This paper considers the expected utility portfolio optimization problem with initial-time and intermediate-time Value-at-Risk (VaR) constraints on terminal wealth. We derive the closed-form solutions which are optimal among all feasible strategies at initial time, i.e., precommitted strategies. Moreover, the precommitted strategies are also optimal at the intermediate time for "bad" market states. A contingent claim on Merton's portfolio is constructed to replicate the optimal portfolio. We fi nd that risk management with intermediate-time risk constraints is prudent in hedging "bad" intermediate market states and performs signifi cantly better than the one terminal-wealth risk constraint solutions under the relative loss ratio measure.
{"title":"Precommitted Strategies with Initial-time and Intermediate-time VaR Constraints","authors":"Chufang Wu, Jiawen Gu, W. Ching","doi":"10.2139/ssrn.3943822","DOIUrl":"https://doi.org/10.2139/ssrn.3943822","url":null,"abstract":"This paper considers the expected utility portfolio optimization problem with initial-time and intermediate-time Value-at-Risk (VaR) constraints on terminal wealth. We derive the closed-form solutions which are optimal among all feasible strategies at initial time, i.e., precommitted strategies. Moreover, the precommitted strategies are also optimal at the intermediate time for \"bad\" market states. A contingent claim on Merton's portfolio is constructed to replicate the optimal portfolio. We fi nd that risk management with intermediate-time risk constraints is prudent in hedging \"bad\" intermediate market states and performs signifi cantly better than the one terminal-wealth risk constraint solutions under the relative loss ratio measure.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121815920","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}
This paper studies an optimal asset allocation problem for a surplus-driven financial institution facing a quantile-based constraint (a Value-at-Risk or an Average Value-at-Risk constraint), or a shortfall-based constraint (an expected shortfall or an expected discounted shortfall constraint). We obtain closed-form solutions to the optimal wealth for the non-concave utility maximization problem under constraints. We find that the quantile- and shortfall-based regulation can effectively reduce the probability of default for a surplus-driven financial institution. However, the liability holders' benefits typically cannot be fully protected under either type of regulation.
{"title":"Success and Failure of the Financial Regulation on a Surplus-Driven Financial Company","authors":"A. Chen, M. Stadje, Fangyuan Zhang","doi":"10.2139/ssrn.3920338","DOIUrl":"https://doi.org/10.2139/ssrn.3920338","url":null,"abstract":"This paper studies an optimal asset allocation problem for a surplus-driven financial institution facing a quantile-based constraint (a Value-at-Risk or an Average Value-at-Risk constraint), or a shortfall-based constraint (an expected shortfall or an expected discounted shortfall constraint). We obtain closed-form solutions to the optimal wealth for the non-concave utility maximization problem under constraints. We find that the quantile- and shortfall-based regulation can effectively reduce the probability of default for a surplus-driven financial institution. However, the liability holders' benefits typically cannot be fully protected under either type of regulation.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125860597","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}
Expectiles are the most popular generalized quantile, but they can be enigmatic to unfamiliar users. We organize nine interpretations for expectiles along different perspectives. An expectile is the minimizer of an asymmetric least squares criterion, making it a weighted average but also meaning that the expectile is the true mean of the distribution in two special cases. Specifically, an expectile of a distribution is a value that would be the mean if values above it were more likely to occur than they actually are. Expectiles summarize a distribution in a manner similar to quantiles, but also quantiles are expectiles in location models and expectiles are quantiles, albeit not always of the original distribution. Expectiles are also m-estimators, m-quantiles, and Lp-quantiles, families containing the majority of simple statistics commonly in use.
{"title":"Interpreting Expectiles","authors":"Collin Philipps","doi":"10.2139/ssrn.3881402","DOIUrl":"https://doi.org/10.2139/ssrn.3881402","url":null,"abstract":"Expectiles are the most popular generalized quantile, but they can be enigmatic to unfamiliar users. We organize nine interpretations for expectiles along different perspectives. An expectile is the minimizer of an asymmetric least squares criterion, making it a weighted average but also meaning that the expectile is the true mean of the distribution in two special cases. Specifically, an expectile of a distribution is a value that would be the mean if values above it were more likely to occur than they actually are. Expectiles summarize a distribution in a manner similar to quantiles, but also quantiles are expectiles in location models and expectiles are quantiles, albeit not always of the original distribution. Expectiles are also m-estimators, m-quantiles, and Lp-quantiles, families containing the majority of simple statistics commonly in use.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"20 21-22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116722988","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}
The standard metric for assessing risk in the financial realm has been the Value-at-Risk (VaR) with several parametric and non-parametric approaches and its derivatives which is Conditional Value-at-Risk (CVaR). The inability of VaR to tell loss severity beyond the confidence threshold and its incoherency gave birth to CVaR which accounted for both shortcomings and is also sub-additive. However, backtesting a 1-day CVaR model is almost impossible and VaR estimates gives better accuracy for fat tails than CVaR which makes CVaR also defective. Hence, there is need for a better measure which will capture the shortcomings of both metrics. This research will employ other risk measures beyond the conventional VaR and CVaR using the historical return of developing markets; South African Stock exchange (JTOPI-40) and the Nigerian Stock Exchange (NSE-30). In Particular, we will consider Hull-White Value-at-Risk (HWVaR) and Bubble Value-at-Risk (BVaR) and finally compare and contrast them with the two conventional metrics.
{"title":"Beyond Value at Risk for Developing Markets","authors":"Ibraheem Abiodun Yahayah, Monsur Bolaji Olowoyo, Kenrick Abbott","doi":"10.2139/ssrn.3855643","DOIUrl":"https://doi.org/10.2139/ssrn.3855643","url":null,"abstract":"The standard metric for assessing risk in the financial realm has been the Value-at-Risk (VaR) with several parametric and non-parametric approaches and its derivatives which is Conditional Value-at-Risk (CVaR). The inability of VaR to tell loss severity beyond the confidence threshold and its incoherency gave birth to CVaR which accounted for both shortcomings and is also sub-additive. However, backtesting a 1-day CVaR model is almost impossible and VaR estimates gives better accuracy for fat tails than CVaR which makes CVaR also defective. Hence, there is need for a better measure which will capture the shortcomings of both metrics. This research will employ other risk measures beyond the conventional VaR and CVaR using the historical return of developing markets; South African Stock exchange (JTOPI-40) and the Nigerian Stock Exchange (NSE-30). In Particular, we will consider Hull-White Value-at-Risk (HWVaR) and Bubble Value-at-Risk (BVaR) and finally compare and contrast them with the two conventional metrics.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131098719","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}
En los últimos días, se han encendido todas las alarmas ante el riesgo de recesión de algunas de las principales economías del mundo (Alemania, Reino Unido, Italia, Brasil y México). La desaceleración afecta a varias regiones del mundo y puede llegar generalizarse, agravando la desconfianza de los inversores y la inestabilidad de los mercados financieros provocada por la guerra comercial entre EE. UU. y China, entre otros factores de incertidumbre. Los inversores han trasladado parte de sus carteras de inversión a activos considerados refugio, como los bonos soberanos; la desconfianza de los inversores se encuentra en mínimos históricos de los últimos años. Gestionar tu cartera de inversión cuando se avecina un final de ciclo económico puede ser peliagudo. Si bien hay expertos que recomiendan reequilibrar la distribución de tus activos, comprar bonos del tesoro, enfocarte en materias primas, productos básicos o inversión inmobiliaria, lo realmente importante es aprender a gestionar el riesgo. En el actual contexto de incertidumbre y condiciones de mercado adversas, evaluar la optimización del desempeño de las carteras de inversión, así como el riesgo de liquidez, es esencial, como explico en el capítulo “Theoretical and practical foundations of liquidity-adjusted value-at-risk (LVaR): optimization algorithms for portfolio selection and management”, el cual está incluido en el libro Expert Systems in Finance. Smart Financial Applications in Big Data Environments (Routledge, Taylor & Francis Group, 2019), publicado recientemente.
在过去的几天里，世界上一些主要经济体(德国、英国、意大利、巴西和墨西哥)对衰退风险的所有警告都被点燃了。经济放缓影响到世界许多地区，并可能蔓延到更广泛的地区，加剧投资者的不信任和美国与美国之间的贸易战引发的金融市场的不稳定。哦。中国，以及其他不确定因素。投资者已将部分投资组合转向主权债券等避风港资产;投资者的不信任处于近年来的历史低点。当经济周期即将结束时，管理你的投资组合可能是棘手的。虽然有专家建议重新平衡你的资产配置，购买国债，专注于大宗商品、大宗商品或房地产投资，但真正重要的是学会管理风险。在目前的不确定性和市场条件不利的背景下,业绩评估优化投资组合,以及流动性风险,至关重要,正如第一章“理论和实践基础的liquidity-adjusted value-at-risk (LVaR):优化算法为项目组合的选择和管理,这是包括在书Expert Systems in Finance。大数据环境中的智能金融应用(Routledge, Taylor &弗朗西斯集团，2019)，最近出版。
{"title":"La importancia de medir el riesgo de liquidez con aplicaciones inteligentes","authors":"Mazin A. M. Al Janabi","doi":"10.2139/ssrn.3840336","DOIUrl":"https://doi.org/10.2139/ssrn.3840336","url":null,"abstract":"En los últimos días, se han encendido todas las alarmas ante el riesgo de recesión de algunas de las principales economías del mundo (Alemania, Reino Unido, Italia, Brasil y México). La desaceleración afecta a varias regiones del mundo y puede llegar generalizarse, agravando la desconfianza de los inversores y la inestabilidad de los mercados financieros provocada por la guerra comercial entre EE. UU. y China, entre otros factores de incertidumbre. Los inversores han trasladado parte de sus carteras de inversión a activos considerados refugio, como los bonos soberanos; la desconfianza de los inversores se encuentra en mínimos históricos de los últimos años. Gestionar tu cartera de inversión cuando se avecina un final de ciclo económico puede ser peliagudo. Si bien hay expertos que recomiendan reequilibrar la distribución de tus activos, comprar bonos del tesoro, enfocarte en materias primas, productos básicos o inversión inmobiliaria, lo realmente importante es aprender a gestionar el riesgo. En el actual contexto de incertidumbre y condiciones de mercado adversas, evaluar la optimización del desempeño de las carteras de inversión, así como el riesgo de liquidez, es esencial, como explico en el capítulo “Theoretical and practical foundations of liquidity-adjusted value-at-risk (LVaR): optimization algorithms for portfolio selection and management”, el cual está incluido en el libro Expert Systems in Finance. Smart Financial Applications in Big Data Environments (Routledge, Taylor & Francis Group, 2019), publicado recientemente.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"43 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120906539","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}
Medir y predecir el riesgo de liquidez es complejo, ya que depende de muchos factores interconectados. Por ello, he desarrollado un algoritmo de optimización para mejorar el proceso de distribución de activos en carteras de múltiples activos combinando modelos sólidos de LVaR (Liquidity Value-At-Risk) con sistemas expertos y avanzados en técnicas de modelaje. Mediante este algoritmo de modelaje se obtienen mejores resultados que con los métodos de Markowitz, siendo una herramienta de selección y gestión de carteras más sólida y con aplicaciones en el mundo real tanto para fondos de inversión, gestores de riesgo e instituciones financieras como para reguladores y legisladores de economías desarrolladas y emergentes, sobre todo tras la última crisis financiera de 2007-2009.[enter Abstract Body]
{"title":"Cómo Optimizar Tu Cartera De Inversión En Un Contexto De Desaceleración","authors":"Mazin A. M. Al Janabi","doi":"10.2139/ssrn.3838021","DOIUrl":"https://doi.org/10.2139/ssrn.3838021","url":null,"abstract":"Medir y predecir el riesgo de liquidez es complejo, ya que depende de muchos factores interconectados. Por ello, he desarrollado un algoritmo de optimización para mejorar el proceso de distribución de activos en carteras de múltiples activos combinando modelos sólidos de LVaR (Liquidity Value-At-Risk) con sistemas expertos y avanzados en técnicas de modelaje. Mediante este algoritmo de modelaje se obtienen mejores resultados que con los métodos de Markowitz, siendo una herramienta de selección y gestión de carteras más sólida y con aplicaciones en el mundo real tanto para fondos de inversión, gestores de riesgo e instituciones financieras como para reguladores y legisladores de economías desarrolladas y emergentes, sobre todo tras la última crisis financiera de 2007-2009.[enter Abstract Body]","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132975586","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}
To manage the risk of insurance companies, a reinsurance transaction is among the myriad risk management mechanisms the top ranked choice. In this paper, we study the design of optimal reinsurance contracts within a risk measure minimization framework and subject to the Vajda condition. The Vajda condition requires the reinsurer to take an increasing proportion of the loss when it increases and therefore imposes constraints on the indemnity function. The distortion-risk-measure-based objective function is very generic, and allows for various constraints, an objective to minimize the risk-adjusted value of the insurer's liability, and for heterogeneous beliefs regarding the distribution function of the underlying loss by the insurer and reinsurer. Under a mild condition, we propose a backward-forward optimization method that is based on a marginal indemnification function formulation. To show the applicability and simplicity of our strategy, we provide three concrete examples with the VaR: one with the risk-adjusted value of the insurer's liability, one with an objective function that follows from imposing Pareto-optimality, and one with heterogeneous beliefs.
{"title":"A Marginal Indemnity Function Approach to Optimal Reinsurance under the Vajda Condition","authors":"T. Boonen, Wenjun Jiang","doi":"10.2139/ssrn.3811740","DOIUrl":"https://doi.org/10.2139/ssrn.3811740","url":null,"abstract":"To manage the risk of insurance companies, a reinsurance transaction is among the myriad risk management mechanisms the top ranked choice. In this paper, we study the design of optimal reinsurance contracts within a risk measure minimization framework and subject to the Vajda condition. The Vajda condition requires the reinsurer to take an increasing proportion of the loss when it increases and therefore imposes constraints on the indemnity function. The distortion-risk-measure-based objective function is very generic, and allows for various constraints, an objective to minimize the risk-adjusted value of the insurer's liability, and for heterogeneous beliefs regarding the distribution function of the underlying loss by the insurer and reinsurer. Under a mild condition, we propose a backward-forward optimization method that is based on a marginal indemnification function formulation. To show the applicability and simplicity of our strategy, we provide three concrete examples with the VaR: one with the risk-adjusted value of the insurer's liability, one with an objective function that follows from imposing Pareto-optimality, and one with heterogeneous beliefs.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132909283","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}
In this paper, we consider the optimal investment problem with both probability distor- tion/weighting and general non-concave utility functions with possibly finite number of inflection points. Our model contains the model under cumulative prospect theory (CPT) as a special case, which has inverse S-shaped probability weighting and S-shaped utility function (i.e. one inflection point). Existing literature have shown the equivalent relationships (strong duality) between the concavified problem and the original one by either assuming the presence of probability weighting or the non-concavity of utility functions, but not both. In this paper, we combine both features and propose a step-wise relaxation method to handle general non-concave utility functions and probability distortion functions. The necessary and sufficient conditions on eliminating the duality gap for the Lagrange method based on the step-wise relaxation have been provided under this circumstance. We have applied this solution method to solve in closed-form several representative examples in mathematical behavioral finance including the CPT model, Value-at-Risk based risk management (VAR-RM) model with probability distortions, Yarri’s dual model and the goal reaching model. We obtain a closed-form optimal trading strategy for a special example of the CPT model, where a “distorted” Merton line has been shown exactly. The slope of the “distorted” Merton line is given by an inflation factor multiplied by the standard Merton ratio, and an interesting finding is that the inflation factor is solely dependent on the probability distortion rather than the non-concavity of the utility function.
{"title":"Optimal Investment Problem Under Behavioral Setting: A Lagrange Duality Perspective","authors":"X. Bi, Zhenyu Cui, Jiacheng Fan, Lv Yuan, Shuguang Zhang","doi":"10.2139/ssrn.3801926","DOIUrl":"https://doi.org/10.2139/ssrn.3801926","url":null,"abstract":"In this paper, we consider the optimal investment problem with both probability distor- tion/weighting and general non-concave utility functions with possibly finite number of inflection points. Our model contains the model under cumulative prospect theory (CPT) as a special case, which has inverse S-shaped probability weighting and S-shaped utility function (i.e. one inflection point). Existing literature have shown the equivalent relationships (strong duality) between the concavified problem and the original one by either assuming the presence of probability weighting or the non-concavity of utility functions, but not both. In this paper, we combine both features and propose a step-wise relaxation method to handle general non-concave utility functions and probability distortion functions. The necessary and sufficient conditions on eliminating the duality gap for the Lagrange method based on the step-wise relaxation have been provided under this circumstance. We have applied this solution method to solve in closed-form several representative examples in mathematical behavioral finance including the CPT model, Value-at-Risk based risk management (VAR-RM) model with probability distortions, Yarri’s dual model and the goal reaching model. We obtain a closed-form optimal trading strategy for a special example of the CPT model, where a “distorted” Merton line has been shown exactly. The slope of the “distorted” Merton line is given by an inflation factor multiplied by the standard Merton ratio, and an interesting finding is that the inflation factor is solely dependent on the probability distortion rather than the non-concavity of the utility function.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"552 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133988514","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}
Quantile regression is an efficient tool when it comes to estimate popular measures of tail risk such as the conditional quantile Value at Risk. In this paper we exploit the availability of data at mixed frequency to build a volatility model for daily returns with low-- (for macro--variables) and high--frequency (which may include an virg{--X} term related to realized volatility measures) components. The quality of the suggested quantile regression model, labeled MF--Q--ARCH--X, is assessed in a number of directions: we derive weak stationarity properties, we investigate its finite sample properties by means of a Monte Carlo exercise and we apply it on financial real data. VaR forecast performances are evaluated by backtesting and Model Confidence Set inclusion among competitors, showing that the MF--Q--ARCH--X has a consistently accurate forecasting capability.
{"title":"Using Mixed-Frequency and Realized Measures in Quantile Regression","authors":"V. Candila, G. Gallo, L. Petrella","doi":"10.2139/ssrn.3722927","DOIUrl":"https://doi.org/10.2139/ssrn.3722927","url":null,"abstract":"Quantile regression is an efficient tool when it comes to estimate popular measures of tail risk such as the conditional quantile Value at Risk. In this paper we exploit the availability of data at mixed frequency to build a volatility model for daily returns with low-- (for macro--variables) and high--frequency (which may include an virg{--X} term related to realized volatility measures) components. The quality of the suggested quantile regression model, labeled MF--Q--ARCH--X, is assessed in a number of directions: we derive weak stationarity properties, we investigate its finite sample properties by means of a Monte Carlo exercise and we apply it on financial real data. VaR forecast performances are evaluated by backtesting and Model Confidence Set inclusion among competitors, showing that the MF--Q--ARCH--X has a consistently accurate forecasting capability.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115481198","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}
The historical simulation is a standard technique in market risk estimation, in which the key choice to be made is whether to use absolute or relative shifts for the observed returns of the risk factors. To avoid this ambiguity, Fries et al. develop an approach called displaced historical simulation, which dynamically interpolates between a normal and a log-normal model. In the estimation of value-at-risk, the parameter governing this interpolation fluctuates strongly over time, which could be considered an obstacle in using this approach in practical applications. However, in this paper we show that the fluctuations do not impact the resulting shift scenarios significantly for the time series examined. Additionally, we present an alternative approach which sheds light on the origin of these fluctuations and allows us to assess the impact of some further assumptions made in the displaced historical simulation.
{"title":"Alternatives to Log-Normal and Normal Models in Market Risk: The Displaced Historical Simulation and the Mixed Model","authors":"C. Böinghoff, Martin Sprenger","doi":"10.2139/ssrn.3681809","DOIUrl":"https://doi.org/10.2139/ssrn.3681809","url":null,"abstract":"The historical simulation is a standard technique in market risk estimation, in which the key choice to be made is whether to use absolute or relative shifts for the observed returns of the risk factors. To avoid this ambiguity, Fries et al. develop an approach called displaced historical simulation, which dynamically interpolates between a normal and a log-normal model. In the estimation of value-at-risk, the parameter governing this interpolation fluctuates strongly over time, which could be considered an obstacle in using this approach in practical applications. However, in this paper we show that the fluctuations do not impact the resulting shift scenarios significantly for the time series examined. Additionally, we present an alternative approach which sheds light on the origin of these fluctuations and allows us to assess the impact of some further assumptions made in the displaced historical simulation.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127805331","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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