We consider the optimal solutions to the trade execution problem in the two different classes of i) fully adapted or adaptive and ii) deterministic or static strategies, comparing them. We do this in two different benchmark models. The first model is a discrete time framework with an information flow process, dealing with both permanent and temporary impact, minimizing the expected cost of the trade. The second model is a continuous time framework where the objective function is the sum of the expected cost and a value at risk (or expected shortfall) type risk criterion. Optimal adapted solutions are known in both frameworks from the original works of Bertsimas and Lo (1998) and Gatheral and Schied (2011). In this paper we derive the optimal static strategies for both benchmark models and we study quantitatively the improvement in optimality when moving from static strategies to fully adapted ones. We conclude that, in the benchmark models we study, the difference is not relevant, except for extreme unrealistic cases for the model or impact parameters. This indirectly confirms that in the similar framework of Almgren and Chriss (2000) one is fine deriving a static optimal solution, as done by those authors, as opposed to a fully adapted one, since the static solution happens to be tractable and known in closed form.
{"title":"Static vs Adapted Optimal Execution Strategies in Two Benchmark Trading Models","authors":"D. Brigo, C. Piat","doi":"10.2139/ssrn.2840290","DOIUrl":"https://doi.org/10.2139/ssrn.2840290","url":null,"abstract":"We consider the optimal solutions to the trade execution problem in the two different classes of i) fully adapted or adaptive and ii) deterministic or static strategies, comparing them. We do this in two different benchmark models. The first model is a discrete time framework with an information flow process, dealing with both permanent and temporary impact, minimizing the expected cost of the trade. The second model is a continuous time framework where the objective function is the sum of the expected cost and a value at risk (or expected shortfall) type risk criterion. Optimal adapted solutions are known in both frameworks from the original works of Bertsimas and Lo (1998) and Gatheral and Schied (2011). In this paper we derive the optimal static strategies for both benchmark models and we study quantitatively the improvement in optimality when moving from static strategies to fully adapted ones. We conclude that, in the benchmark models we study, the difference is not relevant, except for extreme unrealistic cases for the model or impact parameters. This indirectly confirms that in the similar framework of Almgren and Chriss (2000) one is fine deriving a static optimal solution, as done by those authors, as opposed to a fully adapted one, since the static solution happens to be tractable and known in closed form.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"169 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114261695","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}
Optimal forms of reinsurance policies have been studied for a long time in actuarial literature. Most existing results are from the insurer's point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement which might be very attractive to one party (e.g., insurer) can be quite unacceptable to the other party (e.g., reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party's risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaRs of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values.
{"title":"Optimal Reinsurance Policies When the Interests of Both the Cedent and the Reinsurer are Taken into Account","authors":"Wenjun Jiang, Jiandong Ren, R. Zitikis","doi":"10.2139/ssrn.2840218","DOIUrl":"https://doi.org/10.2139/ssrn.2840218","url":null,"abstract":"Optimal forms of reinsurance policies have been studied for a long time in actuarial literature. Most existing results are from the insurer's point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement which might be very attractive to one party (e.g., insurer) can be quite unacceptable to the other party (e.g., reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party's risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaRs of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127399908","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 highly integrated markets, news spreads at a fast pace and bedevils risk monitoring and optimal asset allocation. We therefore propose global and disaggregated measures of variance transmission that allow one to assess spillovers locally in time. Key to our approach is the vector ARMA representation of the second-order dynamics of the popular BEKK model. In an empirical application to a four-dimensional system of US asset classes - equity, fixed income, foreign exchange and commodities - we illustrate the second-order transmissions at various levels of (dis)aggregation. Moreover, we demonstrate that the proposed spillover indices are informative on the value-at-risk violations of portfolios composed of the considered asset classes.
{"title":"Measuring Spot Variance Spillovers When (Co)Variances are Time-Varying - The Case of Multivariate GARCH Models","authors":"Matthias R. Fengler, H. Herwartz","doi":"10.2139/ssrn.2800209","DOIUrl":"https://doi.org/10.2139/ssrn.2800209","url":null,"abstract":"In highly integrated markets, news spreads at a fast pace and bedevils risk monitoring and optimal asset allocation. We therefore propose global and disaggregated measures of variance transmission that allow one to assess spillovers locally in time. Key to our approach is the vector ARMA representation of the second-order dynamics of the popular BEKK model. In an empirical application to a four-dimensional system of US asset classes - equity, fixed income, foreign exchange and commodities - we illustrate the second-order transmissions at various levels of (dis)aggregation. Moreover, we demonstrate that the proposed spillover indices are informative on the value-at-risk violations of portfolios composed of the considered asset classes.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130235967","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 present paper looks into the question of whether it provides the investor diversification benefits to include sukuk (Islamic bonds) in their portfolio of bonds, and what these might be quantitatively. Analysed are sovereign bonds of Bahrain, Pakistan, Qatar, Malaysia, and the UAE. The conclusion is that using sukuk to diversify a portfolio yields substantial benefits.
{"title":"Comparative Analysis of Sukuk and Conventional Bonds Based on the Value-At-Risk Model","authors":"Bakhshi Armenovich Kostandyan","doi":"10.2139/ssrn.2786096","DOIUrl":"https://doi.org/10.2139/ssrn.2786096","url":null,"abstract":"The present paper looks into the question of whether it provides the investor diversification benefits to include sukuk (Islamic bonds) in their portfolio of bonds, and what these might be quantitatively. Analysed are sovereign bonds of Bahrain, Pakistan, Qatar, Malaysia, and the UAE. The conclusion is that using sukuk to diversify a portfolio yields substantial benefits.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117094659","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}
We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence.
{"title":"Explicit Diversification Beneift for Dependent Risks","authors":"M. Dacorogna, Laila Elbahtouri, M. Kratz","doi":"10.2139/ssrn.2765403","DOIUrl":"https://doi.org/10.2139/ssrn.2765403","url":null,"abstract":"We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127777698","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}
We generalize the refinement ordering for well calibrated probability forecasters to the case were the debtors under consideration are not necessarily identical. This ordering is consistent with many well known skill scores used in practice. We also add an illustration using default predictions made by the leading rating agencies Moody’s and S&P.
{"title":"Comparing Default Predictions in the Rating Industry for Different Sets of Obligors","authors":"W. Kraemer, Simon Neumaerker","doi":"10.17877/DE290R-16552","DOIUrl":"https://doi.org/10.17877/DE290R-16552","url":null,"abstract":"We generalize the refinement ordering for well calibrated probability forecasters to the case were the debtors under consideration are not necessarily identical. This ordering is consistent with many well known skill scores used in practice. We also add an illustration using default predictions made by the leading rating agencies Moody’s and S&P.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123811046","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}
We propose a new time-varying peaks over threshold model to study tail risk dynamics in equity markets: the laws of motion for the parameters are defined through the score-based approach. We apply the model to daily returns from U.S. size-sorted decile stock portfolios and show that large firms' tail risk increases during recessions more than small firms' tail risk. Our results are consistent with the granular hypothesis of aggregate fluctuations, and we quantify the impact of large firms' tail risk shocks on the economy. A measure of tail connectedness is proposed: evidence from international equity markets shows that tail connectedness increases during periods of turmoil. This paper was accepted by Lauren Cohen, finance.
{"title":"Tail Risk Dynamics in Stock Returns: Links to the Macroeconomy and Global Markets Connectedness","authors":"D. Massacci","doi":"10.2139/ssrn.2517198","DOIUrl":"https://doi.org/10.2139/ssrn.2517198","url":null,"abstract":"We propose a new time-varying peaks over threshold model to study tail risk dynamics in equity markets: the laws of motion for the parameters are defined through the score-based approach. We apply the model to daily returns from U.S. size-sorted decile stock portfolios and show that large firms' tail risk increases during recessions more than small firms' tail risk. Our results are consistent with the granular hypothesis of aggregate fluctuations, and we quantify the impact of large firms' tail risk shocks on the economy. A measure of tail connectedness is proposed: evidence from international equity markets shows that tail connectedness increases during periods of turmoil. \u0000 \u0000This paper was accepted by Lauren Cohen, finance.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115640554","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}
Pub Date : 2016-01-11DOI: 10.3390/ECONOMETRICS4010003
Manuela Braione, N. Scholtes
Financial asset returns are known to be conditionally heteroskedastic and generally non-normally distributed, fat-tailed and often skewed. These features must be taken into account to produce accurate forecasts of Value-at-Risk (VaR). We provide a comprehensive look at the problem by considering the impact that different distributional assumptions have on the accuracy of both univariate and multivariate GARCH models in out-of-sample VaR prediction. The set of analyzed distributions comprises the normal, Student, Multivariate Exponential Power and their corresponding skewed counterparts. The accuracy of the VaR forecasts is assessed by implementing standard statistical backtesting procedures used to rank the different specifications. The results show the importance of allowing for heavy-tails and skewness in the distributional assumption with the skew-Student outperforming the others across all tests and confidence levels.
{"title":"Forecasting Value-at-Risk under Different Distributional Assumptions","authors":"Manuela Braione, N. Scholtes","doi":"10.3390/ECONOMETRICS4010003","DOIUrl":"https://doi.org/10.3390/ECONOMETRICS4010003","url":null,"abstract":"Financial asset returns are known to be conditionally heteroskedastic and generally non-normally distributed, fat-tailed and often skewed. These features must be taken into account to produce accurate forecasts of Value-at-Risk (VaR). We provide a comprehensive look at the problem by considering the impact that different distributional assumptions have on the accuracy of both univariate and multivariate GARCH models in out-of-sample VaR prediction. The set of analyzed distributions comprises the normal, Student, Multivariate Exponential Power and their corresponding skewed counterparts. The accuracy of the VaR forecasts is assessed by implementing standard statistical backtesting procedures used to rank the different specifications. The results show the importance of allowing for heavy-tails and skewness in the distributional assumption with the skew-Student outperforming the others across all tests and confidence levels.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134513831","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}
Paweł Mielcarz, Dmytro Osiichuk, Ryszard Owczarkowski
This paper aims to present an iterative algorithm that yields the amount of debt contracting/repayment or equity investment necessary to achieve the target capital structure. The model also helps to estimate the gains in shareholder value that result from financial restructuring process and lead to the optimal leverage ratio.,The paper maintains that certain benchmarks – i.e. industry average financial leverage and unlevered beta corrected for cash – make it possible to determine the parameters of the optimal capital structure for the company, so a failure to adjust to the target may result in value destruction.,The paper presents an iterative algorithm that yields the amount of debt contracting/repayment or equity investment necessary to achieve the target capital structure.,The proposed algorithm overcomes the methodological problems of existing approaches to the estimation of shareholder value gained through financial restructuring and implicitly solves the circularity problem in the calculation of the weighted average cost of capital.
{"title":"Financial Restructuring and Target Capital Structure: An Iterative Algorithm for Shareholder Value Maximization","authors":"Paweł Mielcarz, Dmytro Osiichuk, Ryszard Owczarkowski","doi":"10.2139/ssrn.2861513","DOIUrl":"https://doi.org/10.2139/ssrn.2861513","url":null,"abstract":"This paper aims to present an iterative algorithm that yields the amount of debt contracting/repayment or equity investment necessary to achieve the target capital structure. The model also helps to estimate the gains in shareholder value that result from financial restructuring process and lead to the optimal leverage ratio.,The paper maintains that certain benchmarks – i.e. industry average financial leverage and unlevered beta corrected for cash – make it possible to determine the parameters of the optimal capital structure for the company, so a failure to adjust to the target may result in value destruction.,The paper presents an iterative algorithm that yields the amount of debt contracting/repayment or equity investment necessary to achieve the target capital structure.,The proposed algorithm overcomes the methodological problems of existing approaches to the estimation of shareholder value gained through financial restructuring and implicitly solves the circularity problem in the calculation of the weighted average cost of capital.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126826214","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}
We propose two new tests for detecting clustering in multivariate Value-at-Risk (VaR) forecasts. First, we consider CUSUM-tests to detect non-constant expectations in the matrix of VaR-violations. Second, we propose χ2-tests for detecting cross-sectional and serial dependence in the VaR-forecasts. Moreover, we combine our new backtests with a test of unconditional coverage to yield two new backtests of multivariate conditional coverage. Results from a simulation study underline the usefulness of our new backtests for controlling portfolio risks across a bank’s business lines. In an empirical study, we show how our multivariate backtests can be employed by regulators to backtest a banking system.
{"title":"Evaluating Value-at-Risk Forecasts: A New Set of Multivariate Backtests","authors":"Dominik Wied, Gregor N. F. Weiß, D. Ziggel","doi":"10.2139/ssrn.2593526","DOIUrl":"https://doi.org/10.2139/ssrn.2593526","url":null,"abstract":"We propose two new tests for detecting clustering in multivariate Value-at-Risk (VaR) forecasts. First, we consider CUSUM-tests to detect non-constant expectations in the matrix of VaR-violations. Second, we propose χ2-tests for detecting cross-sectional and serial dependence in the VaR-forecasts. Moreover, we combine our new backtests with a test of unconditional coverage to yield two new backtests of multivariate conditional coverage. Results from a simulation study underline the usefulness of our new backtests for controlling portfolio risks across a bank’s business lines. In an empirical study, we show how our multivariate backtests can be employed by regulators to backtest a banking system.","PeriodicalId":203996,"journal":{"name":"ERN: Value-at-Risk (Topic)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123185983","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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