
on Risk Management 
By:  Shuo Gong; Yijun Hu; Linxiao Wei 
Abstract:  The risk of a financial position shines through by means of the fluctuation of its market price. The factors affecting the price of a financial position include not only market internal factors, but also other various market external factors. The latter can be understood as sorts of environments to which financial positions have to expose. Motivated by this observation, this paper aims to design a novel axiomatic approach to risk measures in random environments. We construct a new distortiontype risk measure, which can appropriately evaluate the risk of financial positions in the presence of environments. After having studied its fundamental properties, we also axiomatically characterize it. Furthermore, its coherence and dual representation are investigated. The new class of risk measures in random environments is large enough, for example, it not only can recover some known risk measures such as the common weighted value at risk and range value at risk, but also can induce other new specific risk measures such as risk measures in the presence of background risk. Examples are given to illustrate the new framework of risk measures. This paper gives some theoretical results about risk measures in random environments, helping one to have an insight look at the potential impact of environments on risk measures of positions. 
Date:  2022–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2211.00520&r=rmg 
By:  Yoshihiro Shirai 
Abstract:  Given a pure jump Levy process $X$, spectral risk measures define a class of nonlinear expectations for a claim $C = f(X_T)$ for $T > 0$ that are the supremum and the infimum over a set of measures of (linear) expectations of $C$. Existence of probability measures $\mathbb{Q}^U$ and $\mathbb{Q}^L$, here referred to as upper/lower spectral martingale measures, where such extrema are attained, is shown and a formula for the Levy density of $X$ under $\mathbb{Q}^U$ and $\mathbb{Q}^L$ is obtained. Applications explored include empirical tests for spectral risk measures, and the risksensitive portfolio selection problem. In addition, we define a noncoherent dynamic risk measure, referred to as dynamic rebated spectral risk measure, and illustrate its uses as a financial objective. 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2210.13671&r=rmg 
By:  Achraf Tamtalini (LMM  Laboratoire Manceau de Mathématiques  UM  Le Mans Université); Anis Matoussi (LMM  Laboratoire Manceau de Mathématiques  UM  Le Mans Université); Sarah Kaakai (LMM  Laboratoire Manceau de Mathématiques  UM  Le Mans Université) 
Abstract:  We present a framework for constructing multivariate risk measures that is inspired from univariate Optimized Certainty Equivalent (OCE) risk measures. We show that this new class of risk measures verifies the desirable properties such as convexity, monotonocity and cash invariance. We also address numerical aspects of their computations using stochastic algorithms instead of using Monte Carlo or Fourier methods that do not provide any error of the estimation. 
Keywords:  Multivariate risk measures,Optimized certainty equivalent,Numerical methods,stochastic algorithms,risk allocations 
Date:  2022–10–24 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03817818&r=rmg 
By:  Alessandro Bondi; Sergio Pulido (ENSIIE  Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise, LaMME  Laboratoire de Mathématiques et Modélisation d'Evry  INRA  Institut National de la Recherche Agronomique  UEVE  Université d'ÉvryVald'Essonne  ENSIIE  CNRS  Centre National de la Recherche Scientifique); Simone Scotti 
Abstract:  We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkestype process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the FourierLaplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic RiccatiVolterra equations, which can be efficiently approximated using a multifactor approximation technique. We calibrate a parsimonious specification of our model characterized by a power kernel and an exponential law for the jumps. We show that our parsimonious setup is able to simultaneously capture, with a high precision, the behavior of the implied volatility smile for both S&P 500 and VIX options. In particular, we observe that in our setting the usual shift in the implied volatility of VIX options is explained by a very low value of the power in the kernel. Our findings demonstrate the relevance, under an affine framework, of rough volatility and selfexciting jumps in order to capture the joint evolution of the S&P 500 and VIX. 
Keywords:  Stochastic volatility,Rough volatility,Hawkes processes,Jump clusters,Leverage effect,affine Volterra processes,VIX,joint calibration of S&P 500 and VIX smiles 
Date:  2022–10–24 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03827332&r=rmg 
By:  Constantin Bürgi; Bo Jiang 
Abstract:  How much deposits and equity a bank has influences how a banks’ lending responds to monetary policy. While the responsiveness for the bank lending channel has been well established, this is not the case for the risktaking channel (RTC). We show in a valueatrisk RTC model that the lending for banks with relatively more equity and noninterestbearing deposits should respond less to monetary policy tightening. This suggests that noninterestbearing deposits act as “pseudo capital”. In a panel of US banks, we find strong evidence in support of our model for various risk measures. 
Keywords:  bank lending, deposits, valueatrisk, pseudo capital 
JEL:  E43 E52 G21 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_9995&r=rmg 
By:  Kevin Hu (Massachusetts Institute of Technology); Retsef Levi (Massachusetts Institute of Technology); Raphael Yahalom (Massachusetts Institute of Technology); El Ghali Zerhouni (Massachusetts Institute of Technology) 
Abstract:  This paper provides the first largescale datadriven analysis to evaluate the predictive power of different attributes for assessing risk of cyberattack data breaches. Furthermore, motivated by rapid increase in third party enabled cyberattacks, the paper provides the first quantitative empirical evidence that digital supplychain attributes are significant predictors of enterprise cyber risk. The paper leverages outsidein cyber risk scores that aim to capture the quality of the enterprise internal cybersecurity management, but augment these with supply chain features that are inspired by observed third party cyberattack scenarios, as well as concepts from network science research. The main quantitative result of the paper is to show that supply chain network features add significant detection power to predicting enterprise cyber risk, relative to merely using enterpriseonly attributes. Particularly, compared to a base model that relies only on internal enterprise features, the supply chain network features improve the outofsample AUC by 2.3\%. Given that each cyber data breach is a low probability high impact risk event, these improvements in the prediction power have significant value. Additionally, the model highlights several cybersecurity risk drivers related to third party cyberattack and breach mechanisms and provides important insights as to what interventions might be effective to mitigate these risks. 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2210.15785&r=rmg 
By:  Tchoudi, William; Sergeenko, Grigory 
Abstract:  This study focuses on optimal portfolio trading allocation, using historic trading data to propose an optimal allocation with risk consideration. The risk factors used sequentially in this study are Sharp Ratio (SR) and Maximum Drawdown (MDD). We use the Sequential Least Squares programming (SLSQP) solver to minimise the negative adapted Sharp Ratio for trading profit and loss (PNL) and then we use the Triple Penance Rule assumption for modelling a mathematical formula to represent the relationship between the MDD and the Time under Water (TUW). In this paper, we introduce the risk measure driven by the MDD as the area of the curve during the TUW. The inverse of this area is used to define a proportional weight to the MDD value. The final weight is obtained by applying an algorithm for removing all MDD outliers in the dataset after SLSQP optimization. The final optimal weight is a combination of the calculated proportional PNL weights and the weights from the MDD area. The benchmark is the equal weight portfolio and the maximal return portfolio from Monte Carlo Simulation (MCS). The tested portfolios are two portfolios made from stocks and securities of the Dow Jones Industrial Average (DOJI) and the NASDAQ Composite (COMP). The initial selection is made from only securities that offer at least five years of historical prices. The results show a good compromise in weight allocation between maximising the PNL and minimising MDD and Sharp ratio. 
Date:  2022–06–10 
URL:  http://d.repec.org/n?u=RePEc:osf:africa:uef3y&r=rmg 
By:  Max Nendel; Alessandro Sgarabottolo 
Abstract:  In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the distribution of a possibly infinitedimensional risk factor. We allow for perturbations around a baseline model, measured via Wasserstein distance, and we investigate to which extent this form of probabilistic imprecision can be parametrized. The aim is to come up with a convex risk functional that incorporates a sefety margin with respect to nonparametric uncertainty and still can be approximated through parametrized models. The particular form of the parametrization allows us to develop a numerical method, based on neural networks, which gives both the value of the risk functional and the optimal perturbation of the reference measure. Moreover, we study the problem under additional constraints on the perturbations, namely, a mean and a martingale constraint. We show that, in both cases, under suitable conditions on the loss function, it is still possible to estimate the risk functional by passing to a parametric family of perturbed models, which again allows for a numerical approximation via neural networks. 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2210.14340&r=rmg 
By:  Geon Lee; TaeKyoung Kim; HyunGyoon Kim; Jeonggyu Huh 
Abstract:  In finance, implied volatility is an important indicator that reflects the market situation immediately. Many practitioners estimate volatility using iteration methods, such as the NewtonRaphson (NR) method. However, if numerous implied volatilities must be computed frequently, the iteration methods easily reach the processing speed limit. Therefore, we emulate the NR method as a network using PyTorch, a wellknown deep learning package, and optimize the network further using TensorRT, a package for optimizing deep learning models. Comparing the optimized emulation method with the NR function in SciPy, a popular implementation of the NR method, we demonstrate that the emulation network is up to 1,000 times faster than the benchmark function. 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2210.15969&r=rmg 
By:  Yasin Kürsat Önder () 
Abstract:  I investigate the introduction of GDPindexed bonds as an additional source of government borrowing in a quantitative default model. The idea of linking debt payments to developments in GDP resurfaced with the 1980s debt crisis and peaked with the COVID19 outbreak. I show that the gains from this idea depend on the underlying indexation method and are highest if payments are symmetrically tied to developments in GDP. Optimized indexed debt can eradicate default risk, halve consumption volatility, and increase asset prices while raising the government’s debt balances. These changes occur because an optimally chosen indexation method does a better job at completing the markets. 
Keywords:  GDPindexed bonds, sovereign default, risk sharing, statecontingent assets 
JEL:  G11 G23 F34 
Date:  2022–11 
URL:  http://d.repec.org/n?u=RePEc:rug:rugwps:22/1056&r=rmg 
By:  Suchetana Sadhukhan; Shiv Manjaree Gopaliya; Pushpdant Jain 
Abstract:  Volatility prediction in the financial market helps to understand the profit and involved risks in investment. However, due to irregularities, high fluctuations, and noise in the time series, predicting volatility poses a challenging task. In the recent Covid19 pandemic situation, volatility prediction using complex intelligence techniques has attracted enormous attention from researchers worldwide. In this paper, a novel and simple approach based on the robust least squares method in two approaches a) with least absolute residuals (LAR) and b) without LAR, have been applied to the Chicago Board Options Exchange (CBOE) Volatility Index (VIX) for a period of ten years. For a deeper analysis, the volatility time series has been decomposed into longterm trends, and seasonal, and random fluctuations. The data sets have been divided into parts viz. training data set and testing data set. The validation results have been achieved using root mean square error (RMSE) values. It has been found that robust least squares method with LAR approach gives better results for volatility (RMSE = 0.01366) and its components viz. long term trend (RMSE = 0.10087), seasonal (RMSE = 0.010343) and remainder fluctuations (RMSE = 0.014783), respectively. For the first time, generalized prediction equations for volatility and its three components have been presented. Young researchers working in this domain can directly use the presented prediction equations to understand their data sets. 
Date:  2022–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2211.00528&r=rmg 
By:  Anusha Chari; Karlye Dilts Stedman; Christian Lundblad 
Abstract:  Global risk and risk aversion shocks have distinct distributional impacts on emerging market capital flows and returns. In particular, we find salient consequences of these different global shocks for tail risk in emerging markets. Openend mutual fund trading provides a key mechanism linking shocks facing global investors to extreme capital flow and return realizations. The effects are heterogeneous across asset classes and fund types. The limited discretion and higher conformity of passive fund investments linked to benchmarking amplify passthrough effects that engender abnormal comovements in emerging market flows and returns. 
JEL:  F3 F32 G11 G15 
Date:  2022–10 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:30577&r=rmg 
By:  Jaqueson Galimberti (School of Economics, Auckland University of Technology); Lydia Cheung (School of Economics, Auckland University of Technology); Philip Vermeulen (School of Economics, Auckland University of Technology) 
Keywords:  idiosyncratic risk, house prices, housing markets 
JEL:  G1 R1 
Date:  2022–11 
URL:  http://d.repec.org/n?u=RePEc:aut:wpaper:202205&r=rmg 
By:  Vanhaverbeke, Steven; Balsmeier, Benjamin; Doherr, Thorsten 
Abstract:  When firms are forced to publicly disclose financial information, credit rating agencies are supposed to improve their risk assessments. Theory predicts such an information quality effect but also an adverse reputational concerns effect because credit analysts may become increasingly concerned about alleged rating failures. We empirically examine these predictions using a large scale quasinatural experiment in Germany, where firms were required to publicly disclose annual financial statements. Consistent with the reputational concern hypothesis, we find an average increase in credit rating downgrades that is entirely driven by changes in the discretionary assessment of the credit analysts rather than changes in firm fundamentals. Analysts tend to give positive private information a lower weight in their risk assessment, while they put a higher weight on negative public information. A last set of results indicate that professional credit providers understand that the resulting downgrades are not warranted, while unsophisticated lenders did indeed reduce the provision of trade credit in response to the rating downgrades. 
Keywords:  Credit Ratings,Disclosure Regulation,Private Firms,Reputational Concerns 
JEL:  G14 G18 G24 M41 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:zewdip:22043&r=rmg 
By:  Auld, T. 
Abstract:  We present a model linking prices of political binary options to financial assets that applies in the very particular circumstance of the overnight session following an election. Contrary to most of the existing literature, the model is derived from economic first principles and applies in a general setting. We find that under suitable assumptions, election and financial markets will be cointegrated. Deviations from risk neutrality lead to the presence of a nonlinear term relating to risk in the cointegrating relationship. The model is tested on three recent political events: The 2014 Scottish independence referendum, the 2016 Brexit referendum and the 2016 US presidential election. Strong support is found for two events (the Brexit referendum and the 2016 Trump win). We find that weak market efficiency broadly holds although there are violations of the order of minutes to tens of minutes. This is apparently caused by betting markets leading financial markets, a phenomena that is observed for all three events. This finding is consistent with the conclusion of the existing literature that prediction markets have superior forecasting ability to other methods. A realistic exante trading strategy is presented for Brexit that profits from these inefficiencies. However, the success is not repeated for the 2016 presidential election. This is due to an apparent deviation from risk neutrality that is not observed on the night of Brexit. 
Keywords:  Elections, Election market, Political risk, High frequency data, Pricing of risk 
JEL:  C51 D72 G12 G14 G15 
Date:  2022–11–02 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:2263&r=rmg 
By:  Du, Chuan (Bank of England) 
Abstract:  In periods of stress, acute liquidity squeeze can manifest in the riskier segments of the credit market, even amid a surplus of aggregate liquidity. In such scenarios, central bank interventions that directly lower the risky interest rate can be more effective than reductions in the riskfree interest rate. Specifically, the central bank lends to the market at more favourable interest rates while simultaneously reducing the haircuts imposed on eligible collateral. In doing so, the central bank takes on greater credit risk, but achieves an outcome that is more productively efficient than simply reducing the riskfree interest rate. 
Keywords:  Collateral; leverage; credit conditions; monetary policy; general equilibrium 
JEL:  D53 E44 E51 E52 E58 
Date:  2022–07–21 
URL:  http://d.repec.org/n?u=RePEc:boe:boeewp:0987&r=rmg 