This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
We propose alternative structural credit risk models for determining probabilities of default (PD... more We propose alternative structural credit risk models for determining probabilities of default (PDs) based on two well-known Levy processes - the Variance Gamma (VG) process and the Normal Inverse Gaussian (NIG) process, respectively. In particular, using Levy processes, we propose a methodology to overcome the distributional drawbacks of the classical Merton model. Therefore, we discuss an empirical comparison of estimated PDs obtained from the VG and the NIG models on a dataset of 24 companies with strong capitalization in the US market. The empirical evidence suggests that both the models are able to capture the situation of instability that affects each company in considered period and, in fact, are very sensitive to the periods of the financial crisis.
The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the... more The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the performance of a selected target benchmark and it is sometimes referred to as to active portfolio management. It is well known that many professional investors achieve this benchmarking strategy: The aim of this work is to solve the benchmark tracking problem implementing active strategies to manage a portfolio with the aim to outperform the benchmark index. We develop linear formulation portfolio optimization problems which maximize some performance measures. Then, introducing first and second order stochastic dominance constraints, we evaluate their impact in the invested portfolio wealth path in a high dimensionality framework.
This paper explores and analyzes the implications and the advantages of safety first analysis in ... more This paper explores and analyzes the implications and the advantages of safety first analysis in portfolio choice problems. In particular, we consider a safety first model in order to describe the market bounds and the market trend when limited short sales are allowed and the returns are elliptical distributed.
This paper examines the impact of the joints tails of the portfolio return and its empirical vola... more This paper examines the impact of the joints tails of the portfolio return and its empirical volatility on the optimal portfolio choices. We assume that the portfolio return and its volatility dynamic is approximated by a bivariate Markov chain constructed on its historical distribution. This allows the introduction of a non parametric stochastic volatility portfolio model without the explicit use of a GARCH type or other parametric stochastic volatility models. We describe the bi-dimensional tree structure of the Markov chain and discuss alternative portfolio strategies based on the maximization of the Sharpe ratio and of a modified Sharpe ratio that takes into account the behaviour of a market benchmark. Finally, we empirically evaluate the impact of the portfolio and its stochastic volatility joint tails on optimal portfolio choices. In particular, we examine and compare the out of sample wealth obtained optimizing the portfolio performances conditioned on the joint tails of the proposed stochastic volatility model.
The consequences of any extreme event can deteriorate any system at all levels: socially, economi... more The consequences of any extreme event can deteriorate any system at all levels: socially, economically, and operationally. The COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), provides a good example of the tremendous impact that can be produced by such extreme events. To effectively measure and mitigate the impact of the COVID-19 pandemic and relaunch the Moroccan economy, policymakers need to determine which sectors have been most impacted. Due to the high level of uncertainty and complexity surrounding this health crisis, this study first develops a new technique for dealing with decision problems under uncertainty using exclusive-or (XOR) logic, called the XOR-analytic network process (XOR-ANP). Then, the proposed technique is adopted to assess the impact of COVID-19 on seven relevant sectors (tourism, transport, industrial, financial, agriculture, education, and healthcare) by considering social, operational, and economic dimensions. The key findings show that COVID-19 has a significant impact on Moroccan’s tourism, healthcare, and transport sectors, with respect to social-economic and operational dimensions by 30.99%, 21.81%, and 17.88%, respectively. These results indicate that most of the United Nations Sustainable Development Goals for 2030, such as “Healthy Lives”, “Decent Work” and “Economic Growth” have been severely impacted, thus, assistance and recovery are urgently needed.
The aim of this study is verify whether the Average Value at Risk (AVaR) can be a good alternativ... more The aim of this study is verify whether the Average Value at Risk (AVaR) can be a good alternative to Value at Risk (VaR), for estimating great portfolio losses, especially regarding tail events. To do so we use copula framework to estimate dependence between stock returns of a portfolio composed by 94 stock of the S&P100 in order to compute AVaR and VaR and compare the results with respect to a Gaussian Exponentially Weighted Moving Average (EWMA). For computing simulated returns, we use the algorithm presented in [Biglova et all, 2014] and then the model is back-tested with Kupiec's and Christoffersen's tests. The results are coherent with the literature and in particular VaR computed both via copula and EWMA seems to fail to provide an accurate risk measurement while AVaR under copula and EWMA looks more reliable.
In this paper, we deal with portfolio selection decisions when the portfolio returns are approxim... more In this paper, we deal with portfolio selection decisions when the portfolio returns are approximated by stable Paretian distributions. Therefore, we examine some dominance rules to determine the optimal choices of non-satiable risk averse investors. In particular, we first preselect a subclass of assets which are not dominated by the point of view of non-satiable and risk-averse investors. Then, we optimize a multi-parametric portfolio optimization problem that takes into account the asymptotic stochastic dominance rule. Finally, we compare the ex-post wealth obtained by optimal portfolios with different levels of asymptotic skewness and stability index.
This paper discusses two different methods to estimate the conditional expectation. The kernel no... more This paper discusses two different methods to estimate the conditional expectation. The kernel nonparametric regression method allows to estimate the regression function, which is a realization of the conditional expectation . A recent alternative approach consists in estimating the conditional expectation (intended as a random variable), based on an appropriate approximation of the σ-algebra generated by X. In this paper, we propose a new procedure to estimate the distribution of the conditional expectation based on the kernel method, so that it is possible to compare the two approaches by verifying which one better estimates the true distribution of . In particular, if we assume that the two-dimensional variable is normally distributed, then the true distribution of can be computed quite easily, and the comparison can be performed in terms of goodness-offit tests. Keywords—Conditional Expectation, Kernel, Non Parametric, Regression.
In this paper we propose a new procedure for testing independence of random variables, which is b... more In this paper we propose a new procedure for testing independence of random variables, which is based on the conditional expectation. As it is well known, the behaviour of the conditional expectation may determine a necessary condition for stochastic independence, that is, the so called mean independence. We provide a necessary and sufficient condition for independence in terms of conditional expectation and propose an alternative method to test independence based on this result. Consequently, we provide general class of tests. Observe that generally some non-parametric methods are needed to approximate the conditional expectation, since its exact expression (given the joint distribution) is usually unknown, except for few trivial cases (e.g. Gaussian): we generalize this well known result to the family of elliptical distributions. In order to obtain a sufficiently accurate approximation of the conditional expectation, we propose to use the kernel method or, alternatively, the recen...
In this paper, we present different approaches to evaluate the presence of the arbitrage opportun... more In this paper, we present different approaches to evaluate the presence of the arbitrage opportunities in the market. In particular, we investigate empirically the well-known put-call parity no-arbitrage relation and the state price density. First, we measure the violation of the put call parity as the difference in implied volatilities between call and put options. Then, we examine the nonnegativity of the state price density. We evaluate the effectiveness of the proposed approaches by an empirical analysis on S&P 500 index options data. Moreover, we propose alternative approaches to estimate the state price density under the classical hypothesis of the Black and Scholes model. To this end, we use the classical nonparametric estimator based on kernel and a recent alternative the so called OLP estimator that uses a different approach to evaluate the conditional expectation consistently.
The aim of this study is to verify whether the average value at risk (AVaR) can be a good alterna... more The aim of this study is to verify whether the average value at risk (AVaR) can be a good alternative to the value at risk (VaR) for estimating portfolio losses, especially regarding tail events. To achieve this aim, we use a copula framework to estimate the dependence between the stock returns of a portfolio composed of 94 components of the S&P100 index to compute the AVaR and VaR and compare the results with respect to the Gaussian exponentially weighted moving average (EWMA). To compute the simulated returns, we employ the algorithm used by Biglova et al. (2014) in portfolio selection problems and then back test the model with Kupiec’s and Christoffersen’s tests. The results are coherent with the literature, in particular, the VaR computed both via the copula and via the EWMA seems to fail to provide an accurate risk measurement while the AVaR with the copula and EWMA appears to be more reliable.
The paper proposes a multivariate comparison among different financial markets, using risk/variab... more The paper proposes a multivariate comparison among different financial markets, using risk/variability measures consistent with investors’ preferences. First of all, we recall a recent classification of multivariate stochastic orderings and properly define the selection problem among different financial markets. Then, we propose an empirical financial application, using multivariate stochastic orderings consistent with the non-satiable and risk averse investors’ preferences. For the empirical analysis we examine two different approaches; first, we assume that the return are normally distributed; second, we deal with the more generalassumption that the returns’ distribution follow a stable sub-Gaussian law.
This paper proposes an alternative method to evaluate the independence between random variables. ... more This paper proposes an alternative method to evaluate the independence between random variables. The new method is particularly useful when the tested random variables are continuous, because the most used tests for independence are not able to give precise evaluations. In particular, we analyze and compare two different methods to test the independence among financial variables. The first is the classical chi-squared test generally used to evaluatethe independence of historical observations in the portfolio risk valuation. The new alternative method is based on a conditional expectation estimator. Thus, we can compare the results of the two methods by evaluating the performance in terms of goodness-of-fittests.
In this paper, we discuss how to approximate the conditional expectation of a random variable Y g... more In this paper, we discuss how to approximate the conditional expectation of a random variable Y given a random variable X, i.e. E (Y|X). We propose and compare two different non parametric methodologies to approximate E (Y|X). The first approach (namely the OLP method) is based on a suitable approximation of the sigma-algebra generated by X. A second procedure is based on the well known kernel non-parametric regression method. We analyze the convergence properties of the OLP estimator and we compare the two approaches with a simulation study.
In this paper, we discuss and examine the portfolio optimization problems in the Italian fixed in... more In this paper, we discuss and examine the portfolio optimization problems in the Italian fixed income market considering two main sources of risk: prices risk and market risk. To achieve this aim, we propose a two-step optimization problem for two types of bonds. In particular, we manage the price risk implementing the classical immunization method and then, using the ex-post results from the optimal immunization problem, we are able to deal with market risk maximizing the portfolio wealth in a reward-risk framework. Adopting this approach, the paper then explores empirical applications on the Italian fixed income market using data for the period 2005-2015. Empirical results shows that the two-step optimization build efficient portfolios that minimize the price risk and the market risk. This ex-post analysis indicates the usefulness of the proposed methodology, maximizing the investor’s wealth and understanding the dynamics of the bonds.
In this paper, we examine the performance of the BRICS bond markets, trying to evaluate whether t... more In this paper, we examine the performance of the BRICS bond markets, trying to evaluate whether these markets can represent a profitable investment for non-satiable and risk averse investors. First, we analyze the main statistical characteristics of the returns in each of this markets. Then, we propose an empirical comparison of profitability of investment strategies among the BRICS markets. Specifically, we compare the ex-post sample paths of the wealth, obtained investing in the bond BRICS markets, following the classical theory according to Fisher and Weil immunization theory. Moreover, we also evaluate the portfolio investments based on Inflation-Linked Bonds of these emerging markets.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
We propose alternative structural credit risk models for determining probabilities of default (PD... more We propose alternative structural credit risk models for determining probabilities of default (PDs) based on two well-known Levy processes - the Variance Gamma (VG) process and the Normal Inverse Gaussian (NIG) process, respectively. In particular, using Levy processes, we propose a methodology to overcome the distributional drawbacks of the classical Merton model. Therefore, we discuss an empirical comparison of estimated PDs obtained from the VG and the NIG models on a dataset of 24 companies with strong capitalization in the US market. The empirical evidence suggests that both the models are able to capture the situation of instability that affects each company in considered period and, in fact, are very sensitive to the periods of the financial crisis.
The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the... more The active benchmark tracking portfolio problem is a investment strategy which aims to exceed the performance of a selected target benchmark and it is sometimes referred to as to active portfolio management. It is well known that many professional investors achieve this benchmarking strategy: The aim of this work is to solve the benchmark tracking problem implementing active strategies to manage a portfolio with the aim to outperform the benchmark index. We develop linear formulation portfolio optimization problems which maximize some performance measures. Then, introducing first and second order stochastic dominance constraints, we evaluate their impact in the invested portfolio wealth path in a high dimensionality framework.
This paper explores and analyzes the implications and the advantages of safety first analysis in ... more This paper explores and analyzes the implications and the advantages of safety first analysis in portfolio choice problems. In particular, we consider a safety first model in order to describe the market bounds and the market trend when limited short sales are allowed and the returns are elliptical distributed.
This paper examines the impact of the joints tails of the portfolio return and its empirical vola... more This paper examines the impact of the joints tails of the portfolio return and its empirical volatility on the optimal portfolio choices. We assume that the portfolio return and its volatility dynamic is approximated by a bivariate Markov chain constructed on its historical distribution. This allows the introduction of a non parametric stochastic volatility portfolio model without the explicit use of a GARCH type or other parametric stochastic volatility models. We describe the bi-dimensional tree structure of the Markov chain and discuss alternative portfolio strategies based on the maximization of the Sharpe ratio and of a modified Sharpe ratio that takes into account the behaviour of a market benchmark. Finally, we empirically evaluate the impact of the portfolio and its stochastic volatility joint tails on optimal portfolio choices. In particular, we examine and compare the out of sample wealth obtained optimizing the portfolio performances conditioned on the joint tails of the proposed stochastic volatility model.
The consequences of any extreme event can deteriorate any system at all levels: socially, economi... more The consequences of any extreme event can deteriorate any system at all levels: socially, economically, and operationally. The COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), provides a good example of the tremendous impact that can be produced by such extreme events. To effectively measure and mitigate the impact of the COVID-19 pandemic and relaunch the Moroccan economy, policymakers need to determine which sectors have been most impacted. Due to the high level of uncertainty and complexity surrounding this health crisis, this study first develops a new technique for dealing with decision problems under uncertainty using exclusive-or (XOR) logic, called the XOR-analytic network process (XOR-ANP). Then, the proposed technique is adopted to assess the impact of COVID-19 on seven relevant sectors (tourism, transport, industrial, financial, agriculture, education, and healthcare) by considering social, operational, and economic dimensions. The key findings show that COVID-19 has a significant impact on Moroccan’s tourism, healthcare, and transport sectors, with respect to social-economic and operational dimensions by 30.99%, 21.81%, and 17.88%, respectively. These results indicate that most of the United Nations Sustainable Development Goals for 2030, such as “Healthy Lives”, “Decent Work” and “Economic Growth” have been severely impacted, thus, assistance and recovery are urgently needed.
The aim of this study is verify whether the Average Value at Risk (AVaR) can be a good alternativ... more The aim of this study is verify whether the Average Value at Risk (AVaR) can be a good alternative to Value at Risk (VaR), for estimating great portfolio losses, especially regarding tail events. To do so we use copula framework to estimate dependence between stock returns of a portfolio composed by 94 stock of the S&P100 in order to compute AVaR and VaR and compare the results with respect to a Gaussian Exponentially Weighted Moving Average (EWMA). For computing simulated returns, we use the algorithm presented in [Biglova et all, 2014] and then the model is back-tested with Kupiec's and Christoffersen's tests. The results are coherent with the literature and in particular VaR computed both via copula and EWMA seems to fail to provide an accurate risk measurement while AVaR under copula and EWMA looks more reliable.
In this paper, we deal with portfolio selection decisions when the portfolio returns are approxim... more In this paper, we deal with portfolio selection decisions when the portfolio returns are approximated by stable Paretian distributions. Therefore, we examine some dominance rules to determine the optimal choices of non-satiable risk averse investors. In particular, we first preselect a subclass of assets which are not dominated by the point of view of non-satiable and risk-averse investors. Then, we optimize a multi-parametric portfolio optimization problem that takes into account the asymptotic stochastic dominance rule. Finally, we compare the ex-post wealth obtained by optimal portfolios with different levels of asymptotic skewness and stability index.
This paper discusses two different methods to estimate the conditional expectation. The kernel no... more This paper discusses two different methods to estimate the conditional expectation. The kernel nonparametric regression method allows to estimate the regression function, which is a realization of the conditional expectation . A recent alternative approach consists in estimating the conditional expectation (intended as a random variable), based on an appropriate approximation of the σ-algebra generated by X. In this paper, we propose a new procedure to estimate the distribution of the conditional expectation based on the kernel method, so that it is possible to compare the two approaches by verifying which one better estimates the true distribution of . In particular, if we assume that the two-dimensional variable is normally distributed, then the true distribution of can be computed quite easily, and the comparison can be performed in terms of goodness-offit tests. Keywords—Conditional Expectation, Kernel, Non Parametric, Regression.
In this paper we propose a new procedure for testing independence of random variables, which is b... more In this paper we propose a new procedure for testing independence of random variables, which is based on the conditional expectation. As it is well known, the behaviour of the conditional expectation may determine a necessary condition for stochastic independence, that is, the so called mean independence. We provide a necessary and sufficient condition for independence in terms of conditional expectation and propose an alternative method to test independence based on this result. Consequently, we provide general class of tests. Observe that generally some non-parametric methods are needed to approximate the conditional expectation, since its exact expression (given the joint distribution) is usually unknown, except for few trivial cases (e.g. Gaussian): we generalize this well known result to the family of elliptical distributions. In order to obtain a sufficiently accurate approximation of the conditional expectation, we propose to use the kernel method or, alternatively, the recen...
In this paper, we present different approaches to evaluate the presence of the arbitrage opportun... more In this paper, we present different approaches to evaluate the presence of the arbitrage opportunities in the market. In particular, we investigate empirically the well-known put-call parity no-arbitrage relation and the state price density. First, we measure the violation of the put call parity as the difference in implied volatilities between call and put options. Then, we examine the nonnegativity of the state price density. We evaluate the effectiveness of the proposed approaches by an empirical analysis on S&P 500 index options data. Moreover, we propose alternative approaches to estimate the state price density under the classical hypothesis of the Black and Scholes model. To this end, we use the classical nonparametric estimator based on kernel and a recent alternative the so called OLP estimator that uses a different approach to evaluate the conditional expectation consistently.
The aim of this study is to verify whether the average value at risk (AVaR) can be a good alterna... more The aim of this study is to verify whether the average value at risk (AVaR) can be a good alternative to the value at risk (VaR) for estimating portfolio losses, especially regarding tail events. To achieve this aim, we use a copula framework to estimate the dependence between the stock returns of a portfolio composed of 94 components of the S&P100 index to compute the AVaR and VaR and compare the results with respect to the Gaussian exponentially weighted moving average (EWMA). To compute the simulated returns, we employ the algorithm used by Biglova et al. (2014) in portfolio selection problems and then back test the model with Kupiec’s and Christoffersen’s tests. The results are coherent with the literature, in particular, the VaR computed both via the copula and via the EWMA seems to fail to provide an accurate risk measurement while the AVaR with the copula and EWMA appears to be more reliable.
The paper proposes a multivariate comparison among different financial markets, using risk/variab... more The paper proposes a multivariate comparison among different financial markets, using risk/variability measures consistent with investors’ preferences. First of all, we recall a recent classification of multivariate stochastic orderings and properly define the selection problem among different financial markets. Then, we propose an empirical financial application, using multivariate stochastic orderings consistent with the non-satiable and risk averse investors’ preferences. For the empirical analysis we examine two different approaches; first, we assume that the return are normally distributed; second, we deal with the more generalassumption that the returns’ distribution follow a stable sub-Gaussian law.
This paper proposes an alternative method to evaluate the independence between random variables. ... more This paper proposes an alternative method to evaluate the independence between random variables. The new method is particularly useful when the tested random variables are continuous, because the most used tests for independence are not able to give precise evaluations. In particular, we analyze and compare two different methods to test the independence among financial variables. The first is the classical chi-squared test generally used to evaluatethe independence of historical observations in the portfolio risk valuation. The new alternative method is based on a conditional expectation estimator. Thus, we can compare the results of the two methods by evaluating the performance in terms of goodness-of-fittests.
In this paper, we discuss how to approximate the conditional expectation of a random variable Y g... more In this paper, we discuss how to approximate the conditional expectation of a random variable Y given a random variable X, i.e. E (Y|X). We propose and compare two different non parametric methodologies to approximate E (Y|X). The first approach (namely the OLP method) is based on a suitable approximation of the sigma-algebra generated by X. A second procedure is based on the well known kernel non-parametric regression method. We analyze the convergence properties of the OLP estimator and we compare the two approaches with a simulation study.
In this paper, we discuss and examine the portfolio optimization problems in the Italian fixed in... more In this paper, we discuss and examine the portfolio optimization problems in the Italian fixed income market considering two main sources of risk: prices risk and market risk. To achieve this aim, we propose a two-step optimization problem for two types of bonds. In particular, we manage the price risk implementing the classical immunization method and then, using the ex-post results from the optimal immunization problem, we are able to deal with market risk maximizing the portfolio wealth in a reward-risk framework. Adopting this approach, the paper then explores empirical applications on the Italian fixed income market using data for the period 2005-2015. Empirical results shows that the two-step optimization build efficient portfolios that minimize the price risk and the market risk. This ex-post analysis indicates the usefulness of the proposed methodology, maximizing the investor’s wealth and understanding the dynamics of the bonds.
In this paper, we examine the performance of the BRICS bond markets, trying to evaluate whether t... more In this paper, we examine the performance of the BRICS bond markets, trying to evaluate whether these markets can represent a profitable investment for non-satiable and risk averse investors. First, we analyze the main statistical characteristics of the returns in each of this markets. Then, we propose an empirical comparison of profitability of investment strategies among the BRICS markets. Specifically, we compare the ex-post sample paths of the wealth, obtained investing in the bond BRICS markets, following the classical theory according to Fisher and Weil immunization theory. Moreover, we also evaluate the portfolio investments based on Inflation-Linked Bonds of these emerging markets.
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