
on Risk Management 
By:  Martin Waltz; Abhay Kumar Singh; Ostap Okhrin 
Abstract:  This paper proposes an important extension to Conditional ValueatRisk (CoVaR), the popular systemic risk measure, and investigates its properties on the cryptocurrency market. The proposed VulnerabilityCoVaR (VCoVaR) is defined as the ValueatRisk (VaR) of a financial system or institution, given that at least one other institution is equal or below its VaR. The VCoVaR relaxes normality assumptions and is estimated via copula. While important theoretical findings of the measure are detailed, the empirical study analyzes how different distressing events of the cryptocurrencies impact the risk level of each other. The results show that Litecoin displays the largest impact on Bitcoin and that each cryptocurrency is significantly affected if an event of joint distress among the remaining market participants occurs. The VCoVaR is shown to capture domino effects better than other CoVaR extensions. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.10777&r= 
By:  Samuel N. Cohen; Christoph Reisinger; Sheng Wang 
Abstract:  In this paper, we examine the capacity of an arbitragefree neuralSDE market model to produce realistic scenarios for the joint dynamics of multiple European options on a single underlying. We subsequently demonstrate its use as a risk simulation engine for option portfolios. Through backtesting analysis, we show that our models are more computationally efficient and accurate for evaluating the ValueatRisk (VaR) of option portfolios, with better coverage performance and less procyclicality than standard filtered historical simulation approaches. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.07148&r= 
By:  Wosnitza, Jan Henrik 
Abstract:  The transformation of credit scores into probabilities of default plays an important role in credit risk estimation. The linear logistic regression has developed into a standard calibration approach in the banking sector. With the advent of machine learning techniques in the discriminatory phase of credit risk models, however, the standard calibration approach is currently under scrutiny again. In particular, the assumptions behind the linear logistic regression provide critics with a target. Previous literature has converted the calibration problem into a regression task without any loss of generality. In this paper, we draw on recent academic results in order to suggest two new oneparametric families of differentiable functions as candidates for this regression. The derivation of these two families of differentiable functions is based on the maximum entropy principle and, thus, they rely on a minimum number of assumptions. We compare the performance of four calibration approaches on a realworld data set and find that one of the new oneparametric families outperforms the linear logistic regression. Furthermore, we develop an approach in order to quantify the part of the general estimation error of probabilities of default that stems from the statistical dispersion of the discriminatory power. 
Keywords:  Calibration,credit score,cumulative accuracy profile,logistic regression,margin of conservatism,probability of default 
JEL:  G17 G21 G33 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:bubdps:042022&r= 
By:  Frido Rolloos 
Abstract:  Exact relationships between the short timetomaturity ATM implied volatility slope, the (dual) volatility swap, and the (dual) zero vanna implied volatility are given. 
Date:  2022–02 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2202.07542&r= 
By:  Ziteng Cheng; Sebastian Jaimungal 
Abstract:  The Kusuoka representation of proper lower semicontinuous law invariant coherent risk measures allows one to cast them in terms of average valueatrisk. Here, we introduce the notion of Kusuokatype conditional riskmappings and use it to define a dynamic risk measure. We use such dynamic risk measures to study infinite horizon Markov decision processes with random costs and random actions. Under mild assumptions, we derive a dynamic programming principle and prove the existence of an optimal policy. We also derive the Qlearning version of the dynamic programming principle, which is important for applications. Furthermore, we provide a sufficient condition for when deterministic actions are optimal. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.09612&r= 
By:  John Cotter (Smurfit School of Business, University College Dublin); Enrique Salvador (Universitat Jaume I) 
Abstract:  We estimate a discrete approximation of the riskreturn tradeoff for the US market by using the whole universe of stocks from July 1963 to September 2017. We find the relationship between return and total risk to be timevarying and also dependent on the level of risk considered. The proposed positive tradeoff is mainly observed during low volatility periods and when we move from low risk up to mediumhigh risk investments. However, the direction of the tradeoff is inverted for the highest risk alternatives especially during high volatility periods. The temporal variation of the risk return tradeoff can be explained by a series of sentiment, macro, credit risk, liquidity and corporate variables. All these determinants suggest that the positive relationship between return and risk is more evident during periods where economic, financial and market conditions improve. 
Keywords:  timevarying riskreturn tradeoff, nonlinear dependence, cyclical variation, panel regressions, asset pricing 
JEL:  G10 G12 G15 
Date:  2022–02–01 
URL:  http://d.repec.org/n?u=RePEc:ucd:wpaper:202203&r= 
By:  Alhonita Yatie (BSE  Bordeaux Sciences Economiques  UB  Université de Bordeaux  CNRS  Centre National de la Recherche Scientifique) 
Abstract:  As the first crisis faced by Cryptoassets, Covid19 updated the debate about their safehaven properties. Our paper tries to analyze the safehaven properties of Cryptoassets and Gold for European assets. We find that Gold has not been more efficient than Cryptoassets (Tether, Cardano and Dogecoin) as safehaven during the market crash due to Covid19 in March 2020. We also found that during the study period Bitcoin, Ethereum, Litecoin and Ripple were just diversifiers for the European indices. Finally, Tether, Cardano and Dogecoin showed hedging properties like Gold before and after the market crash. 
Keywords:  Gold,Bitcoin,Safehaven,Covid19,Cryptoassets 
Date:  2022–02–21 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal03579957&r= 
By:  Krüger, Ulrich; Roling, Christoph; Silbermann, Leonid; Wong, Lui Hsian 
Abstract:  In this paper we introduce two measures, the Systemic Liquidity Buffer (SLB) and the Systemic Liquidity Shortfall (SLS) to assess liquidity in the banking system. The SLB takes an aggregated perspective on liquidity risks in the banking system. In contrast, the SLS focusses on the problematic banks which suffer a liquidity shortfall. These measures provide an addon to regulatory liquidity measures such as the LCR because they better incorporate a systemic perspective: (1) They model the impact of a funding shock by valuing assets at depressed market prices, (2) Doing so, they explicitly incorporate banks' strategic responses to a market undergoing sharp price declines. We test our approach using several applications capturing both a short (5 days) and a mediumterm (30 days) stress scenario, a sudden rise in interest rates, the impact of banks' US dollar business and the recent COVID19 crisis. 
Keywords:  Systemic liquidity risk,market liquidity,funding liquidity,contagion,fire sales 
JEL:  C63 G01 G17 G21 G28 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:zbw:bubdps:062022&r= 
By:  Bingyan Han 
Abstract:  This work studies distributionally robust evaluation of expected function values over temporal data. A set of alternative measures is characterized by the causal optimal transport. We prove the strong duality and recast the causality constraint as minimization over an infinitedimensional test function space. We approximate test functions by neural networks and prove the sample complexity with Rademacher complexity. Moreover, when structural information is available to further restrict the ambiguity set, we prove the dual formulation and provide efficient optimization methods. Simulation on stochastic volatility and empirical analysis on stock indices demonstrate that our framework offers an attractive alternative to the classic optimal transport formulation. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.10571&r= 
By:  Fuzhou Gong; Ting Wang 
Abstract:  In this paper, we propose and study a novel continuoustime model, based on the wellknown constant elasticity of variance (CEV) model, to describe the asset price process. The basic idea is that the volatility elasticity of the CEV model can not be treated as a constant from the perspective of stochastic analysis. To address this issue, we deduce the price process of assets from the perspective of volatility elasticity, propose the constant volatility elasticity (CVE) model, and further derive a more general variable volatility elasticity (VVE) model. Moreover, our model can describe the positive correlation between volatility and asset prices existing in the commodity markets, while CEV model can only describe the negative correlation. Through the empirical research on the financial market, many assets, especially commodities, often show this positive correlation phenomenon in some time periods, which shows that our model has strong practical application value. Finally, we provide the explicit pricing formula of European options based on our model. This formula has an elegant form convenient to calculate, which is similarly to the renowned BlackScholes formula and of great significance to the research of derivatives market. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.09177&r= 
By:  Ryan, Ellen 
Abstract:  The investment fund sector has expanded dramatically since the crisis of 20082009. As the sector grows, so do the implications of its risktaking for the wider financial system and real economy. This paper provides empirical evidence for the existence of widespread risktaking incentives in the investment fund sector, with a particular focus on incentives for synchronised, cyclical risktaking which could have systemic effects. Incentives arise from the positive response of investors to returns achieved through cyclical risktaking and nonlinearities in the relationship between fund returns and fund flows, which may keep managers from fully internalising the effects of adverse outcomes on their portfolios. The fact that market discipline may not be sufficient to ensure prudential behaviour among managers, combined with the externalities of this risktaking for the wider system, creates a clear case for macroprudential regulatory intervention. JEL Classification: G23, G11, G28 
Keywords:  Financial stability, incentive, investment funds, macroprudential policy, risktaking 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20222652&r= 
By:  Tomás Caravello; Turalay Kenc; Martín Sola 
Abstract:  We develop and estimate a consumptionbased asset pricing model that assumes recursive utility using historical US financial data, allowing for regime changes, priced regime risk, and intrinsic bubbles. We also estimate several restricted versions which include only a subset of these features. We find that switching risk is an essential component of the equity risk premium, explaining up to fifty percent of it. Furthermore, a model which does not take this into account would overestimate the degree of risk aversion of the public, mistakenly assigning the observed risk premium to highrisk aversion instead of priced regimeswitching. Intrinsic bubbles are not crucial in explaining the risk premia, but they substantially improve the model’s fit at the end of the sample. 
Keywords:  Intrinsic Bubbles; Macroeconomic Risk; Stochastic Differential Utility,Markov Chain; Equity Risk Premium. 
JEL:  G00 G12 E44 C32 
Date:  2021–12 
URL:  http://d.repec.org/n?u=RePEc:udt:wpecon:2021_08&r= 
By:  Dupret, JeanLoup (Université catholique de Louvain, LIDAM/ISBA, Belgium); Hainaut, Donatien (Université catholique de Louvain, LIDAM/ISBA, Belgium) 
Abstract:  Subdiffusions appear as good candidates for modeling illiquidity in financial markets. Existing subdiffusive models of asset prices are indeed able to capture the motionless periods in the quotes of thinlytraded assets. However, they fail at reproducing the jumps and the timevarying volatility observed in the price of these assets. The aim of this work is hence to propose a new model of subdiffusive asset prices reproducing the main characteristics exhibited in illiquid markets. This is done by considering a stochastic volatility jump model, timechanged by an inverse subordinator. We derive the forward fractional partial differential equations (PDE) governing the probability density function of the introduced model and we prove that it leads to an arbitragefree and incomplete market. By proposing a new procedure for estimating the model parameters and using a series expansion for solving numerically the obtained fractional PDE, we are able to price various financial derivatives on illiquid assets and to propose a corresponding hedging strategy. This way, we show that the introduced subdiffusive stochastic volatility jump model yields consistent and more reliable results in illiquid markets. 
Keywords:  Illiquidity modeling ; subdiffusion ; fractional FokkerPlanck equations ; stochastic volatility jump model ; option pricing 
Date:  2022–01–01 
URL:  http://d.repec.org/n?u=RePEc:aiz:louvad:2022001&r= 
By:  Paul Gassiat 
Abstract:  Simulation of rough volatility models involves discretization of stochastic integrals where the integrand is a function of a (correlated) fractional Brownian motion of Hurst index $H \in (0,1/2)$. We obtain results on the rate of convergence for the weak error of such approximations, in the special cases when either the integrand is the fBm itself, or the test function is cubic. Our result states that the convergence is of order $(3H+ \frac{1}{2}) \wedge 1$ for the Cholesky scheme, and of order $H+\frac{1}{2}$ for the hybrid scheme with wellchosen weights. 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2203.09298&r= 
By:  José Alves; João Quental Gonçalves 
Abstract:  The present work offers a review on two divergent schools of thought regarding the subject of money and highlights why understanding it is important to grasp the workings and nature of the concept of money. We adopt a spontaneous order perspective on social institutions, considering money as one. Such framework allows for the construction of axioms from which we formulate our problem allowing us to ask how old forms of money such as Gold and Silver hold up in today’s world regarding their hedging properties. Moreover, we also do so for Bitcoin since we consider it an appropriate asset due to its specific characteristics and its (at the time of writing) more than 10year life span. We resort to the Autoregressive Distributed Lag (ARDL) methodology in order to study our three assets in the context of the US dollar and the US Economy for two different time periods. We analyse price dynamics from 1980 to 2020 for gold and silver resorting to annual data. Regarding bitcoin we employ quarterly data from 2009 to 2020. We conclude that the theories that explain what money is, how it comes to be so and how certain types of “money assets” may serve both as an indirect hedge against inflation in the two interpretations of the word and as a “stock of value” have merits that might deserve further investigation. 
Keywords:  Money; Inflation; Gold; Silver; Bitcoin 
JEL:  B25 D46 E42 E51 
Date:  2022–03 
URL:  http://d.repec.org/n?u=RePEc:ise:remwps:wp02222022&r= 
By:  Bu, R.; Li, D.; Linton, O.; Wang, H. 
Abstract:  In this paper, we consider estimating spot/instantaneous volatility matrices of highfrequency data collected for a large number of assets. We first combine classic nonparametric kernelbased smoothing with a generalised shrinkage technique in the matrix estimation for noisefree data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot volatility matrix estimator with convergence rates comparable to the optimal minimax one. For the highfrequency data contaminated by the microstructure noise, we introduce a localised preaveraging estimation method in the highdimensional setting which first prewhitens data via a kernel filter and then uses the estimation tool developed in the noisefree scenario, and further derive the uniform convergence rates for the developed spot volatility matrix estimator. In addition, we also combine the kernel smoothing with the shrinkage technique to estimate the timevarying volatility matrix of the highdimensional noise vector, and establish the relevant uniform consistency result. Numerical studies are provided to examine performance of the proposed estimation methods in finite samples. 
Keywords:  Brownian semimartingale, Kernel smoothing, Microstructure noise, Sparsity, Spot volatility matrix, Uniform consistency 
JEL:  C10 C14 C22 
Date:  2022–03–16 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:2218&r= 
By:  Hafner, Christian (Université catholique de Louvain, LIDAM/ISBA, Belgium); Linton, Oliver (obl20@cam.ac.uk); Wang, Linqi (Université catholique de Louvain, LIDAM/LFIN, Belgium) 
Abstract:  We introduce a new class of semiparametric dynamic autoregressive models forthe Amihud illiquidity measure, which captures both the longrun trend in the illiquidity series with a nonparametric component and the shortrun dynamics with an autoregressive component. We develop a GMM estimator based on conditional moment restrictions and an efficient semiparametric ML estimator based on an iid assumption. We derive large sample properties for both estimators. We further develop a methodology to detect the occurrence of permanent and transitory breaks in the illiquidity process. Finally, we demonstrate the model performance and its empirical relevance on two applications. First, we study the impact of stock splits on the illiquidity dynamics of the five largest US technology company stocks. Second, we investigate how the different components of the illiquidity process obtained from our model relate to the stock market risk premium using data on the S&P 500 stock market index. 
Keywords:  Nonparametric ; Semiparametric ; Splits ; Structural Change 
JEL:  C12 C14 
Date:  2022–02–23 
URL:  http://d.repec.org/n?u=RePEc:aiz:louvad:2022009&r= 