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on Risk Management |
| By: | Federico Gatta; Fabrizio Lillo; Piero Mazzarisi |
| Abstract: | In financial risk management, Value at Risk (VaR) is widely used to estimate potential portfolio losses. VaR's limitation is its inability to account for the magnitude of losses beyond a certain threshold. Expected Shortfall (ES) addresses this by providing the conditional expectation of such exceedances, offering a more comprehensive measure of tail risk. Despite its benefits, ES is not elicitable on its own, complicating its direct estimation. However, joint elicitability with VaR allows for their combined estimation. Building on this, we propose a new methodology named Conditional Autoregressive Expected Shortfall (CAESar), inspired by the CAViaR model. CAESar handles dynamic patterns flexibly and includes heteroskedastic effects for both VaR and ES, with no distributional assumption on price returns. CAESar involves a three-step process: estimating VaR via CAViaR regression, formulating ES in an autoregressive manner, and jointly estimating VaR and ES while ensuring a monotonicity constraint to avoid crossing quantiles. By employing various backtesting procedures, we show the effectiveness of CAESar through extensive simulations and empirical testing on daily financial data. Our results demonstrate that CAESar outperforms existing regression methods in terms of forecasting performance, making it a robust tool for financial risk management. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.06619 |
| By: | Parisa Davar; Fr\'ed\'eric Godin; Jose Garrido |
| Abstract: | This paper tackles the problem of mitigating catastrophic risk (which is risk with very low frequency but very high severity) in the context of a sequential decision making process. This problem is particularly challenging due to the scarcity of observations in the far tail of the distribution of cumulative costs (negative rewards). A policy gradient algorithm is developed, that we call POTPG. It is based on approximations of the tail risk derived from extreme value theory. Numerical experiments highlight the out-performance of our method over common benchmarks, relying on the empirical distribution. An application to financial risk management, more precisely to the dynamic hedging of a financial option, is presented. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.15612 |
| By: | Corrado De Vecchi; Max Nendel; Jan Streicher |
| Abstract: | In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal couplings, as a generalization of well-known correlation statistics such as the Pearson correlation. The first main result states that even an arbitrarily small positive dependence between losses can result in perfectly correlated tails beyond a certain threshold and seemingly complete independence before this threshold. In a second step, we focus on the aggregation of individual risks with known marginal distributions by means of arbitrary nondecreasing left-continuous aggregation functions. In this context, we show that under an arbitrarily small positive dependence, the tail risk of the aggregate loss might coincide with the one of perfectly correlated losses. A similar result is derived for expectiles under mild conditions. In a last step, we discuss our results in the context of credit risk, analyzing the potential effects on the value at risk for weighted sums of Bernoulli distributed losses. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.19242 |
| By: | Elie Bouri (Adnan Kassar School of Business, Lebanese American University, Lebanon); Matteo Foglia (Department of Economics and Finance, University of Bari “Aldo Moro†, Italy); Sayar Karmakar (Department of Statistics, University of Florida, USA); Rangan Gupta (Department of Economics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa) |
| Abstract: | Based on the rationale that returns and volatility are interrelated, we apply a multilayer network framework involving the return layer and volatility layer of cryptocurrencies, NFTs, and DeFi assets over the period January 1, 2018 - January 23, 2024. The results show significant connectedness in each of the return and volatility layers, with major cryptocurrencies such as Bitcoin and Ethereum playing a central role. Large spikes in the level of connectedness are noticed around COVID-19 pandemic and Russia-Ukraine conflict, and Bitcoin and Ethereum emerge are net transmitters of returns and volatility shocks, emphasizing their significant role around these crisis periods. Notably, a strong positive rank correlation exists between the return and volatility layers, highlighting the significant risk-return relationship in the digital asset class. The findings suggest that economic actors should not ignore the interconnectedness between the return and volatility layers in the system of cryptocurrencies, NFTs, and DeFi assets for the sake of a comprehensive analysis of information flow. Otherwise, a share of the information flow concerning the return-volatility nexus across these digital assets would be missed, possibly leading to inferences regarding asset pricing, portfolio allocation, and risk management. |
| Keywords: | Multilayer networks, Spillover effects, return-volatility, cryptocurrencies, NFTs, DeFi, COVID-19, Russia-Ukraine conflict |
| JEL: | C32 G10 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:pre:wpaper:202432 |
| By: | Duy Pham, Son (University of Aberdeen Business School, Dunbar Street, Aberdeen, UK); Do, Hung Xuan (School of Economics and Finance, Massey University, New Zealand); Nepal, Rabindra (Faculty of Business and Law, School of Business, University of Wollongong, Australia); Jamasb, Tooraj (Department of Economics, Copenhagen Business School) |
| Abstract: | The tail risks can exhibit different and important features than average measures of risk in interconnected electricity markets. This paper examines the interconnectedness of tail risks within the regionally interconnected Australian National Electricity Market. We use the Conditional Autoregressive Value-at-Risk (CAViaR) and time-varying parameter vector autoregression (TVP-VAR) connectedness approach. Analysing historical data between 01 January 2006 and 04 February 2024. The results show significant levels of connectedness for both negative and positive tail risks, highlighting the dynamic and interdependent nature of these markets. Notably, we identify asymmetries in the transmission of tail risks and their key drivers, including oil market volatility and global geopolitical risks. Our findings show that some regions play a pivotal role in the risk dynamics across the regions of the network and the influence of energy source diversity on risk profiles. The study underscores the complexity of managing the expected increase in tail risks in interconnected electricity markets, emphasizing the need for adaptive, forward-thinking strategies tailored to evolving global and local conditions. |
| Keywords: | Electricity markets; Tail risk; TVP-VAR connectedness; Australia; CAViaR |
| JEL: | D40 L94 Q43 |
| Date: | 2024–07–02 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:cbsnow:2024_009 |
| By: | Marcelo Righi |
| Abstract: | We study the general properties of robust convex risk measures as worst-case values under uncertainty on random variables. We establish general concrete results regarding convex conjugates and sub-differentials. We refine some results for closed forms of worstcase law invariant convex risk measures under two concrete cases of uncertainty sets for random variables: based on the first two moments and Wasserstein balls. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.12999 |
| By: | Alexander Lipton; Vladimir Lucic; Artur Sepp |
| Abstract: | We develop static and dynamic approaches for hedging of the impermanent loss (IL) of liquidity provision (LP) staked at Decentralised Exchanges (DEXes) which employ Uniswap V2 and V3 protocols. We provide detailed definitions and formulas for computing the IL to unify different definitions occurring in the existing literature. We show that the IL can be seen a contingent claim with a non-linear payoff for a fixed maturity date. Thus, we introduce the contingent claim termed as IL protection claim which delivers the negative of IL payoff at the maturity date. We apply arbitrage-based methods for valuation and risk management of this claim. First, we develop the static model-independent replication method for the valuation of IL protection claim using traded European vanilla call and put options. We extend and generalize an existing method to show that the IL protection claim can be hedged perfectly with options if there is a liquid options market. Second, we develop the dynamic model-based approach for the valuation and hedging of IL protection claims under a risk-neutral measure. We derive analytic valuation formulas using a wide class of price dynamics for which the characteristic function is available under the risk-neutral measure. As base cases, we derive analytic valuation formulas for IL protection claim under the Black-Scholes-Merton model and the log-normal stochastic volatility model. We finally discuss estimation of risk-reward of LP staking using our results. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.05146 |
| By: | Liu, Mengqiao; Zhang, Yu Yvette; Jia, Ruixin |
| Keywords: | Financial Economics, Risk And Uncertainty |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea22:343698 |
| By: | Andrei Renatovich Batyrov |
| Abstract: | There are several approaches to modeling and forecasting time series as applied to prices of commodities and financial assets. One of the approaches is to model the price as a non-stationary time series process with heteroscedastic volatility (variance of price). The goal of the research is to generate probabilistic forecasts of day-ahead electricity prices in a spot marker employing stochastic volatility models. A typical stochastic volatility model - that treats the volatility as a latent stochastic process in discrete time - is explored first. Then the research focuses on enriching the baseline model by introducing several exogenous regressors. A better fitting model - as compared to the baseline model - is derived as a result of the research. Out-of-sample forecasts confirm the applicability and robustness of the enriched model. This model may be used in financial derivative instruments for hedging the risk associated with electricity trading. Keywords: Electricity spot prices forecasting, Stochastic volatility, Exogenous regressors, Autoregression, Bayesian inference, Stan |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.19405 |
| By: | Anita Behme |
| Abstract: | We introduce generalizations of the COGARCH model of Kl\"uppelberg et al. from 2004 and the volatility and price model of Barndorff-Nielsen and Shephard from 2001 to a Markov-switching environment. These generalizations allow for exogeneous jumps of the volatility at times of a regime switch. Both models are studied within the framework of Markov-modulated generalized Ornstein-Uhlenbeck processes which allows to derive conditions for stationarity, formulas for moments, as well as the autocovariance structure of volatility and price process. It turns out that both models inherit various properties of the original models and therefore are able to capture basic stylized facts of financial time-series such as uncorrelated log-returns, correlated squared log-returns and non-existence of higher moments in the COGARCH case. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.05866 |
| By: | Xu, Yongdeng (Cardiff Business School); Guan, Bo (Cardiff Business School); Lu, Wenna (Cardiff Metropolitan University, Cardiff, United Kingdom); Heravi, Saeed (Cardiff Business School) |
| Abstract: | This paper introduces a novel model to analyse the impact of macroeconomic shocks on volatility spillovers within key financial markets, such as Stock, Bond, Gold and Crude Oil. By treating macroeconomic variables as external factors to financial market volatility, our study distinguishes between internal financial volatility spillovers and external shocks arising from macroeconomic changes. Our analysis reveals that without macroeconomic shocks, the Stock market predominantly acts as the main source of volatility spillovers, with Crude Oil being the principal spillover recipient. However, the Stock market’s role in driving volatility spillover, especially towards the Crude Oil market, changes markedly in the context of macroeconomic shocks. These shocks exert a more substantial impact on Crude Oil compared to other markets. In contrast, the Bond and Gold markets exhibit a lower level of volatility transmission and are less influenced by macroeconomic shocks, thereby reinforcing their roles as stabilizers within the financial system. |
| Keywords: | Volatility spillover, Macroeconomic shocks, Multiplicative error model, Realized volatility, Financial markets |
| JEL: | C32 C52 G14 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:cdf:wpaper:2024/15 |
| By: | Jinniao Qiu; Antony Ware; Yang Yang |
| Abstract: | This paper is devoted to the price-storage dynamics in natural gas markets. A novel stochastic path-dependent volatility model is introduced with path-dependence in both price volatility and storage increments. Model calibrations are conducted for both the price and storage dynamics. Further, we discuss the pricing problem of discrete-time swing options using the dynamic programming principle, and a deep learning-based method is proposed for numerical approximations. A numerical algorithm is provided, followed by a convergence analysis result for the deep-learning approach. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.16400 |
| By: | Chavas, Jean-Paul; Li, Jian; Wang, Linjie |
| Keywords: | Agricultural Finance, Risk And Uncertainty, Demand And Price Analysis |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ags:aaea22:343544 |
| By: | Pehr-Johan Norbäck; Lars Persson; Joacim Tåg |
| Abstract: | The creation and scaling of startups are inherently linked to risk-taking, with various types of owners handling these risks differently. This paper investigates the influence of an active venture capital (VC) market on startups’ decisions regarding research and scaling. It outlines conditions under which VC-backed startups prefer riskier, yet potentially more rewarding strategies compared to independent startups. VC firms, by means of temporary ownership and compensation structures, introduce ”exit costs” that make high-risk strategies more attractive to VC-backed startups. Moreover, an active VC market prompts startups to undertake higher initial risks, as VC firms provide support for pivoting after setbacks. Additionally, the presence of VC intensifies research risk among established firms, as their research initiatives are strategic complements to the risk choices of startups. |
| Keywords: | entrepreneurship, pivoting, research, scaling, venture capital |
| JEL: | G24 L26 M13 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11178 |