{"title":"COMEX Copper Futures Volatility Forecasting: Econometric Models and Deep Learning","authors":"Zian Wang, Xinyi Lu","doi":"arxiv-2409.08356","DOIUrl":"https://doi.org/arxiv-2409.08356","url":null,"abstract":"This paper investigates the forecasting performance of COMEX copper futures\u0000realized volatility across various high-frequency intervals using both\u0000econometric volatility models and deep learning recurrent neural network\u0000models. The econometric models considered are GARCH and HAR, while the deep\u0000learning models include RNN (Recurrent Neural Network), LSTM (Long Short-Term\u0000Memory), and GRU (Gated Recurrent Unit). In forecasting daily realized\u0000volatility for COMEX copper futures with a rolling window approach, the\u0000econometric models, particularly HAR, outperform recurrent neural networks\u0000overall, with HAR achieving the lowest QLIKE loss function value. However, when\u0000the data is replaced with hourly high-frequency realized volatility, the deep\u0000learning models outperform the GARCH model, and HAR attains a comparable QLIKE\u0000loss function value. Despite the black-box nature of machine learning models,\u0000the deep learning models demonstrate superior forecasting performance,\u0000surpassing the fixed QLIKE value of HAR in the experiment. Moreover, as the\u0000forecast horizon extends for daily realized volatility, deep learning models\u0000gradually close the performance gap with the GARCH model in certain loss\u0000function metrics. Nonetheless, HAR remains the most effective model overall for\u0000daily realized volatility forecasting in copper futures.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249777","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}
{"title":"A market resilient data-driven approach to option pricing","authors":"Anindya Goswami, Nimit Rana","doi":"arxiv-2409.08205","DOIUrl":"https://doi.org/arxiv-2409.08205","url":null,"abstract":"In this paper, we present a data-driven ensemble approach for option price\u0000prediction whose derivation is based on the no-arbitrage theory of option\u0000pricing. Using the theoretical treatment, we derive a common representation\u0000space for achieving domain adaptation. The success of an implementation of this\u0000idea is shown using some real data. Then we report several experimental results\u0000for critically examining the performance of the derived pricing models.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"419 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216317","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}
{"title":"Ergodicity and Law-of-large numbers for the Volterra Cox-Ingersoll-Ross process","authors":"Mohamed Ben Alaya, Martin Friesen, Jonas Kremer","doi":"arxiv-2409.04496","DOIUrl":"https://doi.org/arxiv-2409.04496","url":null,"abstract":"We study the Volterra Volterra Cox-Ingersoll-Ross process on $mathbb{R}_+$\u0000and its stationary version. Based on a fine asymptotic analysis of the\u0000corresponding Volterra Riccati equation combined with the affine transformation\u0000formula, we first show that the finite-dimensional distributions of this\u0000process are asymptotically independent. Afterwards, we prove a law-of-large\u0000numbers in $L^p$(Omega)$ with $p geq 2$ and show that the stationary process\u0000is ergodic. As an application, we prove the consistency of the method of\u0000moments and study the maximum-likelihood estimation for continuous and discrete\u0000high-frequency observations.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216318","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}
{"title":"Irreversible investment under weighted discounting: effects of decreasing impatience","authors":"Pengyu Wei, Wei Wei","doi":"arxiv-2409.01478","DOIUrl":"https://doi.org/arxiv-2409.01478","url":null,"abstract":"This paper employs an intra-personal game-theoretic framework to investigate\u0000how decreasing impatience influences irreversible investment behaviors in a\u0000continuous-time setting. We consider a capacity expansion problem under\u0000weighted discount functions, a class of nonexponential functions that exhibit\u0000decreasing impatience, including the hyperbolic discount function as a special\u0000case. By deriving the Bellman system that characterizes the equilibrium, we\u0000establish the framework for analyzing investment behaviors of agents subject to\u0000decreasing impatience. From an economic perspective, we demonstrates that\u0000decreasing impatience prompts early investment. From a technical standpoint, we\u0000warn that decreasing impatience can lead to the failure of the smooth pasting\u0000principle.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216339","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}
{"title":"Long-term decomposition of robust pricing kernels under G-expectation","authors":"Jaehyun Kim, Hyungbin Park","doi":"arxiv-2409.00535","DOIUrl":"https://doi.org/arxiv-2409.00535","url":null,"abstract":"This study develops a BSDE method for the long-term decomposition of pricing\u0000kernels under the G-expectation framework. We establish the existence,\u0000uniqueness, and regularity of solutions to three types of quadratic G-BSDEs:\u0000finite-horizon G-BSDEs, infinite-horizon G-BSDEs, and ergodic G-BSDEs.\u0000Moreover, we explore the Feynman--Kac formula associated with these three types\u0000of quadratic G-BSDEs. Using these results, a pricing kernel is uniquely\u0000decomposed into four components: an exponential discounting component, a\u0000transitory component, a symmetric G-martingale, and a decreasing component that\u0000captures the volatility uncertainty of the G-Brownian motion. Furthermore,\u0000these components are represented through a solution to a PDE. This study\u0000extends previous findings obtained under a single fixed probability framework\u0000to the G-expectation context.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216345","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}
{"title":"Brief Synopsis of the Scientific Career of T. R. Hurd","authors":"Matheus R. Grasselli, Lane P. Hughston","doi":"arxiv-2408.16891","DOIUrl":"https://doi.org/arxiv-2408.16891","url":null,"abstract":"As an introduction to a Special Issue of International Journal of Theoretical\u0000and Applied Finance in Honour of the Memory of Thomas Robert Hurd we present a\u0000brief synopsis of Tom Hurd's scientific career and a bibliography of his\u0000scientific publications.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216340","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}
{"title":"Option Pricing with Stochastic Volatility, Equity Premium, and Interest Rates","authors":"Nicole Hao, Echo Li, Diep Luong-Le","doi":"arxiv-2408.15416","DOIUrl":"https://doi.org/arxiv-2408.15416","url":null,"abstract":"This paper presents a new model for options pricing. The Black-Scholes-Merton\u0000(BSM) model plays an important role in financial options pricing. However, the\u0000BSM model assumes that the risk-free interest rate, volatility, and equity\u0000premium are constant, which is unrealistic in the real market. To address this,\u0000our paper considers the time-varying characteristics of those parameters. Our\u0000model integrates elements of the BSM model, the Heston (1993) model for\u0000stochastic variance, the Vasicek model (1977) for stochastic interest rates,\u0000and the Campbell and Viceira model (1999, 2001) for stochastic equity premium.\u0000We derive a linear second-order parabolic PDE and extend our model to encompass\u0000fixed-strike Asian options, yielding a new PDE. In the absence of closed-form\u0000solutions for any options from our new model, we utilize finite difference\u0000methods to approximate prices for European call and up-and-out barrier options,\u0000and outline the numerical implementation for fixed-strike Asian call options.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216341","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}
{"title":"Asset pricing under model uncertainty with finite time and states","authors":"Shuzhen Yang, Wenqing Zhang","doi":"arxiv-2408.13048","DOIUrl":"https://doi.org/arxiv-2408.13048","url":null,"abstract":"In this study, we consider the asset pricing under model uncertainty with\u0000finite time and under a family of probability, and explore its relationship\u0000with risk neutral probability meastates structure. For the single-period\u0000securities model, we give a novel definition of arbitrage sure. Focusing on the\u0000financial market with short sales prohibitions, we separately investigate the\u0000necessary and sufficient conditions for no-arbitrage asset pricing based on\u0000nonlinear expectation which composed with a family of probability. When each\u0000linear expectation driven by the probability in the family of probability\u0000becomes martingale measure, the necessary and sufficient conditions are same,\u0000and coincide with the existing results. Furthermore, we expand the main results\u0000of single-period securities model to the case of multi-period securities model.\u0000By-product, we obtain the superhedging prices of contingent claim under model\u0000uncertainty.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216342","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}
{"title":"A case study on different one-factor Cheyette models for short maturity caplet calibration","authors":"Arun Kumar Polala, Bernhard Hientzsch","doi":"arxiv-2408.11257","DOIUrl":"https://doi.org/arxiv-2408.11257","url":null,"abstract":"In [1], we calibrated a one-factor Cheyette SLV model with a local volatility\u0000that is linear in the benchmark forward rate and an uncorrelated CIR stochastic\u0000variance to 3M caplets of various maturities. While caplet smiles for many\u0000maturities could be reasonably well calibrated across the range of strikes, for\u0000instance the 1Y maturity could not be calibrated well across that entire range\u0000of strikes. Here, we study whether models with alternative local volatility\u0000terms and/or alternative stochastic volatility or variance models can calibrate\u0000the 1Y caplet smile better across the strike range better than the model\u0000studied in [1]. This is made possible and feasible by the generic simulation,\u0000pricing, and calibration frameworks introduced in [1] and some new frameworks\u0000presented in this paper. We find that some model settings calibrate well to the\u00001Y smile across the strike range under study. In particular, a model setting\u0000with a local volatility that is piece-wise linear in the benchmark forward rate\u0000together with an uncorrelated CIR stochastic variance and one with a local\u0000volatility that is linear in the benchmark rate together with a correlated\u0000lognormal stochastic volatility with quadratic drift (QDLNSV) as in [2]\u0000calibrate well. We discuss why the later might be a preferable model. [1] Arun Kumar Polala and Bernhard Hientzsch. Parametric differential machine\u0000learning for pricing and calibration. arXiv preprint arXiv:2302.06682 , 2023. [2] Artur Sepp and Parviz Rakhmonov. A Robust Stochastic Volatility Model for\u0000Interest Rate Dynamics. Risk Magazine, 2023","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216343","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}
{"title":"Optimal stopping and divestment timing under scenario ambiguity and learning","authors":"Andrea Mazzon, Peter Tankov","doi":"arxiv-2408.09349","DOIUrl":"https://doi.org/arxiv-2408.09349","url":null,"abstract":"Aiming to analyze the impact of environmental transition on the value of\u0000assets and on asset stranding, we study optimal stopping and divestment timing\u0000decisions for an economic agent whose future revenues depend on the realization\u0000of a scenario from a given set of possible futures. Since the future scenario\u0000is unknown and the probabilities of individual prospective scenarios are\u0000ambiguous, we adopt the smooth model of decision making under ambiguity\u0000aversion of Klibanoff et al (2005), framing the optimal divestment decision as\u0000an optimal stopping problem with learning under ambiguity aversion. We then\u0000prove a minimax result reducing this problem to a series of standard optimal\u0000stopping problems with learning. The theory is illustrated with two examples:\u0000the problem of optimally selling a stock with ambigous drift, and the problem\u0000of optimal divestment from a coal-fired power plant under transition scenario\u0000ambiguity.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216346","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}