Single name credit default swaptions meet single sided jump models

Credit risk modeling is about modeling losses. These losses are typically coming unexpectedly and triggered by shocks. So any process modeling the stochastic nature of losses should reasonable include jumps. In this paper we review a few jump driven models for the valuation of Credit Default Swaps (CDSs) and show how under these dynamic models also pricing of (exotic) derivatives on single name CDSs is possible. More precisely, we set up fundamental firm-value models that allow for fast pricing of the ‘vanillas’ of the CDS derivative markets: payer and receiver swaptions. It turns out that the proposed model is able to produce realistic implied volatility smiles. Moreover, we detail how a CDS spread simulator can be set up under this framework and illustrate its use for the pricing of exotic derivatives with single name CDSs as underliers.     

Flexible dependence modeling of operational risk losses and its impact on total capital requirements

Operational risk data, when available, are usually scarce, heavy-tailed and possibly dependent. In this work, we introduce a model that captures such real-world characteristics and explicitly deals with heterogeneous pairwise and tail dependence of losses. By considering flexible families of copulas, we can easily move beyond modeling bivariate dependence among losses and estimate the total risk capital for the seven- and eight-dimensional distributions of event types and business lines. Using real-world data, we then evaluate the impact of realistic dependence modeling on estimating the total regulatory capital, which turns out to be up to 38% smaller than what the standard Basel approach would prescribe.     

Approximation of aggregate and extremal losses within the very heavy tails framework

The loss distribution approach is one of the three advanced measurement approaches to the Pillar I modeling proposed by Basel II in 2001. In this paper, one possible approximation of the aggregate and maximum loss distribution in the extremely low frequency/high severity case is given, i.e. the case of infinite mean of the loss sizes and loss inter-arrival times. In this study, independent but not identically distributed losses are considered. The minimum loss amount is considered increasing over time. A Monte Carlo simulation algorithm is presented and several quantiles are estimated. The same approximation is used for modeling the maximum and aggregate worldwide economy losses caused by very rare and very extreme events such as 9/11, the Russian rouble crisis, and the U.S. subprime mortgage crisis. The model parameters are fit on a data sample of operational losses. The respective aggregate and extremal loss quantiles are calculated.     

A Theoretical Framework for Incorporating Scenarios into Operational Risk Modeling

In this paper, I introduce a theoretically justified framework that incorporates scenario analysis into operational risk modeling. The basis for the framework is the idea that only worst-case scenarios contain valuable information about the tail behavior of operational losses. In addition, worst-case scenarios introduce a natural order among scenarios that makes possible a comparison of the ordered scenario losses with the corresponding quantiles of the severity distribution that research derives from historical losses. Worst-case scenarios contain information that enters the quantification process in the form of lower bound constraints on the specific quantiles of the severity distribution. The framework gives rise to several alternative approaches to incorporating scenarios.     

Modeling Frost Losses: Application to Pricing Frost Insurance

The main objective of this article is to model the losses caused by frost events and use it to price frost insurance. Since the data on frost events are either unavailable or rarely available, we have chosen to obtain a model for frost losses based on temperature by using some fundamental agricultural engineering findings on frost damage. The main challenges in modeling frost loss variables are, first, the nonlinearity of the frost losses with respect to the temperature and, second, the fruit resistance to the first few hours of low temperature. We address both issues when introducing our frost loss variable. Then after finding the loss model, we use it to price frost insurance for a general family of insurance contracts that do not generate any risk of moral hazard. In particular, we will find the premiums of stop-loss policies for losses to citrus fruits using Value at Risk, Conditional Value at Risk, and Wang's premium based on temperature data from San Joaquin Drainage in California.     

Factor Copula Approaches for Assessing Spatially Dependent High-Dimensional Risks

In this article, we propose an innovative approach for modeling spatial dependence among losses from various geographical locations. The proposed model converts the challenging task of modeling complex spatial dependence structures into a relatively easier task of estimating a continuous function, of which the arguments can be the coordinates of the locations. The approach is based on factor copula models, which can capture various linear and nonlinear dependence. We use radial basis functions as the kernel smoother for estimating the key function that models all the spatial dependence structures. A case study on a thunderstorm wind loss dataset demonstrates the analysis and the usefulness of the proposed approach. Extensions to spatiotemporal models and to models for discrete data are briefly introduced, with an example given for modeling loss frequency with excess zeros.     

Cybersecurity Insurance: Modeling and Pricing

Cybersecurity risk has attracted considerable attention in recent decades. However, the modeling of cybersecurity risk is still in its infancy, mainly because of its unique characteristics. In this study, we develop a framework for modeling and pricing cybersecurity risk. The proposed model consists of three components: the epidemic model, loss function, and premium strategy. We study the dynamic upper bounds for the infection probabilities based on both Markov and non-Markov models. A simulation approach is proposed to compute the premium for cybersecurity risk for practical use. The effects of different infection distributions and dependence among infection processes on the losses are also studied.     

Multivariate Cox Hidden Markov models with an application to operational risk

ABSTRACT

Modeling multivariate time-series aggregate losses is an important actuarial topic that is very challenging due to the fact that losses can be serially dependent with heterogeneous dependence structures across loss types and business lines. In this paper, we investigate a flexible class of multivariate Cox Hidden Markov Models for the joint arrival process of loss events. Some of the nice properties possessed by this class of models, such as closed-form expressions, thinning properties and model versatility are discussed in details. We provide the expectation-maximization (EM) algorithm for efficient model calibration. Applying the proposed model to an operational risk dataset, we demonstrate that the model offers sufficient flexibility to capture most characteristics of the observed loss frequencies. By modeling the log-transformed loss severities through mixture of Erlang distributions, we can model the aggregate losses. Finally, out-of-sample testing shows that the proposed model is adequate to predict short-term future operational risk losses.     

Reserve risk estimation in a linear model

This paper presents the linear model, a framework for stochastic modeling of known methods as well as for the development of new methods of loss reserving. The linear model allows the determination of optimal predictors of non-observable cumulated and incremental losses and thus the derivation of optimal reserves by minimization of the expected squared prediction error.     

Systemic Weather Risk and Crop Insurance: The Case of China

This article explores the possibility of spatial diversification of weather risk for 17 agricultural production regions in China. We investigate the relation between the size of the buffer load and the size of the trading area of a hypothetical temperature‐based insurance. The analysis adopts the hierarchical Archimedean copula approach that allows for flexible modeling of the dependence structure of insured losses. We find that the spatial diversification effect depends on the type of the weather index and the strike level of the insurance. Our findings are relevant for the current discussion on the viability of private crop insurance in China.     

Measuring financial risks with copulas

This paper is concerned with the statistical modeling of the dependence structure of multivariate financial data using the concept of copulas. We select some special copulas and identify the type of dependency captured by each one. We fit copulas to daily returns and simulate from the fitted models. We compare the effect of the choice of copula on risk measures and assess the variability of one-step-ahead predictions of portfolio losses. We analyze extreme scenarios and fit extreme value copulas to the block maxima and minima from daily returns. The stress scenarios constructed are compared to those obtained using models from the extreme value theory. We illustrate the usefulness of the copula approach using two stock market indexes.     

On stability of operational risk estimates by LDA: From causes to approaches

The stability of estimates is critical when applying advanced measurement approaches (AMA) such as loss distribution approach (LDA) for operational risk capital modeling. Recent studies have identified issues associated with capital estimates by applying the maximum likelihood estimation (MLE) method for truncated distributions: significant upward mean-bias, considerable uncertainty about the estimates, and non-robustness to both small and large losses. Although alternative estimation approaches have been proposed, there has not been any comprehensive study of how alternative approaches perform compared to the MLE method. This paper is the first comprehensive study on the performance of various potentially promising alternative approaches (including minimum distance approach, quantile distance approach, scaling-based bias correction, upward scaling of lower quantiles, and right-truncated distributions) as compared to MLE with regards to accuracy, precision and robustness. More importantly, based on the properties of each estimator, we propose a right-truncation with probability weighted least squares method, by combining the right-truncated distribution and minimizing a probability weighted distance (i.e., the quadratic upper-tail Anderson–Darling distance), and we find it significantly reduces the bias and volatility of capital estimates and improves the robustness of capital estimates to small losses near the threshold or moving the threshold, demonstrated by both simulation results and real data application.     

Credit risk in the leasing industry

This paper is devoted to the credit risk modeling issues of retail lease portfolios. Using a re-sampling method, I estimate the probability density function of losses and VaR measures in a portfolio of 46,732 leases issued between 1990 and 2000 by a major European financial institution. My results show that physical collaterals play a major role in reducing the credit risk associated with lease portfolios. However, because of insufficient recognition of such collaterals under the new regulatory capital framework (Basel II), significant differences are observed between the estimated capital requirements and those calculated in accordance with the various Basel II approaches.     

Estimating loss-given default through advanced credibility theory

The New Basel Accord allows internationally active banking organizations to calculate their credit risk capital requirements using an internal ratings based approach, subject to supervisory review. One of the modeling components is the loss-given default (LGD): it represents the credit loss for a bank when extreme events occur that influence the obligor ability to repay his debts to the bank. Among researchers and practitioners the use of statistical models such as linear regression, Tobit or decision trees is quite common in order to compute LGDs as a forecasting of historical losses. However, these statistical techniques do not seem to provide robust estimation and show low performance. These results could be driven by some factors that make differences in LGD, such as the presence and quality of collateral, timing of the business cycle, workout process management and M&A activity among banks. This paper evaluates an alternative method of modeling LGD using a technique based on advanced credibility theory typically used in actuarial modeling. This technique provides a statistical component to the credit and workout experts’ opinion embedded in the collateral and workout management process and improve the predictive power of forecasting. The model has been applied to an Italian Bank Retail portfolio represented by Overdrafts; the application of credibility theory provides a higher predictive power of LGD estimation and an out-of-time sample backtesting has shown a stable accuracy of estimates with respect to the traditional LGD model.     

区域农业产量风险低估的评价研究

作为我国大力推广的创新型保险产品,区域农业收入保险是对区域农业产量风险与价格风险的双重保障。然而,单产数据空间聚合造成产量风险的低估却是当前农业收入风险评估的一个重要问题,尤其是随着空间区域的增大、产量风险的低估程度就越严重。本文以湖北省黄冈市、咸宁市和十堰市三个地市级水稻产量风险评估为案例,通过两种方法定量评价地市级水稻产量风险的低估程度。方法一是当前最常见的区域产量风险评估方法,直接利用地市级产量数据构建风险评估模型计算产量风险;方法二是收集地市级对应区县产量数据,通过Copula函数构建县级产量损失序列的联合概率分布后,通过Monte Carlo模拟产生区县产量损失序列样本后计算地市级产量风险。通过结果比较发现,方法一获得的三个地级市水稻产量风险较方法二平均低估了51.27%,证明了空间尺度建模不当会带来产量风险评估的严重低估。     

Asymptotic Analysis of the Loss Given Default in the Presence of Multivariate Regular Variation

Consider a portfolio of n obligors subject to possible default. We propose a new structural model for the loss given default, which takes into account the severity of default. Then we study the tail behavior of the loss given default under the assumption that the losses of the n obligors jointly follow a multivariate regular variation structure. This structure provides an ideal framework for modeling both heavy tails and asymptotic dependence. Multivariate models involving Archimedean copulas and mixtures are revisited. As applications, we derive asymptotic estimates for the value at risk and conditional tail expectation of the loss given default and compare them with the traditional empirical estimates.     

信贷损失准备计提的理论分析

本文在预期损失与损失准备概念的基础上,通过对贷款价值、预期损失与违约升水之间关系的分析提出了信贷损失准备计提的理论与方法,指出基于未来现金流量折现法的信贷准备计提方法更能反映贷款的真实价值。最后结合银行信贷损失准备计提的实践,对理论方法与实践中的作法进行了简要的评析。     

Accounting Losses and Earnings Response Coefficients: The Impact of Leverage and Growth Opportunities

This paper investigates how accounting losses affect the relationship between accounting earnings and stock returns, i.e. earnings response coefficients (ERCs), in different leverage and growth categories. In a sample of NYSE firms between 1975 and 1990, the exclusion of losses improves the ERCs considerably. While the impact of losses on ERCs is highest in the subgroup including high growth opportunity firms, the exclusion of losses does not improve ERCs as significantly among firms with low growth opportunities. The results further support the hypothesis that the impact of losses on ERCs is different in different financial leverage subgroups. The measured increase in ERCs is most significant among the least levered firms. The observation that the impact of losses on ERCs is related to growth opportunities and financial leverage is clearly observable also in different size categories. The effects of growth opportunities and financial leverage are also incrementally important with respect to each other. In general, the results indicate that the impact of growth opportunities and financial leverage on ERCs is clearly observable especially when losses and profits are analyzed separately.     

Cyclical correlations, credit contagion, and portfolio losses

We model aggregate credit losses on large portfolios of financial positions contracted with firms subject to both cyclical default correlation and direct default contagion processes. Cyclical correlation is due to the dependence of firms on common economic factors. Contagion is associated with the local interaction of firms with their business partners. We provide an explicit normal approximation of the distribution of portfolio losses. We quantify the relation between the variability of global economic fundamentals, strength of local firm interaction, and the fluctuation of losses. We find that cyclical oscillations in fundamentals dominate average losses, while local interaction causes additional fluctuations of losses around their average. The strength of the contagion-induced loss variability depends on the complexity of the business partner network.     

Forecasting bank loans loss-given-default

With the advent of the new Basel Capital Accord, banking organizations are invited to estimate credit risk capital requirements using an internal ratings based approach. In order to be compliant with this approach, institutions must estimate the loss-given-default, the fraction of the credit exposure that is lost if the borrower defaults. This study evaluates the ability of a parametric fractional response regression and a nonparametric regression tree model to forecast bank loan credit losses. The out-of-sample predictive ability of these models is evaluated at several recovery horizons after the default event. The out-of-time predictive ability is also estimated for a recovery horizon of 1 year. The performance of the models is benchmarked against recovery estimates given by historical averages. The results suggest that regression trees are an interesting alternative to parametric models in modeling and forecasting loss-given-default.