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Fluid-Limits of Fragmented Limit-Order Markets 零散限价市场的流体限价
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-05 DOI: arxiv-2407.04354
Johannes Muhle-Karbe, Eyal Neuman, Yonatan Shadmi
{"title":"Fluid-Limits of Fragmented Limit-Order Markets","authors":"Johannes Muhle-Karbe, Eyal Neuman, Yonatan Shadmi","doi":"arxiv-2407.04354","DOIUrl":"https://doi.org/arxiv-2407.04354","url":null,"abstract":"Maglaras, Moallemi, and Zheng (2021) have introduced a flexible queueing\u0000model for fragmented limit-order markets, whose fluid limit remains remarkably\u0000tractable. In the present study we prove that, in the limit of small and\u0000frequent orders, the discrete system indeed converges to the fluid limit, which\u0000is characterized by a system of coupled nonlinear ODEs with singular\u0000coefficients at the origin. Moreover, we establish that the fluid system is\u0000asymptotically stable for an arbitrary number of limit order books in that,\u0000over time, it converges to the stationary equilibrium state studied by Maglaras\u0000et al. (2021).","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary vs Non-Unitary Time Evolution 用量子随机微积分模拟不确定性波动：单一时间演化与非单一时间演化
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-05 DOI: arxiv-2407.04520
Will Hicks
{"title":"Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary vs Non-Unitary Time Evolution","authors":"Will Hicks","doi":"arxiv-2407.04520","DOIUrl":"https://doi.org/arxiv-2407.04520","url":null,"abstract":"In this article we look at stochastic processes with uncertain parameters,\u0000and consider different ways in which information is obtained when carrying out\u0000observations. For example we focus on the case of a the random evolution of a\u0000traded financial asset price with uncertain volatility. The quantum approach\u0000presented, allows us to encode different volatility levels in a state acting on\u0000a Hilbert space. We consider different means of defining projective\u0000measurements in order to track the evolution of a traded market price, and\u0000discuss the results of different Monte-Carlo simulations.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The second-order Esscher martingale densities for continuous-time market models 连续时间市场模型的二阶埃舍尔马丁格尔密度
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-04 DOI: arxiv-2407.03960
Tahir Choulli, Ella Elazkany, Michèle Vanmaele
{"title":"The second-order Esscher martingale densities for continuous-time market models","authors":"Tahir Choulli, Ella Elazkany, Michèle Vanmaele","doi":"arxiv-2407.03960","DOIUrl":"https://doi.org/arxiv-2407.03960","url":null,"abstract":"In this paper, we introduce the second-order Esscher pricing notion for\u0000continuous-time models. Depending whether the stock price $S$ or its logarithm\u0000is the main driving noise/shock in the Esscher definition, we obtained two\u0000classes of second-order Esscher densities called linear class and exponential\u0000class respectively. Using the semimartingale characteristics to parametrize\u0000$S$, we characterize the second-order Esscher densities (exponential and\u0000linear) using pointwise equations. The role of the second order concept is\u0000highlighted in many manners and the relationship between the two classes is\u0000singled out for the one-dimensional case. Furthermore, when $S$ is a compound\u0000Poisson model, we show how both classes are related to the\u0000Delbaen-Haenzendonck's risk-neutral measure. Afterwards, we restrict our model\u0000$S$ to follow the jump-diffusion model, for simplicity only, and address the\u0000bounds of the stochastic Esscher pricing intervals. In particular, no matter\u0000what is the Esscher class, we prove that both bounds (upper and lower) are\u0000solutions to the same linear backward stochastic differential equation (BSDE\u0000hereafter for short) but with two different constraints. This shows that BSDEs\u0000with constraints appear also in a setting beyond the classical cases of\u0000constraints on gain-processes or constraints on portfolios. We prove that our\u0000resulting constrained BSDEs have solutions in our framework for a large class\u0000of claims' payoffs including any bounded claim, in contrast to the literature,\u0000and we single out the monotonic sequence of BSDEs that ``naturally\" approximate\u0000it as well.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Basket Options with Volatility Skew: Calibrating a Local Volatility Model by Sample Rearrangement 具有波动偏差的一篮子期权：通过样本重排校准局部波动率模型
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-03 DOI: arxiv-2407.02901
Nicola F. Zaugg, Lech A. Grzelak
{"title":"Basket Options with Volatility Skew: Calibrating a Local Volatility Model by Sample Rearrangement","authors":"Nicola F. Zaugg, Lech A. Grzelak","doi":"arxiv-2407.02901","DOIUrl":"https://doi.org/arxiv-2407.02901","url":null,"abstract":"The pricing of derivatives tied to baskets of assets demands a sophisticated\u0000framework that aligns with the available market information to capture the\u0000intricate non-linear dependency structure among the assets. We describe the\u0000dynamics of the multivariate process of constituents with a copula model and\u0000propose an efficient method to extract the dependency structure from the\u0000market. The proposed method generates coherent sets of samples of the\u0000constituents process through systematic sampling rearrangement. These samples\u0000are then utilized to calibrate a local volatility model (LVM) of the basket\u0000process, which is used to price basket derivatives. We show that the method is\u0000capable of efficiently pricing basket options based on a large number of basket\u0000constituents, accomplishing the calibration process within a matter of seconds,\u0000and achieving near-perfect calibration to the index options of the market.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal hedging with variational preferences under convex risk measures 凸风险度量下的变异偏好最优对冲
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-03 DOI: arxiv-2407.03431
Marcelo Righi
{"title":"Optimal hedging with variational preferences under convex risk measures","authors":"Marcelo Righi","doi":"arxiv-2407.03431","DOIUrl":"https://doi.org/arxiv-2407.03431","url":null,"abstract":"We expose a theoretical hedging optimization framework with variational\u0000preferences under convex risk measures. We explore a general dual\u0000representation for the composition between risk measures and utilities. We\u0000study the properties of the optimization problem as a convex and monotone map\u0000per se. We also derive results for optimality and indifference pricing\u0000conditions. We also explore particular examples inside our setup.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Information Entropy of the Financial Market: Modelling Random Processes Using Open Quantum Systems 金融市场的信息熵：利用开放量子系统为随机过程建模
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-06-28 DOI: arxiv-2406.20027
Will Hicks
{"title":"Information Entropy of the Financial Market: Modelling Random Processes Using Open Quantum Systems","authors":"Will Hicks","doi":"arxiv-2406.20027","DOIUrl":"https://doi.org/arxiv-2406.20027","url":null,"abstract":"We discuss the role of information entropy on the behaviour of random\u0000processes, and how this might take effect in the dynamics of financial market\u0000prices. We then go on to show how the Open Quantum Systems approach can be used\u0000as a more flexible alternative to classical methods in terms of modelling the\u0000entropy gain of a random process. We start by describing an open quantum system\u0000that can be used to model the state of a financial market. We then go on to\u0000show how to represent an essentially classical diffusion in this framework.\u0000Finally, we show how by relaxing certain assumptions, one can generate\u0000interesting and essentially non-classical results, which are highlighted\u0000through numerical simulations.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Playing with Fire? A Mean Field Game Analysis of Fire Sales and Systemic Risk under Regulatory Capital Constraints 玩火？监管资本约束下火灾销售与系统性风险的均势博弈分析
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-06-25 DOI: arxiv-2406.17528
Rüdiger Frey, Theresa Traxler
{"title":"Playing with Fire? A Mean Field Game Analysis of Fire Sales and Systemic Risk under Regulatory Capital Constraints","authors":"Rüdiger Frey, Theresa Traxler","doi":"arxiv-2406.17528","DOIUrl":"https://doi.org/arxiv-2406.17528","url":null,"abstract":"We study the impact of regulatory capital constraints on fire sales and\u0000financial stability in a large banking system using a mean field game model. In\u0000our model banks adjust their holdings of a risky asset via trading strategies\u0000with finite trading rate in order to maximize expected profits. Moreover, a\u0000bank is liquidated if it violates a stylized regulatory capital constraint. We\u0000assume that the drift of the asset value is affected by the average change in\u0000the position of the banks in the system. This creates strategic interaction\u0000between the trading behavior of banks and thus leads to a game. The equilibria\u0000of this game are characterized by a system of coupled PDEs. We solve this\u0000system explicitly for a test case without regulatory constraints and\u0000numerically for the regulated case. We find that capital constraints can lead\u0000to a systemic crisis where a substantial proportion of the banking system\u0000defaults simultaneously. Moreover, we discuss proposals from the literature on\u0000macroprudential regulation. In particular, we show that in our setup a systemic\u0000crisis does not arise if the banking system is sufficiently well capitalized or\u0000if improved mechanisms for the resolution of banks violating the risk capital\u0000constraints are in place.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Path-Dependent Volatility Models for Price-Storage Dynamics in Natural Gas Markets and Discrete-Time Swing Option Pricing 天然气市场价格-存储动态和离散时间波动期权定价的随机路径依赖波动模型
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-06-24 DOI: arxiv-2406.16400
Jinniao Qiu, Antony Ware, Yang Yang
{"title":"Stochastic Path-Dependent Volatility Models for Price-Storage Dynamics in Natural Gas Markets and Discrete-Time Swing Option Pricing","authors":"Jinniao Qiu, Antony Ware, Yang Yang","doi":"arxiv-2406.16400","DOIUrl":"https://doi.org/arxiv-2406.16400","url":null,"abstract":"This paper is devoted to the price-storage dynamics in natural gas markets. A\u0000novel stochastic path-dependent volatility model is introduced with\u0000path-dependence in both price volatility and storage increments. Model\u0000calibrations are conducted for both the price and storage dynamics. Further, we\u0000discuss the pricing problem of discrete-time swing options using the dynamic\u0000programming principle, and a deep learning-based method is proposed for\u0000numerical approximations. A numerical algorithm is provided, followed by a\u0000convergence analysis result for the deep-learning approach.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computing the SSR 计算 SSR
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-06-23 DOI: arxiv-2406.16131
Peter K. Friz, Jim Gatheral
{"title":"Computing the SSR","authors":"Peter K. Friz, Jim Gatheral","doi":"arxiv-2406.16131","DOIUrl":"https://doi.org/arxiv-2406.16131","url":null,"abstract":"The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book,\u0000is critically important to options traders, especially market makers. We\u0000present a model-free expression for the SSR in terms of the characteristic\u0000function. In the diffusion setting, it is well-known that the short-term limit\u0000of the SSR is 2; a corollary of our results is that this limit is $H+3/2$ where\u0000$H$ is the Hurst exponent of the volatility process. The general formula for\u0000the SSR simplifies and becomes particularly tractable in the affine forward\u0000variance case. We explain the qualitative behavior of the SSR with respect to\u0000the shape of the forward variance curve, and thus also path-dependence of the\u0000SSR.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strong existence and uniqueness of a calibrated local stochastic volatility model 校准局部随机波动模型的强存在性和唯一性
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-06-20 DOI: arxiv-2406.14074
Scander Mustapha
{"title":"Strong existence and uniqueness of a calibrated local stochastic volatility model","authors":"Scander Mustapha","doi":"arxiv-2406.14074","DOIUrl":"https://doi.org/arxiv-2406.14074","url":null,"abstract":"We study a two-dimensional McKean-Vlasov stochastic differential equation,\u0000whose volatility coefficient depends on the conditional distribution of the\u0000second component with respect to the first component. We prove the strong\u0000existence and uniqueness of the solution, establishing the well-posedness of a\u0000two-factor local stochastic volatility (LSV) model calibrated to the market\u0000prices of European call options. In the spirit of [Jourdain and Zhou, 2020,\u0000Existence of a calibrated regime switching local volatility model.], we assume\u0000that the factor driving the volatility of the log-price takes finitely many\u0000values. Additionally, the propagation of chaos of the particle system is\u0000established, giving theoretical justification for the algorithm [Julien Guyon\u0000and Henry-Labord`ere, 2012, Being particular about calibration.].","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"357 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141525935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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