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on Risk Management |
| By: | Francesco Cesarone; Rosella Giacometti; Manuel Luis Martino; Fabio Tardella |
| Abstract: | In this paper, we propose a general bi-objective model for portfolio selection, aiming to maximize both a diversification measure and the portfolio expected return. Within this general framework, we focus on maximizing a diversification measure recently proposed by Choueifaty and Coignard for the case of volatility as a risk measure. We first show that the maximum diversification approach is actually equivalent to the Risk Parity approach using volatility under the assumption of equicorrelated assets. Then, we extend the maximum diversification approach formulated for general risk measures. Finally, we provide explicit formulations of our bi-objective model for different risk measures, such as volatility, Mean Absolute Deviation, Conditional Value-at-Risk, and Expectiles, and we present extensive out-of-sample performance results for the portfolios obtained with our model. The empirical analysis, based on five real-world data sets, shows that the return-diversification approach provides portfolios that tend to outperform the strategies based only on a diversification method or on the classical risk-return approach. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.09707&r=rmg |
| By: | Roberto Daluiso; Marco Pinciroli; Michele Trapletti; Edoardo Vittori |
| Abstract: | This work studies the dynamic risk management of the risk-neutral value of the potential credit losses on a portfolio of derivatives. Sensitivities-based hedging of such liability is sub-optimal because of bid-ask costs, pricing models which cannot be completely realistic, and a discontinuity at default time. We leverage recent advances on risk-averse Reinforcement Learning developed specifically for option hedging with an ad hoc practice-aligned objective function aware of pathwise volatility, generalizing them to stochastic horizons. We formalize accurately the evolution of the hedger's portfolio stressing such aspects. We showcase the efficacy of our approach by a numerical study for a portfolio composed of a single FX forward contract. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.14044&r=rmg |
| By: | Adil Rengim Cetingoz; Olivier Gu\'eant |
| Abstract: | Portfolio optimization methods have evolved significantly since Markowitz introduced the mean-variance framework in 1952. While the theoretical appeal of this approach is undeniable, its practical implementation poses important challenges, primarily revolving around the intricate task of estimating expected returns. As a result, practitioners and scholars have explored alternative methods that prioritize risk management and diversification. One such approach is Risk Budgeting, where portfolio risk is allocated among assets according to predefined risk budgets. The effectiveness of Risk Budgeting in achieving true diversification can, however, be questioned, given that asset returns are often influenced by a small number of risk factors. From this perspective, one question arises: is it possible to allocate risk at the factor level using the Risk Budgeting approach? This paper introduces a comprehensive framework to address this question by introducing risk measures directly associated with risk factor exposures and demonstrating the desirable mathematical properties of these risk measures, making them suitable for optimization. We also propose a framework to find the portfolio that effectively balances the risk contributions from both assets and factors. Leveraging standard stochastic algorithms, our framework enables the use of a wide range of risk measures. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.11132&r=rmg |
| By: | Gregor Svindland; Alexander Vo{\ss} |
| Abstract: | We introduce a novel class of risk measures for the management of systemic risk in networks. In contrast to most existing approaches, our measures target the topological structure of the network in order to control the risk of a pandemic spread of some contagious peril throughout the network. While the main discussion of the paper is tailored to the management of systemic cyber risk in digital networks, we also draw parallels to similar risk management frameworks for other types of complex systems. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.13884&r=rmg |
| By: | Herbertsson, Alexander (Department of Economics, School of Business, Economics and Law, Göteborg University) |
| Abstract: | We study saddlepoint approximations to the tail-distribution for credit portfolio losses in continuous time intensity based models under conditional independent homogeneous settings. In such models, conditional on the filtration generated by the individual default intensity up to time t, the conditional number of defaults distribution (in the portfolio) will be a binomial distribution that is a function of a factor Z_t which typically is the integrated default intensity up to time t. This will lead to an explicit closed-form solution of the saddlepoint equation for each point used in the number of defaults distribution when conditioning on the factor Z_t, and we hence do not have to solve the saddlepoint equation numerically. The ordo-complexity of our algorithm computing the whole distribution for the number of defaults will be linear in the portfolio size, which is a dramatic improvement compared to e.g. recursive methods which have a quadratic ordo-complexity in the portfolio size. The individual default intensities can be arbitrary as long as they are conditionally independent given the factor Z_t in a homogeneous portfolio. We also outline how our method for computing the number of defaults distribution can be extend to heterogeneous portfolios. Furthermore, we show that all our results can be extended to hold for any factor copula model. We give several numerical applications and in particular, in a setting where the individual default intensities follow a CIR process we study both the tail distribution and the number of defaults distribution. We then repeat similar numerical studies in a one-factor Gaussian copula model. We also numerically benchmark our saddlepoint method to other computational methods. Finally, we apply of our saddlepoint method to efficiently investigate Value-at-Risk for equity portfolios where the individual stock prices have simultaneous downward jumps at the defaults of an exogenous group of defaultable entities driven by a one-factor Gaussian copula model were we focus on Value-at-Risk as function of the default correlation parameter in the one-factor Gaussian copula model. |
| Keywords: | credit portfolio risk; intensity-based models; factor models; credit copula models; Value-at-Risk; conditional independent dependence modelling; saddlepoint-methods; Fourier-transform methods; numerical methods; equity portfolio risk; stock price modelling with jumps |
| JEL: | C02 C63 G13 G32 G33 |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:gunwpe:0839&r=rmg |
| By: | Marcin Pitera; Thorsten Schmidt; {\L}ukasz Stettner |
| Abstract: | The assessment of risk based on historical data faces many challenges, in particular due to the limited amount of available data, lack of stationarity, and heavy tails. While estimation on a short-term horizon for less extreme percentiles tends to be reasonably accurate, extending it to longer time horizons or extreme percentiles poses significant difficulties. The application of theoretical risk scaling laws to address this issue has been extensively explored in the literature. This paper presents a novel approach to scaling a given risk estimator, ensuring that the estimated capital reserve is robust and conservatively estimates the risk. We develop a simple statistical framework that allows efficient risk scaling and has a direct link to backtesting performance. Our method allows time scaling beyond the conventional square-root-of-time rule, enables risk transfers, such as those involved in economic capital allocation, and could be used for unbiased risk estimation in small sample settings. To demonstrate the effectiveness of our approach, we provide various examples related to the estimation of value-at-risk and expected shortfall together with a short empirical study analysing the impact of our method. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.05655&r=rmg |
| By: | Michael Kupper; Max Nendel; Alessandro Sgarabottolo |
| Abstract: | In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we discuss computational aspects related to the nonlinear transform as well as approximations of the risk measures using, for example, neural networks. Our setup comprises a variety of examples, such as classical optimal transport penalties, parametric families of models, uncertainty on path spaces, moment constrains, and martingale constraints. In a last step, we show how to use the theoretical results for the numerical computation of worst-case losses in an insurance context and no-arbitrage prices of European contingent claims after quoted maturities in a model-free setting. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.05973&r=rmg |
| By: | Martin Eling (University of St. Gallen); Anastasia V. Kartasheva (University of St. Gallen); Dingchen Ning (University of St. Gallen) |
| Abstract: | Cyber risk economic losses are large and growing, yet the insurance market for cyber risk is tiny, amounting to 0.4% ($2.8 billion) of premiums in the US property casualty insurance market in 2020. In this paper, we analyze the constraints that the insurance industry faces in providing larger capacity. We argue that cyber risk is special in that it combines (i) heavy-tailedness, (ii) uncertain loss distribution, and (iii) asymmetric information in underwriting. The combination of factors (i)-(iii) creates a tension between a need to raise substantial amounts of capital to finance heavy-tailed and uncertain risks and an expensive compensation demanded by investors due to information frictions. To circumvent asymmetric information costs, insurers can use internal capital. Hence, suppliers of cyber insurance are large insurance groups with a deep internal capital market. However, their capacity is constrained by the group’s size. We document stylized facts about the US cyber risk insurance market. We then establish the causal inference that insurers primarily rely on the internal capital market to supply cyber risk insurance using an exogenous shock of the non-US affiliated reinsurance tax treatment in 2017. Finally, we test which of the three features (i)–(iii) of cyber risk contribute to the cost of external capital and confirm that all of them play a significant role. |
| Keywords: | cyber risk insurance, large risks financing, internal capital market, reinsurance, information frictions |
| JEL: | G22 G32 L11 |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp23118&r=rmg |
| By: | Silvia Faroni; Olivier Le Courtois (EM - emlyon business school); Krzysztof Ostaszewski |
| Abstract: | While a lot of research concentrates on the respective merits of VaR and TCE, which are the two most classic risk indicators used by financial institutions, little has been written on the equivalence between such indicators. Further, TCE, despite its merits, may not be the most accurate indicator to take into account the nature of probability distribution tails. In this paper, we introduce a new risk indicator that extends TCE to take into account higher-order risks. We compare the quantiles of this indicator to the quantiles of VaR in a simple Pareto framework, and then in a generalized Pareto framework. We also examine equivalence results between the quantiles of high-order TCEs. |
| Keywords: | VaR, TCE, extended TCE, Insurance regulation, Risk measurement |
| Date: | 2022–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04325627&r=rmg |
| By: | Spatareanu, Mariana; Manole, Vlad; Kabiri, Ali; Roland, Isabelle |
| Abstract: | How does banks' default risk affect the probability of default of non-financial businesses? The literature has focused on the banks' direct corporate customers. It fails to consider the role of supply chain relationships as a powerful channel for default risk contagion. Our paper fills this gap by analyzing the direct as well as the indirect impact of banks' default risk on firms' default risk in the U.K. Relying on Input-Output tables, we devise methods that enable us to examine this question in the absence of data on firm-to-firm linkages. To capture all potential propagation channels, we account for horizontal and vertical linkages, both between the firm and upstream industries (suppliers) and between the firm and downstream industries (customers). We further examine how trade credit and contract specificity amplify or dampen the propagation of default risk. Our results show that increases in banks’ default risk from the banking crisis of 2007–2008 propagated strongly to U.K. non-financial firms via supply chains. |
| Keywords: | default risk; propagation of banking crises; supply chains |
| JEL: | G21 G34 O30 O16 |
| Date: | 2023–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:117351&r=rmg |
| By: | Radhika Prosad Datta |
| Abstract: | This paper explores the application of Sample Entropy (SampEn) as a sophisticated tool for quantifying and predicting volatility in international oil price returns. SampEn, known for its ability to capture underlying patterns and predict periods of heightened volatility, is compared with traditional measures like standard deviation. The study utilizes a comprehensive dataset spanning 27 years (1986-2023) and employs both time series regression and machine learning methods. Results indicate SampEn's efficacy in predicting traditional volatility measures, with machine learning algorithms outperforming standard regression techniques during financial crises. The findings underscore SampEn's potential as a valuable tool for risk assessment and decision-making in the realm of oil price investments. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.12788&r=rmg |
| By: | Eric André (EM - emlyon business school); Antoine Bommier; François Le Grand (EM - emlyon business school) |
| Abstract: | We analyze the impact of risk aversion and ambiguity aversion on the competing demands for annuities and bequeathable savings using a lifecycle recursive utility model. Our main finding is that risk aversion and ambiguity aversion have similar effects: an increase in either of the two reduces annuity demand and enhances bond holdings. We obtain this unequivocal result in the flexible intertemporal framework of Hayashi and Miao (2011) by assuming that the agent's preferences are monotone with respect to first-order stochastic dominance. Our contribution is then twofold. First, from a decision-theoretic point of view, we show that monotonicity allows one to obtain clear-cut results about the respective roles of risk and ambiguity aversion. Second, from the insurance point of view, our result that the demand for annuities decreases with risk and ambiguity aversion stands in contrast with what is usually found with other insurance products. As such, it may help explain the low annuitization level observed in the data. |
| Keywords: | Recursive utility, Lifecycle model, Ambiguity aversion, Risk aversion, Saving choices, Annuity puzzle |
| Date: | 2022–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04325572&r=rmg |
| By: | Saad Mouti |
| Abstract: | In Gatheral et al. 2018, first posted in 2014, volatility is characterized by fractional behavior with a Hurst exponent $H |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.01426&r=rmg |
| By: | Ulrich Horst; Wei Xu; Rouyi Zhang |
| Abstract: | We establish the weak convergence of the intensity of a nearly-unstable Hawkes process with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market model where orders to buy or sell an asset arrive according to a Hawkes process with power-law kernel. After suitable rescaling the price-volatility process converges weakly to a rough Heston model. Our convergence result is much stronger than previously established ones that have either focused on light-tailed kernels or the convergence of integrated volatility process. The key is to establish the tightness of the family of rescaled volatility processes. This is achieved by introducing a new methods to establish the $C$-tightness of c\`adl\`ag processes based on the classical Kolmogorov-Chentsov tightness criterion for continuous processes. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.08784&r=rmg |
| By: | Francesco Cesarone; Massimiliano Corradini; Lorenzo Lampariello; Jessica Riccioni |
| Abstract: | We focus on a behavioral model, that has been recently proposed in the literature, whose rational can be traced back to the Half-Full/Half-Empty glass metaphor. More precisely, we generalize the Half-Full/Half-Empty approach to the context of positive and negative lotteries and give financial and behavioral interpretations of the Half-Full/Half-Empty parameters. We develop a portfolio selection model based on the Half-Full/Half-Empty strategy, resulting in a nonconvex optimization problem, which, nonetheless, is proven to be equivalent to an alternative Mixed-Integer Linear Programming formulation. By means of the ensuing empirical analysis, based on three real-world datasets, the Half-Full/Half-Empty model is shown to be very versatile by appropriately varying its parameters, and to provide portfolios displaying promising performances in terms of risk and profitability, compared with Prospect Theory, risk minimization approaches and Equally-Weighted portfolios. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.10749&r=rmg |
| By: | Igor Ferreira Batista Martins; Hedibert Freitas Lopes |
| Abstract: | This paper expands traditional stochastic volatility models by allowing for time-varying skewness without imposing it. While dynamic asymmetry may capture the likely direction of future asset returns, it comes at the risk of leading to overparameterization. Our proposed approach mitigates this concern by leveraging sparsity-inducing priors to automatically selects the skewness parameter as being dynamic, static or zero in a data-driven framework. We consider two empirical applications. First, in a bond yield application, dynamic skewness captures interest rate cycles of monetary easing and tightening being partially explained by central banks' mandates. In an currency modeling framework, our model indicates no skewness in the carry factor after accounting for stochastic volatility which supports the idea of carry crashes being the result of volatility surges instead of dynamic skewness. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.00282&r=rmg |
| By: | Alexander M. G. Cox; Annemarie M. Grass |
| Abstract: | The robust option pricing problem is to find upper and lower bounds on fair prices of financial claims using only the most minimal assumptions. It contrasts with the classical, model-based approach and gained prominence in the wake of the 2008 financial crisis, and can be used to understand the extent to which a model-based price is sensitive to the underlying model assumptions. Common approaches involve pricing exotic derivatives such as variance options by incorporating market data through implied volatility. The existing literature focuses largely on incorporating implied volatility information corresponding to the maturity of the exotic option. In this paper, we aim to explain how intermediate data can and should be incorporated. It is natural to expect that this additional information will improve the robust pricing bounds. To investigate this question, we consider variance options, where the bounds of the informed robust pricing problem are known. We proceed to conduct an empirical study uncovering a surprising finding: Contrary to common belief, the incorporation of more information does not lead to an improvement of the robust pricing bounds. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.09201&r=rmg |
| By: | Demetrescu, Matei; Rodrigues, Paulo MM; Taylor, AM Robert |
| Abstract: | We develop new tests for predictability, based on the Lagrange Multiplier [LM] principle, in the context of quantile regression [QR] models which allow for persistent and endogenous predictors driven by conditionally and/or unconditionally heteroskedastic errors. Of the extant predictive QR tests in the literature, only the moving blocks bootstrap implementation, due to Fan and Lee (2019), of theWald-type test of Lee (2016) can allow for conditionally heteroskedastic errors in the context of a QR model with persistent predictors. In common with all other tests in the literature it cannot, however, allow for any form of unconditionally heteroskedastic behaviour in the errors. The LM-based approach we adopt in this paper is obtained from a simple auxiliary linear test regression which facilitates inference based on established instrumental variable methods. We demonstrate that, as a result, the tests we develop, based on either conventional or heteroskedasticity-consistent standard errors in the auxiliary regression, are robust under the null hypothesis of no predictability to conditional heteroskedasticity and to unconditional heteroskedasticity in the errors driving the predictors, with no need for bootstrap implementation. Tests are developed both for predictability at a single quantile, and also jointly over a set of quantiles. Simulation results highlight the superior finite sample size and power properties of our proposed LM tests over the tests of Lee (2016) and Fan and Lee (2019) for both conditionally and unconditionally heteroskedastic errors. An empirical application to the equity premium for the S&P 500 highlights the practical usefulness of our proposed tests, uncovering significant evidence of predictability in the left and right tails of the returns distribution for a number of predictors containing information on market or firm risk. |
| Keywords: | Predictive regression, Conditional quantile, Unknown persistence, Endogeneity, Time-varying volatility |
| Date: | 2024–01–03 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:37486&r=rmg |
| By: | Ju-Hong Lee; Bayartsetseg Kalina; KwangTek Na |
| Abstract: | This paper explores the limitations of existing risk-adjusted returns in portfolio management and introduces a novel metric, the Market-adaptive ratio, to address these shortcomings. Existing risk-adjusted returns neglect the differences between bear and bull markets. Acknowledging that these market conditions demand distinct strategies, the Market-adaptive ratio incorporates the unique attributes of each, enhancing the portfolio performance. By emphasizing the significance of market type in impacting investment outcomes, this novel metric empowers investors to refine their strategies accordingly. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.13719&r=rmg |
| By: | Benjamin Avanzi; Lewis de Felice |
| Abstract: | A retiree's appetite for risk is a common input into the lifetime utility models that are traditionally used to find optimal strategies for the decumulation of retirement savings. In this work, we consider a retiree with potentially differing appetites for the key financial risks of decumulation. We set out to determine whether these differing risk appetites have a significant impact on the retiree's optimal choice of strategy. To do so, we design and implement a framework which selects the optimal decumulation strategy from a general set of admissible strategies in line with a retiree's goals, and under differing appetites for the key risks of decumulation. Overall, we find significant evidence to suggest that a retiree's differing appetites for different decumulation risks will impact their optimal choice of strategy at retirement. Through an illustrative example calibrated to the Australian context, we find results which are consistent with actual behaviours in this jurisdiction (in particular, a shallow market for annuities), which lends support to our framework and may provide some new insight into the so-called annuity puzzle. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.14355&r=rmg |
| By: | Jiong Liu; Hamed Farahani; R. A. Serota |
| Abstract: | We use house prices (HP) and house price indices (HPI) as a proxy to income distribution. Specifically, we analyze sale prices in the 1970-2010 window of over 116, 000 single-family homes in Hamilton County, Ohio, including Cincinnati metro area of about 2.2 million people. We also analyze HPI, published by Federal Housing Finance Agency (FHFA), for nearly 18, 000 US ZIP codes that cover a period of over 40 years starting in 1980's. If HP can be viewed as a first derivative of income, HPI can be viewed as its second derivative. We use generalized beta (GB) family of functions to fit distributions of HP and HPI since GB naturally arises from the models of economic exchange described by stochastic differential equations. Our main finding is that HP and multi-year HPI exhibit a negative Dragon King (nDK) behavior, wherein power-law distribution tail gives way to an abrupt decay to a finite upper limit value, which is similar to our recent findings for realized volatility of S\&P500 index in the US stock market. This type of tail behavior is best fitted by a modified GB (mGB) distribution. Tails of single-year HPI appear to show more consistency with power-law behavior, which is better described by a GB Prime (GB2) distribution. We supplement full distribution fits by mGB and GB2 with direct linear fits (LF) of the tails. Our numerical procedure relies on evaluation of confidence intervals (CI) of the fits, as well as of p-values that give the likelihood that data come from the fitted distributions. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.14325&r=rmg |