{"title":"Monte Carlo methods for real options under parameter uncertainty in multidimensional models","authors":"Ankush Agarwal, C. Ewald, Yihan Zou","doi":"10.2139/ssrn.3549891","DOIUrl":"https://doi.org/10.2139/ssrn.3549891","url":null,"abstract":"In this article we study the evaluation of American options with stochastic volatility models and the optimal fish harvesting decision with stochastic convenience yield models, in the presence of drift ambiguity. From the perspective of an ambiguity averse agent, we transfer the problem to the solution of a reflected backward stochastic differential equations (RBSDE) and prove the uniform Lipschitz continuity of the generator. We then propose a numerical algorithm with the theory of RBSDEs and a general stratification technique, and an alternative algorithm without using the theory of RBSDEs. We test the accuracy and convergence of the numerical schemes. By comparing to the one dimensional case, we highlight the importance of the dynamic structure of the agent’s worst case belief. Results also show that the numerical RBSDE algorithm with stratification is more efficient when the optimal generator is attainable.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84845344","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":"The Nonstationary Newsvendor: Data-Driven Nonparametric Learning","authors":"N. B. Keskin, Xu Min, Jing-Sheng Song","doi":"10.2139/ssrn.3866171","DOIUrl":"https://doi.org/10.2139/ssrn.3866171","url":null,"abstract":"We study a newsvendor problem with unknown demand distribution in a nonstationary demand environment over a multi-period time horizon. The demand in each period consists of a time-varying demand level and an additive random shock. Neither the demand level nor the random shock is separately observable. The amount of change in the demand level over the time horizon is measured by a cumulative variation metric. The problem has widespread applications, such as perishable inventory planning, staffing, and medical resource capacity planning in the wake of COVID-19. We design a nonparametric dynamic ordering policy, termed the moving window ordering policy, that tracks the shifts in the unknown demand level while accounting for the unobservable random demand shocks. To compute the order quantity in each period, this policy only needs the past demand observations, without any access to the underlying demand distribution. For a finite variation \"budget,\" we prove that our ordering policy is first-order optimal in the sense that its regret grows at the smallest possible rate. We also extend our analysis to the case of asymptotically large variation budgets. Through case studies based on real-life data, we show that our policy can save 20-80% of overage and underage costs, relative to policies widely used for perishable inventory replenishment and nurse staffing.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83276609","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":"Comparison of Local Projection Estimators for Proxy Vector Autoregressions","authors":"Martin Bruns, H. Luetkepohl","doi":"10.2139/ssrn.3855339","DOIUrl":"https://doi.org/10.2139/ssrn.3855339","url":null,"abstract":"Different local projection (LP) estimators for structural impulse responses of proxy vector autoregressions are reviewed and compared algebraically andwith respect to their small sample suitability for inference. Conditions for numerical equivalence and similarities of some estimators are provided. A new LP type estimator is also proposed which is very easy to compute. Two generalized least squares (GLS) projection estimators are found to be more accurate than the other LP estimators in small samples. In particular, a lag-augmented GLS estimator tends to be superior to its competitors and to perform as well as a standard VAR estimator for sufficiently large samples.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84859671","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":"Reading the Candlesticks: An OK Estimator for Volatility","authors":"Jia Li","doi":"10.2139/ssrn.3838231","DOIUrl":"https://doi.org/10.2139/ssrn.3838231","url":null,"abstract":"\u0000 We propose an Optimal candlesticK (OK) estimator for the spot volatility using highfrequency candlestick observations. Under a standard infill asymptotic setting, we show that the OK estimator is asymptotically unbiased and has minimal asymptotic variance within a class of linear estimators. Its estimation error can be coupled by a Brownian functional, which permits valid inference. Our theoretical and numerical results suggest that the proposed candlestick-based estimator is much more accurate than the conventional spot volatility estimator based on high-frequency returns. An empirical illustration documents the intraday volatility dynamics of various assets during the Fed Chairman's recent congressional testimony.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73880414","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":"Nonparametric Identification and Inference of First-Price Auctions with Heterogeneous Bidders","authors":"Zheng Li","doi":"10.2139/ssrn.3809922","DOIUrl":"https://doi.org/10.2139/ssrn.3809922","url":null,"abstract":"In the auction literature, it is well established that bidders' asymmetry plays an important role in determining auction revenues. In this paper, we propose a nonparametric methodology to analyze first-price auctions with two popularly adopted asymmetries: heterogeneous risk preferences and asymmetric value distributions. We find that the two competing models provide distinct implications for the bid distributions conditional on heterogeneity. By modeling bidders' asymmetry as unobserved heterogeneity, we show that the conditional bid distributions are identified nonparametrically. These results enable researchers to distinguish between the two competing models. The Monte Carlo experiments demonstrate the good performance of the proposed method. In an application using the US Forest Service timber auction data, we find that the data support the model with heterogeneity in risk preference.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78197775","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":"Testing a Class of Semi- or Nonparametric Conditional Moment Restriction Models using Series Methods","authors":"Jesper Riis-Vestergaard Sørensen","doi":"10.2139/ssrn.3667599","DOIUrl":"https://doi.org/10.2139/ssrn.3667599","url":null,"abstract":"This paper proposes a new test for a class of conditional moment restrictions (CMRs) whose parameterization involves unknown, unrestricted conditional expectation functions. Motivating examples of such CMRs arise from models of discrete choice under uncertainty including certain static games of incomplete information. The proposed test may be viewed as a semi-/nonparametric extension of the Bierens (1982, Journal of Econometrics 20, 105–134) goodness-of-fit test of a parametric model for the conditional mean. Estimating conditional expectations using series methods and employing a Gaussian multiplier bootstrap to obtain critical values, the test is shown to be asymptotically correctly sized and consistent. Simulation studies indicate good finite-sample properties. In an empirical application, the test is used to study the validity of a game-theoretical model for discount store market entry, treating equilibrium beliefs as nonparametric conditional expectations. The test indicates that Walmart and Kmart entry decisions do not result from a static discrete game of incomplete information with linearly specified profits.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77829760","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":"Identifying High-Frequency Shocks with Bayesian Mixed-Frequency VARs","authors":"Alessia Paccagnini, F. Parla","doi":"10.2139/ssrn.3855847","DOIUrl":"https://doi.org/10.2139/ssrn.3855847","url":null,"abstract":"We contribute to research on mixed-frequency regressions by introducing an innovative Bayesian approach. Based on a new “high-frequency” identification scheme, we provide novel empirical evidence of identifying uncertainty shock for the US economy. As main findings, we document a “temporal aggregation bias” when we adopt a common low frequency model instead of estimating a mixed-frequency framework. The bias is amplified when we identify a higher frequency shock.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86790541","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":"Estimating and Testing for Smooth Structural Changes in Moment Condition Models","authors":"Haiqi Li, Jin Zhou, Yongmiao Hong","doi":"10.2139/ssrn.3792747","DOIUrl":"https://doi.org/10.2139/ssrn.3792747","url":null,"abstract":"Numerous studies have been devoted to estimating and testing for moment condition models. Most of the existing studies assume that structural parameters are either fixed or changed abruptly over time. This study considers estimation of and testing for smooth structural changes in moment condition models where the data generating process is assumed to be locally stationary. A novel local generalized method of moment estimator and its boundary-corrected counterpart are proposed to estimate the smoothly changing structural parameters. Consistency and asymptotic normality are established, and an optimal weighting matrix and its consistent estimator are obtained. In particular, a consistent nonparametric test is proposed to check both smooth changes and abrupt breaks in structural parameters. The test is asymptotically pivotal and does not require prior information about the alternative. A Monte Carlo study is performed to illustrate the merits of the proposed test. In an empirical application, we document the time-varying features of the risk aversion parameter in an asset pricing model, which are consistent with business cycles and financial crisis.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76668137","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":"Properties of Subjective Beliefs Estimators","authors":"Anish Ghosh, Taisuke Otsu, Guillaume Roussellet","doi":"10.2139/ssrn.3784757","DOIUrl":"https://doi.org/10.2139/ssrn.3784757","url":null,"abstract":"Information-theoretic methods have recently been proposed for the simultaneous recovery of investors’ beliefs about future macroeconomic and financial outcomes and their risk preferences from observed asset prices. These methods estimate beliefs and preferences to minimize the statistical discrepancy between the recovered beliefs and the true data generating process (DGP), subject to asset pricing Euler equation constraints. This paper develops the asymptotic properties of these subjective beliefs estimators. We compare empirically the beliefs recovered with alternative estimators in this class, that differ on the basis of the statistical divergence functions used to characterize the discrepancy between the beliefs and the DGP.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76174825","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":"The Estimation Risk and the IRB Supervisory Formula","authors":"S. Casellina, S. Landini, M. Uberti","doi":"10.2139/ssrn.3773406","DOIUrl":"https://doi.org/10.2139/ssrn.3773406","url":null,"abstract":"In many standard derivation and presentations of risk measures like the Value-at-Risk or the Expected Shortfall, it is assumed that all the model’s parameters are known. In practice, however, the parameters must be estimated and this introduces an additional source of uncertainty that is usually not accounted for. The Prudential Regulators have formally raised the issue of errors stemming from the internal model estimation process in the context of credit risk, calling for margins of conservatism to cover possible underestimation in capital. Notwithstanding this requirement, to date, a solution shared by banks and regulators/supervisors has not yet been found. In our paper, we investigate the effect of the estimation error in the framework of the Asymptotic Single Risk Factor model that represents the baseline for the derivation of the credit risk measures under the IRB approach. We exploit Monte Carlo simulations to quantify the bias induced by the estimation error and we explore an approach to correct for this bias. Our approach involves only the estimation of the long run average probability of default and not the estimation of the asset correlation given that, in practice, banks are not allowed to modify this parameter. We study the stochastic characteristics of the probability of default estimator that can be derived from the Asymptotic Single Risk Factor framework and we show how to introduce a correction to control for the estimation error. Our approach does not require introducing in the Asymptotic Single Risk Factor model additional elements like the prior distributions or other parameters which, having to be estimated, would introduce another source of estimation error. This simple and easily implemented correction ensures that the probability of observing an exception (i.e. a default rate higher than the estimated quantile of the default rate distribution) is equal to the desired confidence level. We show a practical application of our approach relying on real data.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85454150","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}