{"title":"Extreme measures in continuous time Conic Finance","authors":"Yoshihiro Shirai","doi":"10.3934/fmf.2023021","DOIUrl":"https://doi.org/10.3934/fmf.2023021","url":null,"abstract":"Dynamic spectral risk measures define a claim's valuation bounds as supremum and infimum of expectations of the claim's payoff over a dominated set of measures. The measures at which such extrema are attained are called extreme measures. We determine explicit expressions for their Radon-Nykodim derivatives with respect to the common dominating measure. Based on the formulas found, we estimate the extreme measures in two cases. First, the dominating measure is calibrated to mid prices of options and valuation bounds are given by options bid and ask prices. Second, the dominating measure is estimated from historical mid equity prices and valuation bounds are given by historical 5-day high and low prices. In both experiments, we find that the market determines upper bounds by testing scenarios in which losses are significantly lower than expected under the dominating measure, while lower bounds by ones in which gains are only slightly lower than in the base case.","PeriodicalId":492180,"journal":{"name":"Frontiers of mathematical finance","volume":"307 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134884877","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":"Distributed energy resources flexibility as volumetric options on electricity","authors":"Helyette Geman, Yuanye Ma","doi":"10.3934/fmf.2023018","DOIUrl":"https://doi.org/10.3934/fmf.2023018","url":null,"abstract":"The goal of the paper is twofold: a) following the identification of the merits of Distributed Energy Resources (DERs) by FERC 2222 for the flexibility they bring to the grid, we recognize water heaters and thermostats as mini-batteries and introduce volumetric/swing options that the Aggregator can sell by shifting consumers' consumption while rewarding them; b) We propose to address the pricing complexity of these volumetric options - which are in our setting very general in terms of number of exercises and quantities constraints - by a novel approach that combines Monte Carlo simulations and Recurrent Neural Networks (RNN).","PeriodicalId":492180,"journal":{"name":"Frontiers of mathematical finance","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135594705","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":"Data-driven nonparametric robust control under dependence uncertainty","authors":"Erhan Bayraktar, Tao Chen","doi":"10.3934/fmf.2023004","DOIUrl":"https://doi.org/10.3934/fmf.2023004","url":null,"abstract":"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.","PeriodicalId":492180,"journal":{"name":"Frontiers of mathematical finance","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135535135","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}
Alex Backwell, Andrea Macrina, Erik Schlogl, David Skovmand
{"title":"Term rates, multicurve term structures and overnight rate benchmarks: A roll–over risk approach","authors":"Alex Backwell, Andrea Macrina, Erik Schlogl, David Skovmand","doi":"10.3934/fmf.2023009","DOIUrl":"https://doi.org/10.3934/fmf.2023009","url":null,"abstract":"In the current LIBOR transition to overnight–rate benchmarks, it is important to understand theoretically and empirically what distinguishes actual term rates from overnight benchmarks or 'synthetic' term rates based on such benchmarks. The well–known 'multi–curve' phenomenon of tenor basis spreads between term structures associated with different payment frequencies provides key information on this distinction. This information can be extracted using a modelling framework based on the concept of 'roll–over risk', i.e., the risk a borrower faces of not being able to refinance a loan at (or at a known spread to) a market benchmark rate. Separating the roll–over risk priced by tenor basis spreads into a credit–downgrade and a funding–liquidity component, the theoretical modelling and the empirical evidence show that proper term rates based on the new benchmarks remain elusive and that a multi–curve environment will persist even for rates secured by repurchase agreements.","PeriodicalId":492180,"journal":{"name":"Frontiers of mathematical finance","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135181160","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":"Backtestability and the ridge backtest","authors":"Carlo Acerbi, Balázs Székely","doi":"10.3934/fmf.2023019","DOIUrl":"https://doi.org/10.3934/fmf.2023019","url":null,"abstract":"We propose a formal definition of backtestability for a statistical functional of a distribution: a functional is backtestable if there exists a backtest function depending only on the forecast of the functional and the related random variable, which is strictly monotonic in the former and has zero expected value for an exact forecast. We discuss the relationship with elicitability and identifiability which turn out being necessary conditions for backtestability. The variance and the expected shortfall are not backtestable for this reason. We compare (absolute) model validation in the context of hypothesis tests via backtest functions, versus (relative) model selection between competing forecasting models, via scoring functions. We define a backtest to be sharp when it is strictly monotonic with respect to the real value of the functional and not only to its forecast. This decides whether the expected value of the backtest determines also the prediction discrepancy and not only its significance. We show that the quantile backtest is not sharp and in fact it provides no information whatsoever on its true value. The expectile is also not sharp; we provide bounds for its true value, which are looser for outer confidence levels. We then introduce the notion of ridge backtests, applicable to particular non–backtestable functionals, such as the variance and the expected shortfall, which coincide with the attained minimum of the scoring function of another elicitable auxiliary functional (the mean and the value at risk, respectively). This permits approximated sharp backtests up to a small and one–sided sensitivity to the prediction of the auxiliary variable. The ridge mechanism explains why the variance has always been de–facto backtestable and allows for similar efficient ways to backtest the expected shortfall. We discuss the relevance of this result in the current debate of financial regulation (banking and insurance), where value at risk and expected shortfall are adopted as regulatory risk measures.","PeriodicalId":492180,"journal":{"name":"Frontiers of mathematical finance","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135010282","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}
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