Quant Finance Arxiv submissions 2022-09-12 - 2022-09-18
This is your weekly snap of quant finance submissions to the Arxiv. Papers are sorted in reverse chronological order of the original publication date. i.e. the newest papers are at the top, revisions are lower down the list.
If any paper take your fancy, you're encouraged to submit a link post to the subreddit, and start the discussion in the comments. Or in this thread, what do I care I'm not your boss.
Authors: Joseph Jerome, Leandro Sanchez-Betancourt, Rahul Savani, Martin Herdegen
Categories: Mathematical Finance, Trading and Market Microstructure, Computational Finance
PDF: http://arxiv.org/pdf/2209.07823v1
Dates: originally published: 2022-09-16, updated: 2022-09-16
Summary: Within the mathematical finance literature there is a rich catalogue of mathematical models for studying algorithmic trading problems -- such as market-making and optimal execution -- in limit order books. This paper introduces \mbtgym, a Python module that provides a suite of gym environments for training reinforcement learning (RL) agents to solve such model-based trading problems. The module is set up in an extensible way to allow the combination of different aspects of different models. It supports highly efficient implementations of vectorized environments to allow faster training of RL agents. In this paper, we motivate the challenge of using RL to solve such model-based limit order book problems in mathematical finance, we explain the design of our gym environment, and then demonstrate its use in solving standard and non-standard problems from the literature. Finally, we lay out a roadmap for further development of our module, which we provide as an open source repository on GitHub so that it can serve as a focal point for RL research in model-based algorithmic trading.
Authors: Qi Guo, Anatoliy Swishchuk, Bruno Rémillard
Categories: Mathematical Finance, Pricing of Securities
PDF: http://arxiv.org/pdf/2209.07621v1
Dates: originally published: 2022-09-15, updated: 2022-09-15
Summary: In this paper, we consider pricing of European options and spread options for Hawkes-based model for the limit order book. We introduce multivariate Hawkes process and the multivariable general compound Hawkes process. Exponential multivariate general compound Hawkes processes and limit theorems for them, namely, LLN and FCLT, are considered then. We also consider a special case of one-dimensional EMGCHP and its limit theorems. Option pricing with $1D$ EGCHP in LOB, hedging strategies, and numerical example are presented. We also introduce greeks calculations for those models. Margrabe's spread options valuations with Hawkes-based models for two assets and numerical example are presented. Also, Margrabe's spread option pricing with two $2D$ EMGCHP and numerical example are included. Basket options valuations with numerical example are included. We finally discuss the implied volatility and implied order flow. It reveals the relationship between stock volatility and the order flow in the limit order book system. In this way, the Hawkes-based model can provide more market forecast information than the classical Black-Scholes model.
Authors: Kan Chen, Tuoyuan Cheng
Categories: Statistical Finance, Risk Management
PDF: http://arxiv.org/pdf/2209.07092v1
Dates: originally published: 2022-09-15, updated: 2022-09-15
Summary: Value at risk (VaR) and expected shortfall (ES) are common high quantile-based risk measures adopted in financial regulations and risk management. In this paper, we propose a tail risk measure based on the most probable maximum size of risk events (MPMR) that can occur over a length of time. MPMR underscores the dependence of the tail risk on the risk management time frame. Unlike VaR and ES, MPMR does not require specifying a confidence level. We derive the risk measure analytically for several well-known distributions. In particular, for the case where the size of the risk event follows a power law or Pareto distribution, we show that MPMR also scales with the number of observations $n$ (or equivalently the length of the time interval) by a power law, $\text{MPMR}(n) \propto n{\eta}$, where $\eta$ is the scaling exponent. The scale invariance allows for reasonable estimations of long-term risks based on the extrapolation of more reliable estimations of short-term risks. The scaling relationship also gives rise to a robust and low-bias estimator of the tail index (TI) $\xi$ of the size distribution, $\xi = 1/\eta$. We demonstrate the use of this risk measure for describing the tail risks in financial markets as well as the risks associated with natural hazards (earthquakes, tsunamis, and excessive rainfall).
Authors: Jatin Nainani, K. J. Somaiya College of Engineering, Nirman Taterh, K. J. Somaiya College of Engineering, Md Ausaf Rashid, K. J. Somaiya College of Engineering, Ankit Khivasara, K. J. Somaiya College of Engineering
Categories: Statistical Finance
PDF: http://arxiv.org/pdf/2209.12664v1
Dates: originally published: 2022-09-14, updated: 2022-09-14
Summary: For a long time predicting, studying and analyzing financial indices has been of major interest for the financial community. Recently, there has been a growing interest in the Deep-Learning community to make use of reinforcement learning which has surpassed many of the previous benchmarks in a lot of fields. Our method provides a feature rich environment for the reinforcement learning agent to work on. The aim is to provide long term profits to the user so, we took into consideration the most reliable technical indicators. We have also developed a custom indicator which would provide better insights of the Bitcoin market to the user. The Bitcoin market follows the emotions and sentiments of the traders, so another element of our trading environment is the overall daily Sentiment Score of the market on Twitter. The agent is tested for a period of 685 days which also included the volatile period of Covid-19. It has been capable of providing reliable recommendations which give an average profit of about 69%. Finally, the agent is also capable of suggesting the optimal actions to the user through a website. Users on the website can also access the visualizations of the indicators to help fortify their decisions.
Authors: Ludovic Goudenege, Andrea Molent, Antonino Zanette
Categories: Computational Finance
PDF: http://arxiv.org/pdf/2209.06485v1
Dates: originally published: 2022-09-14, updated: 2022-09-14
Summary: Total value adjustment (XVA) is the change in value to be added to the price of a derivative to account for the bilateral default risk and the funding costs. In this paper, we compute such a premium for American basket derivatives whose payoff depends on multiple underlyings. In particular, in our model, those underlying are supposed to follow the multidimensional Black-Scholes stochastic model. In order to determine the XVA, we follow the approach introduced by Burgard and Kjaer \cite{burgard2010pde} and afterward applied by Arregui et al. \cite{arregui2017pde,arregui2019monte} for the one-dimensional American derivatives. The evaluation of the XVA for basket derivatives is particularly challenging as the presence of several underlings leads to a high-dimensional control problem. We tackle such an obstacle by resorting to Gaussian Process Regression, a machine learning technique that allows one to address the curse of dimensionality effectively. Moreover, the use of numerical techniques, such as control variates, turns out to be a powerful tool to improve the accuracy of the proposed methods. The paper includes the results of several numerical experiments that confirm the goodness of the proposed methodologies.
Authors: D Barrera, UNIANDES, S Crépey, LPSM, UPCité, E Gobet, CMAP, X, Hoang-Dung Nguyen, LPSM, UPCité, B Saadeddine, UPS
Categories: Computational Finance
PDF: http://arxiv.org/pdf/2209.06476v1
Dates: originally published: 2022-09-14, updated: 2022-09-14
Summary: We propose a non-asymptotic convergence analysis of a two-step approach to learn a conditional value-at-risk (VaR) and expected shortfall (ES) in a nonparametric setting using Rademacher and Vapnik-Chervonenkis bounds. Our approach for the VaR is extended to the problem of learning at once multiple VaRs corresponding to different quantile levels. This results in efficient learning schemes based on neural network quantile and least-squares regressions. An a posteriori Monte Carlo (non-nested) procedure is introduced to estimate distances to the ground-truth VaR and ES without access to the latter. This is illustrated using numerical experiments in a Gaussian toy-model and a financial case-study where the objective is to learn a dynamic initial margin.
Authors: Yuan Hu, W. Brent Lindquist, Svetlozar T. Rachev
Categories: Pricing of Securities
PDF: http://arxiv.org/pdf/2209.06276v1
Dates: originally published: 2022-09-13, updated: 2022-09-13
Summary: We consider option pricing using replicating binomial trees, with a two fold purpose. The first is to introduce ESG valuation into option pricing. We explore this in a number of scenarios, including enhancement of yield due to trader information and the impact of the past history of a market driver. The second is to emphasize the use of discrete dynamic pricing, rather than continuum models, as the natural model that governs actual market practice. We further emphasize that discrete option pricing models must use discrete compounding (such as risk-free rate compounding of $1+r_f \Delta t$) rather than continuous compounding (such as $e{r_f \Delta t})$.
Authors: Aurélien Alfonsi, Nerea Vadillo
Categories: Risk Management
PDF: http://arxiv.org/pdf/2209.05918v1
Dates: originally published: 2022-09-13, updated: 2022-09-13
Summary: This paper develops a new stochastic volatility model for the temperature that is a natural extension of the Ornstein-Uhlenbeck model proposed by Benth and Benth (2007). This model allows to be more conservative regarding extreme events while keeping tractability. We give a method based on Conditional Least Squares to estimate the parameters on daily data and estimate our model on eight major European cities. We then show how to calculate efficiently the average payoff of weather derivatives both by Monte-Carlo and Fourier transform techniques. This new model allows to better assess the risk related to temperature volatility.
Authors: Bernhard K Meister
Categories: Portfolio Management
PDF: http://arxiv.org/pdf/2209.05360v1
Dates: originally published: 2022-09-12, updated: 2022-09-12
Summary: Investors trade shifting prices, portfolio values, and in turn their ability to borrow. Concentrated ownership, high price impact and low collateral requirements are propitious for arbitrage.
Authors: Georgios I. Papayiannis, Athanasios N. Yannacopoulos
Categories: Risk Management
PDF: http://arxiv.org/pdf/2209.05211v1
Dates: originally published: 2022-09-12, updated: 2022-09-12
Summary: We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk measures robustly characterize the exposure of the firm, by filtering out appropriately the partial information available in individual sources into an aggregate model for the risk factors of interest. Importantly, the proposed risks can be expressed in closed analytic forms allowing for interesting qualitative interpretations as well as comparative statics and thus facilitate their use in the everyday risk management process of the insurance firms. The potential use of the proposed risk measures in insurance is illustrated by two concrete applications, capital risk allocation and premia calculation under uncertainty.
Authors: Erhan Bayraktar, Tao Chen
Categories: Optimization and Control, Mathematical Finance
PDF: http://arxiv.org/pdf/2209.04976v1
Dates: originally published: 2022-09-12, updated: 2022-09-12
Summary: We consider a multi-period stochastic control problem where the multivariate driving stochastic factor of the system has known marginal distributions but uncertain dependence structure. To solve the problem, we propose to implement the nonparametric adaptive robust control framework. We aim to find the optimal control against the worst-case copulae in a sequence of shrinking uncertainty sets which are generated from continuously observing the data. Then, we use a stochastic gradient descent ascent algorithm to numerically handle the corresponding high dimensional dynamic inf-sup optimization problem. We present the numerical results in the context of utility maximization and show that the controller benefits from knowing more information about the uncertain model.
Authors: Jherek Healy
Categories: Computational Finance
PDF: http://arxiv.org/pdf/2206.10662v7
Dates: originally published: 2022-06-10, updated: 2022-09-12
Summary: In parallelized Monte-Carlo simulations, the order of summation is not always the same. When the mean is calculated in running fashion, this may create an artificial randomness in results which ought to be reproducible. This note takes a look at the problem and proposes to combine the running mean and variance algorithm with an accurate and robust summing algorithm in order to increase the accuracy and robustness of the Monte-Carlo estimates.
Authors: Masato Hisakado, Kodai Hattori, Shintaro Mori
Categories: Risk Management, Data Analysis, Statistics and Probability
PDF: http://arxiv.org/pdf/2205.14146v2
Dates: originally published: 2022-05-20, updated: 2022-09-13
Summary: In this study, we apply a multidimensional self-exciting negative binomial distribution (SE-NBD) process to default portfolios with 13 sectors. The SE-NBD process is a Poisson process with a gamma-distributed intensity function. We extend the SE-NBD process to a multidimensional process. Using the multidimensional SE-NBD process (MD-SE-NBD), we can estimate interactions between these 13 sectors as a network. By applying impact analysis, we can classify upstream and downstream sectors. The upstream sectors are real-estate and financial institution (FI) sectors. From these upstream sectors, shock spreads to the downstream sectors. This is an amplifier of the shock. This is consistent with the analysis of bubble bursts. We compare these results to the multidimensional Hawkes process (MD-Hawkes) that has a zero-variance intensity function.
Authors: Huaxin Wang-Lu
Categories: General Finance
PDF: http://arxiv.org/pdf/2205.04290v3
Dates: originally published: 2022-05-09, updated: 2022-09-15
Summary: The evolution of the pandemic and people's concern over it have an impact on the Bitcoin market, while the extent of individualism could differentiate investor behaviors in the financial market during the pandemic. This paper examines whether public attention to COVID-19 in individualistic countries versus collectivistic countries Granger causes Bitcoin returns between February 11, 2020 and May 09, 2022. To this end, eight large economies with a individualistic or collectivistic tradition are chosen for analyses. By using rolling and recursive-evolving algorithms, it accounts for the timing of COVID-19 issues that vary by country and circumvents the potential estimation bias that a traditional Granger causality test may suffer due largely to Google's sampling variation for different time frames. In general, collectivistic countries are found to have stronger causal impacts on Bitcoin returns than individualistic countries.
Authors: Nick James, Max Menzies, Kevin Chin
Categories: Statistical Finance
PDF: http://arxiv.org/pdf/2203.15911v4
Dates: originally published: 2022-03-29, updated: 2022-09-13
Summary: Motivated by the current fears of a potentially stagflationary global economic environment, this paper uses new and recently introduced mathematical techniques to study multivariate time series pertaining to country inflation (CPI), economic growth (GDP) and equity index behaviours. We begin by assessing the temporal evolution among various economic phenomena, and complement this analysis with `economic driver analysis,' where we decouple country economic trajectories and determine what is most important in their association. Next, we study the temporal self-similarity of global inflation, growth and equity index returns to identify the most anomalous historic periods, and windows in the past that are most similar to current market dynamics. We then introduce a new algorithm to construct economic state classifications and compute an economic state integral, where countries are determined to belong in one of four candidate states based on their inflation and growth behaviours. Finally, we implement a decade-by-decade portfolio optimisation to determine which equity indices and portfolio assets have been most beneficial in maximising portfolio risk-adjusted returns in various market conditions. This could be of great interest to those looking for asset allocation guidance in the current period of high economic uncertainty.
Authors: Arthur Charpentier, Lariosse Kouakou, Matthias Löwe, Philipp Ratz, Franck Vermet
Categories: Economics, Risk Management, Computational Finance
PDF: http://arxiv.org/pdf/2107.02764v2
Dates: originally published: 2021-07-05, updated: 2022-09-12
Summary: The peer-to-peer (P2P) economy has been growing with the advent of the Internet, with well known brands such as Uber or Airbnb being examples thereof. In the insurance sector the approach is still in its infancy, but some companies have started to explore P2P-based collaborative insurance products (eg. Lemonade in the U.S. or Inspeer in France). The actuarial literature only recently started to consider those risk sharing mechanisms, as in Denuit and Robert (2021) or Feng et al. (2021). In this paper, describe and analyse such a P2P product, with some reciprocal risk sharing contracts. Here, we consider the case where policyholders still have an insurance contract, but the first self-insurance layer, below the deductible, can be shared with friends. We study the impact of the shape of the network (through the distribution of degrees) on the risk reduction. We consider also some optimal setting of the reciprocal commitments, and discuss the introduction of contracts with friends of friends to mitigate some possible drawbacks of having people without enough connections to exchange risks.
Authors: Eckhard Platen, Stefan Tappe
Categories: Probability, Mathematical Finance
PDF: http://arxiv.org/pdf/2011.12523v5
Dates: originally published: 2020-11-25, updated: 2022-09-12
Summary: We show that in a financial market given by semimartingales an arbitrage opportunity, provided it exists, can only be exploited through short selling. This finding provides a theoretical basis for differences in regulation for financial services providers that are allowed to go short and those without short sales. The privilege to be allowed to short sell gives access to potential arbitrage opportunities, which creates by design a bankruptcy risk.
Authors: Anastasios Petropoulos, Vassilis Siakoulis, Konstantinos P. Panousis, Loukas Papadoulas, Sotirios Chatzis
Categories: Economics, Computational Finance
PDF: http://arxiv.org/pdf/2009.11075v2
Dates: originally published: 2020-09-23, updated: 2022-09-12
Summary: In the aftermath of the financial crisis, supervisory authorities have considerably altered the mode of operation of financial stress testing. Despite these efforts, significant concerns and extensive criticism have been raised by market participants regarding the considered unrealistic methodological assumptions and simplifications. Current stress testing methodologies attempt to simulate the risks underlying a financial institution's balance sheet by using several satellite models. This renders their integration a really challenging task, leading to significant estimation errors. Moreover, advanced statistical techniques that could potentially capture the non-linear nature of adverse shocks are still ignored. This work aims to address these criticisms and shortcomings by proposing a novel approach based on recent advances in Deep Learning towards a principled method for Dynamic Balance Sheet Stress Testing. Experimental results on a newly collected financial/supervisory dataset, provide strong empirical evidence that our paradigm significantly outperforms traditional approaches; thus, it is capable of more accurately and efficiently simulating real world scenarios.
** Original source code: https://github.com/machalejm/arxiv_scraper **
