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on Risk Management |
| By: | Herbertsson, Alexander (Department of Economics, School of Business, Economics and Law, Göteborg University) |
| Abstract: | In this paper we study equity risk management of stock portfolios where the individual stock prices have downward jumps at the defaults of an exogenous group of defaultable entities. The default times can come from any type of credit portfolio model. In this setting we derive computational tractable formulas for several stock-related quantizes, such as loss distributions of equity portfolios and apply it to Value-at-Risk computations. We start with individual stock prices and then extend the setting to a portfolio framework. In the portfolio case our studies considers both small-time expansions of the loss-distribution for a heterogeneous portfolio via a linearization of the loss, but also for general time points when the stock portfolio is large and homogeneous and where we use a conditional version of the law of large numbers. Most of the derived formulas will heavily rely on the ability to efficiently compute the number of defaults distribution of the entities in the exogenous group of corporates negative affecting the stock prices in our equity portfolio. If the stock prices are unaffected by the exogenous defaults then our framework collapses into the traditional Black-Scholes model under the real probability measure. Finally, we give several numerical applications. For example, in a setting where the jumps in the stock prices are at default times which are generated by a one-factor Gaussian copula model, we study the time evolution of Value-at-Risk (i.e. VaR as function of time) for stock portfolios, both for a 20-day period and for a two-year period. We also perform similar numerical VaR-studies in a setting where the individual default intensities follow a CIR process. Our results are compared with the corresponding VaR-values in the Black-Scholes case with same drift and volatilises as in the jump models. Not surprisingly, we show that the VaR-values in stock portfolios with downward jumps at defaults of external entities, will have substantially higher VaR-values compared to the corresponding Black-Scholes cases. The numerical computations of the number of default distribution will in all our studies use fast and efficient saddlepoint methods. |
| Keywords: | equity portfolio risk; stock price modelling; credit portfolio risk; risk management; Value-at-Risk; intensity-based models; credit copula models; numerical methods |
| JEL: | C02 C63 G13 G32 G33 |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:gunwpe:0836&r=rmg |
| By: | Matthew Stuart; Cindy Yu; David A. Hennessy |
| Abstract: | Crop yields and harvest prices are often considered to be negatively correlated, thus acting as a natural risk management hedge through stabilizing revenues. Storage theory gives reason to believe that the correlation is an increasing function of stocks carried over from previous years. Stock-conditioned second moments have implications for price movements during shortages and for hedging needs, while spatially varying yield-price correlation structures have implications for who benefits from commodity support policies. In this paper, we propose to use semi-parametric quantile regression (SQR) with penalized B-splines to estimate a stock-conditioned joint distribution of yield and price. The proposed method, validated through a comprehensive simulation study, enables sampling from the true joint distribution using SQR. Then it is applied to approximate stock-conditioned correlation and revenue insurance premium for both corn and soybeans in the United States. For both crops, Cornbelt core regions have more negative correlations than do peripheral regions. We find strong evidence that correlation becomes less negative as stocks increase. We also show that conditioning on stocks is important when calculating actuarially fair revenue insurance premiums. In particular, revenue insurance premiums in the Cornbelt core will be biased upward if the model for calculating premiums does not allow correlation to vary with stocks available. The stock-dependent correlation can be viewed as a form of tail dependence that, if unacknowledged, leads to mispricing of revenue insurance products. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.11805&r=rmg |
| By: | Marlon Moresco; M\'elina Mailhot; Silvana Pesenti |
| Abstract: | We introduce a framework for quantifying propagation of uncertainty arising in a dynamic setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete stochastic processes over a finite time horizon. These dynamic uncertainty sets capture the uncertainty surrounding stochastic processes and models, accounting for factors such as distributional ambiguity. Examples of uncertainty sets include those induced by the Wasserstein distance and $f$-divergences. We further define dynamic robust risk measures as the supremum of all candidates' risks within the uncertainty set. In an axiomatic way, we discuss conditions on the uncertainty sets that lead to well-known properties of dynamic robust risk measures, such as convexity and coherence. Furthermore, we discuss the necessary and sufficient properties of dynamic uncertainty sets that lead to time-consistencies of robust dynamic risk measures. We find that uncertainty sets stemming from $f$-divergences lead to strong time-consistency while the Wasserstein distance results in a new notion of non-normalised time-consistency. Moreover, we show that a dynamic robust risk measure is strong or non-normalised time-consistent if and only if it admits a recursive representation of one-step conditional robust risk measures arising from static uncertainty sets. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.12856&r=rmg |
| By: | Olkhov, Victor |
| Abstract: | The accuracy of predictions of price and return probabilities substantially determines the reliability of asset pricing and portfolio theories. We develop successive approximations that link up predictions of the market-based probabilities of price and return for the whole stock market with predictions of price and return probabilities for stocks of a particular company and show that economic complexity limits the accuracy of any forecasts. The economic origin of the restrictions lies in the fact that the predictions of the m-th statistical moments of price and return require descriptions of the economic variables composed by sums of the m-th powers of economic or market transactions during an averaging time interval. The attempts to predict the n-th statistical moments of price and return of stocks that are under the action of a single risk result in estimates of the n-dimensional risk rating vectors for economic agents. In turn, the risk rating vectors play the role of coordinates for the description of the evolution of economic variables. The lack of a model description of the economic variables composed by sums of the 2-d and higher powers of market transactions causes that, in the coming years, the accuracy of the forecasts will be limited at best by the first two statistical moments of price and return, which determine Gaussian distributions. One can ignore existing barriers and limits but cannot overcome or resolve them. That significantly reduces the reliability and veracity of modern asset pricing and portfolio theories. Our results could be essential and fruitful for the largest investors and banks, economic and financial authorities, and market participants. |
| Keywords: | price and return; market trade; risk ratings; statistical moments; probability predictions |
| JEL: | C18 C53 E37 F17 F37 G1 G17 |
| Date: | 2023–08–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:118373&r=rmg |
| By: | Marc Atkins (Paderborn University); Christian Peitz (Paderborn University) |
| Abstract: | We analyse the largest financial markets as well as the most a affected industries of the Regional Comprehensive Economic Partnership (RCEP) zone and examine them for their respective market risk and stability. Trade decisions with RCEP member countries are in uenced by the stability of financial markets within the RCEP free trade area. To this end, we examine the largest financial markets in terms of volatility and risk using various GARCH models. Our focus is on the financial markets of the largest of the 15 RCEP member countries, namely China, Japan, South Korea, Australia, Indonesia and Thailand. We consider whether RCEP's expected entry into force as well as this event itself have an impact on the respective financial markets by means of an event analysis. We further derive the most e ected industries by the agreement and extend our analysis to the sector-level. We examine the largest companies of the automotive industry, the computer, electronic and electrical equipment sector as well as the chemical industry and analyse their performance and volatility over time. |
| Keywords: | ARCH models, trade policy, RCEP, event analysis, financial risk |
| JEL: | C51 F13 G14 G32 |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:pdn:dispap:113&r=rmg |
| By: | Juan Jose Francisco Miguelez; Cristin Buescu |
| Abstract: | We study the problem of valuing a vulnerable derivative with bilateral cash flows between two counterparties in the presence of funding, credit and wrong-way risks, and derive a closed-form valuation formula for an at-the-money (ATM) forward contract as well as a second order approximation for the general case. We posit a model with heterogeneous interest rates and default occurrence and infer a Cauchy problem for the pre-default valuation function of the contract, which includes ab initio any counterparty risk - as opposed to calculating valuation adjustments collectively known as XVA. Under a specific funding policy which linearises the Cauchy problem, we obtain a generic probabilistic representation for the pre-default valuation (Theorem 1). We apply this general framework to the valuation of an equity forward and establish the contract can be expressed as a continuous portfolio of European options with suitably chosen strikes and expiries under a particular probability measure (Theorem 2). Our valuation formula admits a closed-form expression when the forward contract is ATM (Corollary 2) and we derive a second order approximation in moneyness when the contract is close to ATM (Theorem 3). Numerical results of our model show that the forward is more sensitive to funding factors than credit ones, while higher stock funding costs increase sensitivity to credit spreads and wrong-way risk. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.10568&r=rmg |
| By: | Giovanni Federico (Division of Social Sciences, New York University Abu Dhabi and CEPR); Pablo Martinelli Lasheras (Department of Social Sciences, University Carlos III of Madrid and Figuerola Institute) |
| Abstract: | In this paper we provide an economic interpretation of intercropping as a risk management strategy based on spatial diversification of production. We study vine intercropping - i.e., scattering vines across fields rather than concentrating them in specialized vineyards - a traditional practice in Italian agriculture. We claim that, in absence of developed financial markets, spatial diversification provided a third layer of insurance to peasants operating in traditional agrarian economics, different from and in addition to crop diversification at the farm level and risk-sharing through tenancy contracts at the estate level. Spatial diversification increased production costs, in particular transportation costs. Hence, the price of this form of insurance (and the likelihood of its adoption) depended critically on the rural settlement pattern. We test our model with data for 1930s Italy, where intercropping still prevailed in many areas of the country. We show that its adoption was positively related to the pattern of scattered dwellings which dated back to the late Middle Ages and reduced transportation costs to individual plots. The mass exodus from the countryside during the economic miracle of the 1950s and 1960s made intercropping no longer viable. |
| Keywords: | intercropping, diversification, risk management, traditional agriculture, viticulture, Italy |
| JEL: | L23 N63 N64 O13 Q12 R14 |
| Date: | 2023–04 |
| URL: | http://d.repec.org/n?u=RePEc:hes:wpaper:0233&r=rmg |
| By: | Haiyan Liu; Bin Wang; Ruodu Wang; Sheng Chao Zhuang |
| Abstract: | Classic optimal transport theory is built on minimizing the expected cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost. This new formulation is motivated by concrete problems in decision theory, robust optimization, and risk management, and it has many distinct features compared to the classic theory. We choose simple cost functions and study different distortion functions and their implications on the optimal transport plan. We show that on the real line, the comonotonic coupling is optimal for the distorted optimal transport problem when the distortion function is convex and the cost function is submodular and monotone. Some forms of duality and uniqueness results are provided. For inverse-S-shaped distortion functions and linear cost, we obtain the unique form of optimal coupling for all marginal distributions, which turns out to have an interesting ``first comonotonic, then counter-monotonic" dependence structure; for S-shaped distortion functions a similar structure is obtained. Our results highlight several challenges and features in distorted optimal transport, offering a new mathematical bridge between the fields of probability, decision theory, and risk management. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.11238&r=rmg |
| By: | Emma Kroell; Sebastian Jaimungal; Silvana M. Pesenti |
| Abstract: | We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to $n$ insurers whose claims follow different compound Poisson processes. As the reinsurer is uncertain about the insurers' claim severity distributions and frequencies, they design reinsurance contracts that maximise their expected wealth subject to an entropy penalty. Insurers meanwhile seek to maximise their expected utility without ambiguity. We solve this continuous-time Stackelberg game for general reinsurance contracts and find that the reinsurer prices under a distortion of the barycentre of the insurers' models. We apply our results to proportional reinsurance and excess-of-loss reinsurance contracts, and illustrate the solutions numerically. Furthermore, we solve the related problem where the reinsurer maximises, still under ambiguity, their expected utility and compare the solutions. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.11828&r=rmg |
| By: | Philipp Otto; Osman Do\u{g}an; S\"uleyman Ta\c{s}p{\i}nar; Wolfgang Schmid; Anil K. Bera |
| Abstract: | Spatial and spatiotemporal volatility models are a class of models designed to capture spatial dependence in the volatility of spatial and spatiotemporal data. Spatial dependence in the volatility may arise due to spatial spillovers among locations; that is, if two locations are in close proximity, they can exhibit similar volatilities. In this paper, we aim to provide a comprehensive review of the recent literature on spatial and spatiotemporal volatility models. We first briefly review time series volatility models and their multivariate extensions to motivate their spatial and spatiotemporal counterparts. We then review various spatial and spatiotemporal volatility specifications proposed in the literature along with their underlying motivations and estimation strategies. Through this analysis, we effectively compare all models and provide practical recommendations for their appropriate usage. We highlight possible extensions and conclude by outlining directions for future research. |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2308.13061&r=rmg |
| By: | José E. Gutiérrez (Banco de España) |
| Abstract: | This paper presents a contract-theoretic model in which banks choose pre-arranged and ex post funding to finance firms’ liquidity needs through credit lines. When liquidity needs are high, pre-arranged funding is key to sustaining lending and reducing the number of firms going into liquidation. Yet, in the presence of a pecuniary externality on firms’ liquidation values, competitive banks choose insufficient pre-funding compared with a constrained social planner. Constrained efficiency can be restored using regulatory liquidity ratios. The optimal regulatory ratio depends on the frequency of high liquidity need conditions, the value lost after a firm’s liquidation, and the premium on pre-funding. |
| Keywords: | credit lines, bank liquidity risk regulation, LCR, NSFR, Basel III |
| JEL: | G01 G21 G28 G32 |
| Date: | 2023–08 |
| URL: | http://d.repec.org/n?u=RePEc:bde:wpaper:2323&r=rmg |
| By: | Nuno Cassola (CEMAPRE, University of Lisbon, Portugal; Center for European Studies, University of Milano-Bicocca, Italy); Claudio Morana (Center for European Studies, University of Milano-Bicocca, Italy; Rimini Centre for Economic Analysis; CeRP, Collegio Carlo Alberto, Italy); Elisa Ossola (Center for European Studies, University of Milano-Bicocca, Italy; Rimini Centre for Economic Analysis) |
| Abstract: | Climate change poses serious economic, financial, and social challenges to humanity, and green transition policies are now actively implemented in many industrialized countries. Whether financial markets price climate risks is critical to ensuring that the necessary funding flows into environmentally sound projects and that stranded assets risk is adequately managed. In this paper, we assess climate risks for the European stock market within the context of Alessi et al. (2023) greenness and transparency factor. We show that measures of returns spreads of green vs. brown investment might reflect climate risks and assets' exposition to systematic macro-financial risk factors. These latter factors should be filtered out to measure climate risks accurately. We show that climate risks are priced in the European stock market by focusing on aggregate, industry, and company-level data. We propose a market-based green rating procedure, which might be of particular interest to evaluate non-transparent and non-disclosing companies for which ESG information is unavailable. We illustrate its implementation using a sample of over 800 non-transparent firms. |
| Keywords: | Climate risk, environmental disclosure, macro-finance interface, unconditional factor models, asset pricing, European Union |
| JEL: | G01 G11 G12 Q54 |
| Date: | 2023–09 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:23-14&r=rmg |