensure sustainable economic development is given. These tax systems depend on production technologies and gross output volumes. Explicit formulas for such dependencies are found. In a sustainable economy, the value added either exceeds or is strictly less than the value of the product produced. The latter is determined by the tax system. The concept of perfect taxation systems is introduced and their explicit form is found. For perfect taxation systems, it is proved that the vector of gross output should belong to the interior of the cone formed by the vectors of the columns of the total cost matrix. It is shown that under perfect taxation systems the vector of gross output must satisfy a certain system of linear homogeneous equations. It is shown, that under certain conditions there are tax systems under which certain industries require subsidies for their existence. Under such taxation systems, the industries that require subsidies are identified. The family of all non negative solutions of the system of linear equations and inequalities is constructed, which allowed us to formulate a criterion for describing all equilibrium states in which partial clearing of markets occurs.
Pricing and Hedging Strategies for Cross-Currency Equity Protection Swaps
Authors: Marek Rutkowski, Huansang Xu
Date: 2024-09-28 00:00:00

In this paper, we explore the pricing and hedging strategies for an innovative insurance product called the equity protection swap(EPS). Notably, we focus on the application of EPSs involving cross-currency reference portfolios, reflecting the realities of investor asset diversification across different economies. The research examines key considerations regarding exchange rate fluctuations, pricing and hedging frameworks, in order to satisfy dynamic requirements from EPS buyers. We differentiate between two hedging paradigms: one where domestic and foreign equities are treated separately using two EPS products and another that integrates total returns across currencies. Through detailed analysis, we propose various hedging strategies with consideration of different types of returns - nominal, effective, and quanto - for EPS products in both separate and aggregated contexts. The aggregated hedging portfolios contain basket options with cross-currency underlying asset, which only exists in the OTC market, thus we further consider a superhedging strategy using single asset European options for aggregated returns. A numerical study assesses hedging costs and performance metrics associated with these hedging strategies, illuminating practical implications for EPS providers and investors engaged in international markets. We further employ Monte Carlo simulations for the basket option pricing, together with two other approximation methods - geometric averaging and moment matching. This work contributes to enhancing fair pricing mechanisms and risk management strategies in the evolving landscape of cross-currency financial derivatives.
Interest rate derivatives in a CTMC setting: pricing, replication and Ross recovery
Authors: Tim Leung, Matthew Lorig
Date: 2024-09-21 00:00:00

We consider a financial market in which the short rate is modeled by a continuous time Markov chain (CTMC) with a finite state space. In this setting, we show how to price any financial derivative whose payoff is a function of the state of the underlying CTMC at the maturity date. We also show how to replicate such claims by trading only a money market account and zero-coupon bonds. Finally, using an extension of Ross' Recovery Theorem due to Qin and Linetsky, we deduce the real-world dynamics of the CTMC.
Financial Stochastic Models Diffusion: From Risk-Neutral to Real-World Measure
Authors: Mohamed Ben Alaya, Ahmed Kebaier, Djibril Sarr
Date: 2024-09-19 00:00:00
Tasks: Management

This research presents a comprehensive framework for transitioning financial diffusion models from the risk-neutral (RN) measure to the real-world (RW) measure, leveraging results from probability theory, specifically Girsanov's theorem. The RN measure, fundamental in derivative pricing, is contrasted with the RW measure, which incorporates risk premiums and better reflects actual market behavior and investor preferences, making it crucial for risk management. We address the challenges of incorporating real-world dynamics into financial models, such as accounting for market premiums, producing realistic term structures of market indicators, and fitting any arbitrarily given market curve. Our framework is designed to be general, applicable to a variety of diffusion models, including those with non-additive noise such as the CIR++ model. Through case studies involving Goldman Sachs' 2024 global credit outlook forecasts and the European Banking Authority (EBA) 2023 stress tests, we validate the robustness, practical relevance and applicability of our methodology. This work contributes to the literature by providing a versatile tool for better risk measures and enhancing the realism of financial models under the RW measure. Our model's versatility extends to stress testing and scenario analysis, providing practitioners with a powerful tool to evaluate various what-if scenarios and make well-informed decisions, particularly in pricing and risk management strategies.
Algorithmic and High-Frequency Trading Problems for Semi-Markov and Hawkes Jump-Diffusion Models
Authors: Luca Lalor, Anatoliy Swishchuk
Date: 2024-09-19 00:00:00
Tasks: Algorithmic Trading

This paper introduces a jump-diffusion pricing model specifically designed for algorithmic trading and high-frequency trading (HFT). The model incorporates independent jump and diffusion processes, providing a more precise representation of the limit order book (LOB) dynamics within a scaling-limit framework. Given that algorithmic and HFT strategies now dominate major financial markets, accurately modeling LOB dynamics is crucial for developing effective trading algorithms. Recent research has shown that LOB data often exhibit non-Markovian properties, reinforcing the need for models that better capture its evolution. In this paper, we address acquisition and liquidation problems under more general compound semi-Markov and Hawkes jump-diffusion models. We first develop jump-diffusion frameworks to capture these dynamics and then apply diffusion approximations to the jump components so that robust solutions can be given. Optimal trading strategies are formulated using stochastic optimal control (SOC) and solved numerically. Finally, we present strategy simulations analyzing price paths, inventory evolution, trading speed, and average execution prices. This study provides insights into how these models can improve execution strategies under more general price dynamics.
Optimal post-retirement investment under longevity risk in collective funds
Authors: John Armstrong, Cristin Buescu, James Dalby
Date: 2024-09-06 00:00:00

We study the optimal investment problem for a homogeneous collective of $n$ individuals investing in a Black-Scholes model subject to longevity risk with Epstein--Zin preferences. %and with preferences given by power utility. We compute analytic formulae for the optimal investment strategy, consumption is in discrete-time and there is no systematic longevity risk. We develop a stylised model of systematic longevity risk in continuous time which allows us to also obtain an analytic solution to the optimal investment problem in this case. We numerically solve the same problem using a continuous-time version of the Cairns--Blake--Dowd model. We apply our results to estimate the potential benefits of pooling longevity risk over purchasing an insurance product such as an annuity, and to estimate the benefits of optimal longevity risk pooling in a small heterogeneous fund.
Worst-case values of target semi-variances with applications to robust portfolio selection
Authors: Jun Cai, Zhanyi Jiao, Tiantian Mao
Date: 2024-10-02 00:00:00

The expected regret and target semi-variance are two of the most important risk measures for downside risk. When the distribution of a loss is uncertain, and only partial information of the loss is known, their worst-case values play important roles in robust risk management for finance, insurance, and many other fields. Jagannathan (1977) derived the worst-case expected regrets when only the mean and variance of a loss are known and the loss is arbitrary, symmetric, or non-negative. While Chen et al. (2011) obtained the worst-case target semi-variances under similar conditions but focusing on arbitrary losses. In this paper, we first complement the study of Chen et al. (2011) on the worst-case target semi-variances and derive the closed-form expressions for the worst-case target semi-variance when only the mean and variance of a loss are known and the loss is symmetric or non-negative. Then, we investigate worst-case target semi-variances over uncertainty sets that represent undesirable scenarios faced by an investors. Our methods for deriving these worst-case values are different from those used in Jagannathan (1977) and Chen et al. (2011). As applications of the results derived in this paper, we propose robust portfolio selection methods that minimize the worst-case target semi-variance of a portfolio loss over different uncertainty sets. To explore the insights of our robust portfolio selection methods, we conduct numerical experiments with real financial data and compare our portfolio selection methods with several existing portfolio selection models related to the models proposed in this paper.
Two-fund separation under hyperbolically distributed returns and concave utility function
Authors: Nuerxiati Abudurexiti, Erhan Bayraktar, Takaki Hayashi, Hasanjan Sayit
Date: 2024-10-06 00:00:00
Tasks: Portfolio Optimization

Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore, analytical expressions for optimal portfolios are always preferred. In our work, we study portfolio optimization problems under the expected utility criterion for a wide range of utility functions, assuming return vectors follow hyperbolic distributions. Our main result demonstrates that under this setup, the two-fund monetary separation holds. Specifically, an individual with any utility function from this broad class will always choose to hold the same portfolio of risky assets, only adjusting the mix between this portfolio and a riskless asset based on their initial wealth and the specific utility function used for decision making. We provide explicit expressions for this mutual fund of risky assets. As a result, in our economic model, an individual's optimal portfolio is expressed in closed form as a linear combination of the riskless asset and the mutual fund of risky assets. Additionally, we discuss expected utility maximization problems under exponential utility functions over any domain of the portfolio set. In this part of our work, we show that the optimal portfolio in any given convex domain of the portfolio set either lies on the boundary of the domain or is the unique globally optimal portfolio within the entire domain.
Dynamic Portfolio Rebalancing: A Hybrid new Model Using GNNs and Pathfinding for Cost Efficiency
Authors: Diego Vallarino
Date: 2024-10-02 00:00:00
Tasks: Decision Making, Portfolio Optimization

This paper introduces a novel approach to optimizing portfolio rebalancing by integrating Graph Neural Networks (GNNs) for predicting transaction costs and Dijkstra's algorithm for identifying cost-efficient rebalancing paths. Using historical stock data from prominent technology firms, the GNN is trained to forecast future transaction costs, which are then applied as edge weights in a financial asset graph. Dijkstra's algorithm is used to find the least costly path for reallocating capital between assets. Empirical results show that this hybrid approach significantly reduces transaction costs, offering a powerful tool for portfolio managers, especially in high-frequency trading environments. This methodology demonstrates the potential of combining advanced machine learning techniques with classical optimization algorithms to improve financial decision-making processes. Future research will explore expanding the asset universe and incorporating reinforcement learning for continuous portfolio optimization.
A Framework for the Construction of a Sentiment-Driven Performance Index: The Case of DAX40
Authors: Fabian Billert, Stefan Conrad
Date: 2024-09-30 00:00:00
Tasks: Articles

We extract the sentiment from german and english news articles on companies in the DAX40 stock market index and use it to create a sentiment-powered pendant. Comparing it to existing products which adjust their weights at pre-defined dates once per month, we show that our index is able to react more swiftly to sentiment information mined from online news. Over the nearly 6 years we considered, the sentiment index manages to create an annualized return of 7.51% compared to the 2.13% of the DAX40, while taking transaction costs into account. In this work, we present the framework we employed to develop this sentiment index.
Modern Portfolio Diversification with Arte-Blue Chip Index
Authors: Simon Levy, Maxime L. D. Nicolas
Date: 2024-09-27 00:00:00

This paper presents a novel approach to evaluating blue-chip art as a viable asset class for portfolio diversification. We present the Arte-Blue Chip Index, an index that tracks 100 top-performing artists based on 81,891 public transactions from 157 artists across 584 auction houses over the period 1990 to 2024. By comparing blue-chip art price trends with stock market fluctuations, our index provides insights into the risk and return profile of blue-chip art investments. Our analysis demonstrates that a 20% allocation of blue-chip art in a diversified portfolio enhances risk-adjusted returns by around 20%, while maintaining volatility levels similar to the S&P 500.
Shocks-adaptive Robust Minimum Variance Portfolio for a Large Universe of Assets
Authors: Qingliang Fan, Ruike Wu, Yanrong Yang
Date: 2024-09-16 00:00:00

This paper proposes a robust, shocks-adaptive portfolio in a large-dimensional assets universe where the number of assets could be comparable to or even larger than the sample size. It is well documented that portfolios based on optimizations are sensitive to outliers in return data. We deal with outliers by proposing a robust factor model, contributing methodologically through the development of a robust principal component analysis (PCA) for factor model estimation and a shrinkage estimation for the random error covariance matrix. This approach extends the well-regarded Principal Orthogonal Complement Thresholding (POET) method (Fan et al., 2013), enabling it to effectively handle heavy tails and sudden shocks in data. The novelty of the proposed robust method is its adaptiveness to both global and idiosyncratic shocks, without the need to distinguish them, which is useful in forming portfolio weights when facing outliers. We develop the theoretical results of the robust factor model and the robust minimum variance portfolio. Numerical and empirical results show the superior performance of the new portfolio.
On the Local equivalence of the Black Scholes and the Merton Garman equations
Authors: Ivan Arraut
Date: 2024-09-30 00:00:00

It was demonstrated previously that the stochastic volatility emerges as the gauge field necessary for restoring the local symmetry under changes of the prices of the stocks inside the Black-Scholes (BS) equation. When this occurs, then a Merton-Garman-like equation emerges. From the perspective of manifolds, this means that the Black-Scholes equation and the Merton-Garman (MG) one can be considered as locally equivalent. In this scenario, the MG Hamiltonian is a special case of a more general Hamiltonian, here called gauge-Hamiltonian. We then show that the gauge character of the volatility implies some specific functional relation between the prices of the stock and the volatility. The connection between the prices of the stocks and the volatility, is a powerful tool for improving the volatility estimations in the stock market, which is a key ingredient for the investors to make good decisions. Finally, we define an extended version of the martingale condition, defined for the gauge-Hamiltonian.
Application of AI in Credit Risk Scoring for Small Business Loans: A case study on how AI-based random forest model improves a Delphi model outcome in the case of Azerbaijani SMEs
Authors: Nigar Karimova
Date: 2024-10-05 00:00:00

The research investigates how the application of a machine-learning random forest model improves the accuracy and precision of a Delphi model. The context of the research is Azerbaijani SMEs and the data for the study has been obtained from a financial institution which had gathered it from the enterprises (as there is no public data on local SMEs, it was not practical to verify the data independently). The research used accuracy, precision, recall and F-1 scores for both models to compare them and run the algorithms in Python. The findings showed that accuracy, precision, recall and F- 1 all improve considerably (from 0.69 to 0.83, from 0.65 to 0.81, from 0.56 to 0.77 and from 0.58 to 0.79, respectively). The implications are that by applying AI models in credit risk modeling, financial institutions can improve the accuracy of identifying potential defaulters which would reduce their credit risk. In addition, an unfair rejection of credit access for SMEs would also go down having a significant contribution to an economic growth in the economy. Finally, such ethical issues as transparency of algorithms and biases in historical data should be taken on board while making decisions based on AI algorithms in order to reduce mechanical dependence on algorithms that cannot be justified in practice.
Compound V3 Economic Audit Report
Authors: Rik Ghosh, Samrat Gupta, Arka Datta, Abhimanyu Nag, Sudipan Sinha
Date: 2024-10-05 00:00:00

Compound Finance is a decentralized lending protocol that enables the secure and efficient borrowing and lending of cryptocurrencies, utilizing smart contracts and dynamic interest rates based on supply and demand to facilitate transactions. The protocol enables users to supply different crypto assets and accrue interest, while borrowers can avail themselves of loans secured by collateralized assets. Our collaboration with Compound Finance focuses on harnessing the power of the Chainrisk simulation engine to optimize risk parameters of the Compound V3 (Comet) protocol. This report delineates a comprehensive methodology aimed at calculating key risk metrics of the protocol. This optimization framework is pivotal for mitigating systemic risks and enhancing the overall stability of the protocol. By leveraging Chainrisk's Cloud Platform, we conduct millions of simulations to evaluate the protocol's Value at Risk (VaR) and Liquidations at Risk (LaR), ultimately providing recommendations for parameter adjustments.
Best- and worst-case Scenarios for GlueVaR distortion risk measure with Incomplete information
Authors: Mengshuo Zhao, Chuancun Yin
Date: 2024-09-30 00:00:00

This paper derives the best- and worst-case GlueVaR distortion risk measure within a unified framework, based on partial information of the underlying distributions and shape information such as symmetry. In addition, we characterize the extremal distributions of GlueVaR with convex envelopes of the corresponding distortion functions. As examples, extremal cases of VaR, TVaR and RVaR are derived.
Quantile connectedness across BRICS and international grain futures markets: Insights from the Russia-Ukraine conflict
Authors: Yan-Hong Yang, Ying-Hui Shao, Wei-Xing Zhou
Date: 2024-09-28 00:00:00

This study examines the quantile connectedness among grain futures markets in BRICS and international markets, with a particular focus on the ongoing and escalating impacts of the Russia-Ukraine conflict. The findings reveal significant heterogeneity in spillover effects across different quantiles and market conditions. Specifically, the time-varying total connectedness index (TCI) consistently fluctuated around 95\% under both extreme bearish and bullish market conditions, markedly higher than in normal market conditions. Moreover, across all quantile levels, the TCI was higher during the pre-outbreak period than in the post-outbreak period. This systemic risk has notably decreased following the onset of the Russia-Ukraine conflict and the subsequent changes to the Black Sea Grain Initiative. Apart from rice, U.S. grain futures maintained a dominant position as benchmarks for international grain prices, exerting substantial influence over the grain futures markets in BRICS throughout most of the period. Finally, the study highlights that the influence of grain type and regional proximity strengthens pairwise connectedness among futures markets, with short-term spillovers being dominant and the spillover effect generally symmetric across quantiles.
Tail Risk Analysis for Financial Time Series
Authors: Anna Kiriliouk, Chen Zhou
Date: 2024-09-27 00:00:00
Tasks: Time Series

This book chapter illustrates how to apply extreme value statistics to financial time series data. Such data often exhibits strong serial dependence, which complicates assessment of tail risks. We discuss the two main approches to tail risk estimation, unconditional and conditional quantile forecasting. We use the S&P 500 index as a case study to assess serial (extremal) dependence, perform an unconditional and conditional risk analysis, and apply backtesting methods. Additionally, the chapter explores the impact of serial dependence on multivariate tail dependence.
The impact of climate policy uncertainty on financial market resilience: Evidence from China
Authors: Si-yao Wei, Wei-Xing Zhou
Date: 2024-09-27 00:00:00
Tasks: CPU

Resilience serves to assess the ability of the financial market to resist external shocks and to recover from shocks. The intensity and duration, used to indicate resilience, are calculated for China's financial market in this paper, focusing on the performance of each financial sub-market during and after several crises. Also, given that climate issues have been recognized as an important source of risk by financial market, we investigate the connectedness and mechanism of China's climate policy uncertainty (CPU) to its financial market resilience. We have found that the two resilience indicators of each market have a relatively consistent trend, but connectedness among markets has different sensitivities to both. In addition, China's CPU affects its financial market resilience by increasing the investor sentiment index and the non-performing loan ratio of commercial banks, and by reducing the capital and financial account balance. It is further found that China's financial markets' consensus on the unswerving implementation of climate policy, which provides the reference for other countries on how to balance climate policy's introduction and financial market development.