A framework to measure integrated risk

A framework underlying various models that measure the credit risk of a portfolio is extended in this paper to allow the integration of credit risk with a range of market risks using Monte Carlo simulation. A structural model is proposed that allows interest rates to be stochastic and provides closed-form expressions for the market value of a firm's equity and its probability of default. This model is embedded within the integrated framework and the general approach illustrated by measuring the risk of a foreign exchange forward when there is a significant probability of default by the counterparty. For this example moving from a market risk calculation to an integrated risk calculation reduces the expected future value of the instrument by an amount that could not be calculated using the common pre-settlement exposure technique for estimating the credit risk of a derivative.     

Rare disaster risk and the expected equity risk premium

Consistent with the predictions of rare disaster models, we find that a proxy for the time‐varying probability of rare disasters helps to explain fluctuations in expectations of the equity risk premium. Our proxy for disaster risk is a recently developed measure of global political instability, and the expected market risk premium is from Value Line analysts' expected stock returns. Consistent with long‐run risk models, uncertainty about expected GDP growth and expected consumption growth is also significantly positively related to the expected market risk premium. We obtain similar results when we use the earnings–price ratio and the dividend–price ratio as proxies for the expected market risk premium.     

Model risk of contingent claims

Paralleling regulatory developments, we devise value-at-risk and expected shortfall type risk measures for the potential losses arising from using misspecified models when pricing and hedging contingent claims. Essentially, P&L from model risk corresponds to P&L realized on a perfectly hedged position. Model uncertainty is expressed by a set of pricing models, each of which represents alternative asset price dynamics to the model used for pricing. P&L from model risk is determined relative to each of these models. Using market data, a unified loss distribution is attained by weighing models according to a likelihood criterion involving both calibration quality and model parsimony. Examples demonstrate the magnitude of model risk and corresponding capital buffers necessary to sufficiently protect trading book positions against unexpected losses from model risk. A further application of the model risk framework demonstrates the calculation of gap risk of a barrier option when employing a semi-static hedging strategy.     

On long-term credit risk assessment and rating: towards a new set of models

Institutional investors are supposed to assess credit risk by using a combination of quantitative information such as option models and qualitative assessments. Although option models can be easily constructed, they are not so suitable for the assessment of long-term credit risk that is required by institutional investors. This is mainly because the probability of bankruptcy varies so widely depending on the timing of assessment. We propose a new set of assessment models for long-term credit risk which does not necessarily use stock prices and may incorporate business cycles. The new grand model consists of the two pillars: a long-term cash flow prediction model and a credit risk spread assessment model. The calculated values derived from these models are effectively usable for reasonable calculation of risk spreads. It is quite interesting to see that our investigation indicates that rating bias may exist in the credit risk assessment of the market.     

Model risk of the implied GARCH-normal model

Model risk causes significant losses in financial derivative pricing and hedging. Investors may undertake relatively risky investments due to insufficient hedging or overpaying implied by flawed models. The GARCH model with normal innovations (GARCH-normal) has been adopted to depict the dynamics of the returns in many applications. The implied GARCH-normal model is the one minimizing the mean square error between the market option values and the GARCH-normal option prices. In this study, we investigate the model risk of the implied GARCH-normal model fitted to conditional leptokurtic returns, an important feature of financial data. The risk-neutral GARCH model with conditional leptokurtic innovations is derived by the extended Girsanov principle. The option prices and hedging positions of the conditional leptokurtic GARCH models are obtained by extending the dynamic semiparametric approach of Huang and Guo [Statist. Sin., 2009, 19, 1037–1054]. In the simulation study we find significant model risk of the implied GARCH-normal model in pricing and hedging barrier and lookback options when the underlying dynamics follow a GARCH-t model.     

Conditional risk measures in a bipartite market structure

In this paper, we study the effect of network structure between agents and objects on measures for systemic risk. We model the influence of sharing large exogeneous losses to the financial or (re)insurance market by a bipartite graph. Using Pareto-tailed losses and multivariate regular variation, we obtain asymptotic results for conditional risk measures based on the Value-at-Risk and the Conditional Tail Expectation. These results allow us to assess the influence of an individual institution on the systemic or market risk and vice versa through a collection of conditional risk measures. For large markets, Poisson approximations of the relevant constants are provided. Differences of the conditional risk measures for an underlying homogeneous and inhomogeneous random graph are illustrated by simulations.     

Arbitrage risk and market efficiency

This article explores arbitràge risk and models a testable hypothesis for studies in the treasury bill futures market efficiency. The modern mean-variance theory applied to a hedged arbitrage portfolio is used for the analysis. For a given expected arbitrage profit, we derive minimum variance arbitrage (MVA) conditions. A minimum variance arbitrage line (MVAL) is then derived to show the risk-return tradeoff for arbitrage. Market efficiency conditions are discussed by taking into account arbitrage risk along with bid-ask spreads. The analysis in this study helps explain the puzzle of inefficiencies in the T-bill futures market. Because refinancing and variation margin (due to marking-to-market) are required for arbitrage using futures trading in general, our ex ante arbitrage model using the case of T-bill futures can be applied to other futures markets.     

信用风险缓释工具定价研究

通过对信用风险缓释工具定价进行研究得出:(1)CRM定价的主要影响因素包括无风险基准利率,标的债券的风险敞口、违约概率、违约损失率和期限,以及CRM期限等。(2)同期国债利率和央行票据利率作为CRM的基准利率较为恰当,且模型定价对不同期限、不同信用等级的CRM定价区分度较为合理,模型定价与CRM发行交易定价较为接近,适合我国现阶段CRM产品定价。(3)可以从完善CRM定价基础数据库、探索CRM定价无风险基础利率、创新CRM标的债券评级制度、引导CRM市场主体多元化和优化CRM市场做市商制度等方面提出CRM定价优化对策。     

On the economics of the longevity risk transfer market

We present a model of a longevity risk transfer market with different market players (primary insurers, reinsurers, and capital market investors) and investigate how market dynamics and the market players' roles evolve with progressing market saturation. We find that reinsurers' appetite for longevity risk is the key driver in the early stage of market development. Since diversification benefits with other businesses decrease with every transaction, the reinsurance market is intrinsically antimonopolistic. With the increasing saturation of the reinsurance sector as a whole, its competitiveness shrinks leading to rising expected risk-adjusted returns for capital market investors. We show that in a saturated market, reinsurers should assume the entire longevity risk from primary insurers, diversify it within their business mix, and subsequently pass on only specific (nondiversifiable) components of the longevity risk to the capital markets. Our findings provide valuable suggestions on how to make the best use of the market's limited risk absorption capacity.     

Tail risk of coal futures in China's market

This study evaluates the downside tail risk of coal futures contracts (coke, coking coal and thermal coal) traded in the Chinese market between 2011 and 2021, measured by value at risk (VaR). We examine the one-day-ahead VaR forecasting performance with a hybrid econometric and deep learning model (GARCH-LSTM), GARCH family models, extreme value theory models, quantile regression models and two naïve models (historical simulation and exponentially weighted moving average). We use four backtesting techniques and the model confidence set to identify the optimal models. The results suggest that the models focusing on tail risk or utilising long short-term memory generate more effective risk management.     

考虑背景风险的生命周期投资模型评述——兼论居民投资者风险教育

背景风险是指特定居民在生命周期投资过程中承担的市场风险以外的风险。已有的研究文献认为,劳动、职业、健康与房产等背景对居民投资组合会产生影响。不同文献在引入背景风险后均对模型目标函数围绕新的变量做了技术上的不同处理,进而模型背景风险的估计、模型求解方法也产生了相应的差异。对模型结果的解释则陷于市场有效性之争,并无定论。本文最后给出了生命周期投资模型对居民投资者风险教育的启示。     

A PDE approach for risk measures for derivatives with regime switching

This paper considers a partial differential equation (PDE) approach to evaluate coherent risk measures for derivative instruments when the dynamics of the risky underlying asset are governed by a Markov-modulated geometric Brownian motion (GBM); that is, the appreciation rate and the volatility of the underlying risky asset switch over time according to the state of a continuous-time hidden Markov chain model which describes the state of an economy. The PDE approach provides market practitioners with a flexible and effective way to evaluate risk measures in the Markov-modulated Black–Scholes model. We shall derive the PDEs satisfied by the risk measures for European-style options, barrier options and American-style options.      

农业巨灾风险管理的比较制度分析:一个文献研究

很多研究表明巨灾风险的存在是我国农业保险市场失灵的一个主要原因,对其背后的原因从微观层面进行了诸多论证,并提出了相应的巨灾风险分散的手段,但对于农业巨灾风险管理的研究则刚起步.至于从制度层面进行深入研究的文献,更是少之又少.本文以大量的现有文献研究为基础,首次运用比较制度分析对农业巨灾风险管理进行制度层面的分析,认为互...     

Liquidity risk in derivatives valuation: an improved credit proxy method

The models used to calculate post-crisis valuation adjustments, market risk and capital measures for derivatives are subject to liquidity risk due to severe lack of available information to obtain market implied model parameters. The European Banking Authority has proposed an intersection methodology to calculate a proxy CDS or Bond spread. Due to practical issues of this method, Chourdakis et al. introduce a cross-section approach. In this paper, we extend the cross-section methodology using equity returns, and show that our methodology is significantly more accurate compared to both existing methodologies, and produces more reliable, stable and robust market risk and capital measures, and credit valuation adjustment.     

The impact of the choice of VaR models on the level of regulatory capital according to Basel II

The Basel II framework allows the calculation of the capital requirements for market risk with Value-at-Risk models. Since no special model is prescribed in the framework, banks may use simple models with questionable assumptions concerning their underlying distributions. Our numerical analysis reveals that simple VaR models that perform noticeably worse than comparable simple models with more realistic assumptions may lead to a lower level of regulatory capital for banks. For this reason, banks have a major incentive to implement bad models. This is obviously contrary to the interests of regulatory authorities.     

Systemic risk in the European sovereign and banking system

We investigate the systemic risk of the European sovereign and banking system during 2008–2013. We utilize a conditional measure of systemic risk that reflects market perceptions and can be intuitively interpreted as an entity’s conditional joint probability of default, given the hypothetical default of other entities. The measure of systemic risk is applicable to high dimensions and not only incorporates individual default risk characteristics but also captures the underlying interdependent relations between sovereigns and banks in a multivariate setting. In empirical applications, our results reveal significant time variation in systemic risk spillover effects for the sovereign and banking system. We find that systemic risk is mainly driven by risk premiums coupled with a steady increase in physical default risk.     

Jump risk premia across major international equity markets

We decompose the non-diversifiable market risk into continuous and discontinuous components and jump systematic risks into positive vs. negative and small vs. large components. We examine their association with equity risk premia across major equity markets. We show that developed markets jumps are more closely linked to the aggregate market index than emerging and frontier ones. The reward for bearing both the continuous and downside jump risks is positive during the pre-crisis period whereas the reward for bearing the upside and large jump risks is negative during the crisis and post-crisis periods. We also provide evidence of significant continuous and discontinuous leverage effects during the pre-crisis period, suggesting that both continuous and discontinuous price and volatility risks share compensations for common underlying risk factors.     

Generalized Pareto processes and fund liquidity risk

Motivated by the modelling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a modified ARGP and a thresholded ARGP. These models are able to capture key data features apparent in fund liquidity data and reflect the underlying phenomena via easily interpreted, low-dimensional model parameters. We establish stationarity and ergodicity, provide a link to the class of shot-noise processes, and determine the associated interarrival distributions for exceedances. Moreover, we provide estimators for all relevant model parameters and establish consistency and asymptotic normality for all estimators (except the threshold parameter, which is to be estimated in advance). Finally, we illustrate our approach using real-world fund redemption data, and we discuss the goodness-of-fit of the estimated models.     

The world ex ante risk premium: an empirical investigation

A number of recent papers have focused on testing the linearity restrictions implied by international asset pricing models. The tests, however, have not addressed an additional restriction implied by the models; namely, that the risk premium on the world portfolio is positive. This study provides a direct assessment of this restriction. The evidence indicates that the ex ante world market risk premium can be negative. The results are robust to market proxies that are hedged and unhedged with respect to currency risk. Subperiod analysis indicates that the rejection of the positive risk premium restriction is driven by the first half of the sample period.