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am-AMM: An Auction-Managed Automated Market Maker am-AMM： 拍卖管理型自动做市商
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-03-05 DOI: arxiv-2403.03367
Austin Adams, Ciamac Moallemi, Sara Reynolds, Dan Robinson
{"title":"am-AMM: An Auction-Managed Automated Market Maker","authors":"Austin Adams, Ciamac Moallemi, Sara Reynolds, Dan Robinson","doi":"arxiv-2403.03367","DOIUrl":"https://doi.org/arxiv-2403.03367","url":null,"abstract":"Automated market makers (AMMs) have emerged as the dominant market mechanism\u0000for trading on decentralized exchanges implemented on blockchains. This paper\u0000presents a single mechanism that targets two important unsolved problems for\u0000AMMs: reducing losses to informed orderflow, and maximizing revenue from\u0000uninformed orderflow. The \"auction-managed AMM\" works by running a\u0000censorship-resistant onchain auction for the right to temporarily act as \"pool\u0000manager\" for a constant-product AMM. The pool manager sets the swap fee rate on\u0000the pool, and also receives the accrued fees from swaps. The pool manager can\u0000exclusively capture some arbitrage by trading against the pool in response to\u0000small price movements, and also can set swap fees incorporating price\u0000sensitivity of retail orderflow and adapting to changing market conditions,\u0000with the benefits from both ultimately accruing to liquidity providers.\u0000Liquidity providers can enter and exit the pool freely in response to changing\u0000rent, though they must pay a small fee on withdrawal. We prove that under\u0000certain assumptions, this AMM should have higher liquidity in equilibrium than\u0000any standard, fixed-fee AMM.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"140 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140055345","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
Justifying the Volatility of S&P 500 Daily Returns 标准普尔 500 指数每日回报波动的合理性
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-03-02 DOI: arxiv-2403.01088
Hayden Brown
{"title":"Justifying the Volatility of S&P 500 Daily Returns","authors":"Hayden Brown","doi":"arxiv-2403.01088","DOIUrl":"https://doi.org/arxiv-2403.01088","url":null,"abstract":"Over the past 60 years, there has been a gradual increase in the volatility\u0000of daily returns for the S&P 500 Index. Hypothetically, suppose that market\u0000forces determine daily volatility such that a daily leveraged S&P 500 fund\u0000cannot outperform a standard S&P 500 fund in the long run. Then this\u0000hypothetical volatility happens to support the increase in volatility seen in\u0000the S&P 500 index. On this basis, it appears that the classic argument of the\u0000market portfolio being unbeatable in the long run is determining the volatility\u0000of S&P 500 daily returns. Moreover, it follows that the long-term volatility of\u0000the daily returns for the S&P 500 Index should continue to increase until\u0000passing a particular threshold. If, on the other hand, this hypothesis about\u0000market forces increasing volatility is invalid, then there is room for daily\u0000leveraged S&P 500 funds to outperform their unleveraged counterparts in the\u0000long run.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140033489","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
A time-stepping deep gradient flow method for option pricing in (rough) diffusion models 用于（粗略）扩散模型期权定价的时间步进深梯度流方法
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-03-01 DOI: arxiv-2403.00746
Antonis Papapantoleon, Jasper Rou
{"title":"A time-stepping deep gradient flow method for option pricing in (rough) diffusion models","authors":"Antonis Papapantoleon, Jasper Rou","doi":"arxiv-2403.00746","DOIUrl":"https://doi.org/arxiv-2403.00746","url":null,"abstract":"We develop a novel deep learning approach for pricing European options in\u0000diffusion models, that can efficiently handle high-dimensional problems\u0000resulting from Markovian approximations of rough volatility models. The option\u0000pricing partial differential equation is reformulated as an energy minimization\u0000problem, which is approximated in a time-stepping fashion by deep artificial\u0000neural networks. The proposed scheme respects the asymptotic behavior of option\u0000prices for large levels of moneyness, and adheres to a priori known bounds for\u0000option prices. The accuracy and efficiency of the proposed method is assessed\u0000in a series of numerical examples, with particular focus in the lifted Heston\u0000model.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140026187","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
On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients 论具有跳跃和非 Lipschitz 系数的随机 Volterra方程的非负解
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-02-29 DOI: arxiv-2402.19203
Aurélien Alfonsi, Guillaume Szulda
{"title":"On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients","authors":"Aurélien Alfonsi, Guillaume Szulda","doi":"arxiv-2402.19203","DOIUrl":"https://doi.org/arxiv-2402.19203","url":null,"abstract":"We consider one-dimensional stochastic Volterra equations with jumps for\u0000which we establish conditions upon the convolution kernel and coefficients for\u0000the strong existence and pathwise uniqueness of a non-negative c`adl`ag\u0000solution. By using the approach recently developed in arXiv:2302.07758, we show\u0000the strong existence by using a nonnegative approximation of the equation whose\u0000convergence is proved via a variant of the Yamada--Watanabe approximation\u0000technique. We apply our results to L'evy-driven stochastic Volterra equations.\u0000In particular, we are able to define a Volterra extension of the so-called\u0000alpha-stable Cox--Ingersoll--Ross process, which is especially used for\u0000applications in Mathematical Finance.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004517","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
Semistatic robust utility indifference valuation and robust integral functionals 半稳健效用偏好估值和稳健积分函数
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-02-29 DOI: arxiv-2402.18872
Keita Owari
{"title":"Semistatic robust utility indifference valuation and robust integral functionals","authors":"Keita Owari","doi":"arxiv-2402.18872","DOIUrl":"https://doi.org/arxiv-2402.18872","url":null,"abstract":"We consider a discrete-time robust utility maximisation with semistatic\u0000strategies, and the associated indifference prices of exotic options. For this\u0000purpose, we introduce a robust form of convex integral functionals on the space\u0000of bounded continuous functions on a Polish space, and establish some key\u0000regularity and representation results, in the spirit of the classical\u0000Rockafellar theorem, in terms of the duality formed with the space of Borel\u0000measures. These results (together with the standard Fenchel duality and minimax\u0000theorems) yield a duality for the robust utility maximisation problem as well\u0000as a representation of associated indifference prices, where the presence of\u0000static positions in the primal problem appears in the dual problem as a\u0000marginal constraint on the martingale measures. Consequently, the resulting\u0000indifference prices are consistent with the observed prices of vanilla options.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004420","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 positioning in derivative securities in incomplete markets 不完全市场中衍生证券的最佳定位
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-02-29 DOI: arxiv-2403.00139
Tim Leung, Matthew Lorig, Yoshihiro Shirai
{"title":"Optimal positioning in derivative securities in incomplete markets","authors":"Tim Leung, Matthew Lorig, Yoshihiro Shirai","doi":"arxiv-2403.00139","DOIUrl":"https://doi.org/arxiv-2403.00139","url":null,"abstract":"This paper analyzes a problem of optimal static hedging using derivatives in\u0000incomplete markets. The investor is assumed to have a risk exposure to two\u0000underlying assets. The hedging instruments are vanilla options written on a\u0000single underlying asset. The hedging problem is formulated as a utility\u0000maximization problem whereby the form of the optimal static hedge is\u0000determined. Among our results, a semi-analytical solution for the optimizer is\u0000found through variational methods for exponential, power/logarithmic, and\u0000quadratic utility. When vanilla options are available for each underlying\u0000asset, the optimal solution is related to the fixed points of a Lipschitz map.\u0000In the case of exponential utility, there is only one such fixed point, and\u0000subsequent iterations of the map converge to it.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140026271","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 critical disordered pinning measure 临界无序引脚测量
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-02-27 DOI: arxiv-2402.17642
Ran Wei, Jinjiong Yu
{"title":"The critical disordered pinning measure","authors":"Ran Wei, Jinjiong Yu","doi":"arxiv-2402.17642","DOIUrl":"https://doi.org/arxiv-2402.17642","url":null,"abstract":"In this paper, we study a disordered pinning model induced by a random walk\u0000whose increments have a finite fourth moment and vanishing first and third\u0000moments. It is known that this model is marginally relevant, and moreover, it\u0000undergoes a phase transition in an intermediate disorder regime. We show that,\u0000in the critical window, the point-to-point partition functions converge to a\u0000unique limiting random measure, which we call the critical disordered pinning\u0000measure. We also obtain an analogous result for a continuous counterpart to the\u0000pinning model, which is closely related to two other models: one is a critical\u0000stochastic Volterra equation that gives rise to a rough volatility model, and\u0000the other is a critical stochastic heat equation with multiplicative noise that\u0000is white in time and delta in space.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004406","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
Withdrawal Success Optimization in a Pooled Annuity Fund 优化集合年金基金的提取成功率
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-02-27 DOI: arxiv-2402.17164
Hayden Brown
{"title":"Withdrawal Success Optimization in a Pooled Annuity Fund","authors":"Hayden Brown","doi":"arxiv-2402.17164","DOIUrl":"https://doi.org/arxiv-2402.17164","url":null,"abstract":"Consider a closed pooled annuity fund investing in n assets with\u0000discrete-time rebalancing. At time 0, each annuitant makes an initial\u0000contribution to the fund, committing to a predetermined schedule of\u0000withdrawals. Require annuitants to be homogeneous in the sense that their\u0000initial contributions and predetermined withdrawal schedules are identical, and\u0000their mortality distributions are identical and independent. Under the\u0000forementioned setup, the probability for a particular annuitant to complete the\u0000prescribed withdrawals until death is maximized over progressively measurable\u0000portfolio weight functions. Applications consider fund portfolios that mix two\u0000assets: the S&P Composite Index and an inflation-protected bond. The maximum\u0000probability is computed for annually rebalanced schedules consisting of an\u0000initial investment and then equal annual withdrawals until death. A\u0000considerable increase in the maximum probability is achieved by increasing the\u0000number of annuitants initially in the pool. For example, when the per-annuitant\u0000initial contribution and annual withdrawal amount are held constant, starting\u0000with 20 annuitants instead of just 1 can increase the maximum probability\u0000(measured on a scale from 0 to 1) by as much as .15.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"169 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004417","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
Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligence 用生成式人工智能对多变量利维过程模型进行广义期权定价
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-02-27 DOI: arxiv-2402.17919
Young Shin Kim, Hyun-Gyoon Kim
{"title":"Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligence","authors":"Young Shin Kim, Hyun-Gyoon Kim","doi":"arxiv-2402.17919","DOIUrl":"https://doi.org/arxiv-2402.17919","url":null,"abstract":"In this study, we discuss a machine learning technique to price exotic\u0000options with two underlying assets based on a non-Gaussian Levy process model.\u0000We introduce a new multivariate Levy process model named the generalized normal\u0000tempered stable (gNTS) process, which is defined by time-changed multivariate\u0000Brownian motion. Since the probability density function (PDF) of the gNTS\u0000process is not given by a simple analytic formula, we use the conditional\u0000real-valued non-volume preserving (CRealNVP) model, which is a sort of\u0000flow-based generative networks. After that, we discuss the no-arbitrage pricing\u0000on the gNTS model for pricing the quanto option whose underlying assets consist\u0000of a foreign index and foreign exchange rate. We also present the training of\u0000the CRealNVP model to learn the PDF of the gNTS process using a training set\u0000generated by Monte Carlo simulation. Next, we estimate the parameters of the\u0000gNTS model with the trained CRealNVP model using the empirical data observed in\u0000the market. Finally, we provide a method to find an equivalent martingale\u0000measure on the gNTS model and to price the quanto option using the CRealNVP\u0000model with the risk-neutral parameters of the gNTS model.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004709","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
On convergence of forecasts in prediction markets 论预测市场中预测的趋同性
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-02-26 DOI: arxiv-2402.16345
Nina Badulina, Dmitry Shatilovich, Mikhail Zhitlukhin
{"title":"On convergence of forecasts in prediction markets","authors":"Nina Badulina, Dmitry Shatilovich, Mikhail Zhitlukhin","doi":"arxiv-2402.16345","DOIUrl":"https://doi.org/arxiv-2402.16345","url":null,"abstract":"We propose a dynamic model of a prediction market in which agents predict the\u0000values of a sequence of random vectors. The main result shows that if there are\u0000agents who make correct (or asymptotically correct) next-period forecasts, then\u0000the aggregated market forecasts converge to the next-period conditional\u0000expectations of the random vectors.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139978825","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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