基于B-K二叉树利率模型的巨灾债券定价研究

针对一种巨灾保险风险证券化产品-巨灾债券的定价问题,首次考虑了我国短期利率的期限结构,并在此基础上提出了Black-Karasinski利率二叉树建立方法(B-K模型),以此确定了中国短期无风险利率,最后通过Louberge巨灾债券理论定价方法试着对我国假想台风损失巨灾债券进行了具体定价,为我国进行巨灾保险风险证券化定价方面提供了一种新的尝试.     

Catastrophe risk management with counterparty risk using alternative instruments

Since weather-related disasters have an upward trend-cycle movement and the global financial crisis has revealed the severity of counterparty risk, this study reinvestigates and incorporates the catastrophe characteristics and counterparty risk into the valuation of catastrophe products. First, the excess of loss reinsurance is traditionally used to reduce catastrophe risk. Its premium is estimated under these catastrophe characteristics. Second, this paper looks into the price of catastrophe futures and spread option contracts that are based on a catastrophe index. The (re)insurer can apply these exchange-traded derivatives to reduce catastrophe risk without counterparty risk. Third, this paper takes counterparty risk into account to value catastrophe bonds and catastrophe equity puts. Thus, the fair valuations of these two instruments are revealed to the buyer.     

Longstaff利率下巨灾债券定价的一种FFT方法——基于广东省1989~2015台风数据的实证分析

传统的保险市场难以满足日益频发的巨灾风险分散需求,巨灾债券作为一种非传统金融创新工具提供了一种新的分散机制,而精准定价则对巨灾债券的成功发行与交易起着关键作用。本文基于风险中性测度技术,在Longstaff随机利率且巨灾风险累积损失服从复合泊松损失条件下,得到了零息票巨灾债券价格公式;进一步结合广东省1989~2015年台风风暴潮灾害损失数据进行实证分析;最后,针对定价公式复杂性,本文利用快速傅里叶变换方法进行数值求解,结果验证了本文所构模型的可行性。本文的研究是希望能为我国发行巨灾债券与风险测度提供一定的理论基础与技术支持。     

Valuation of catastrophe reinsurance with catastrophe bonds

This study develops a contingent-claim framework for valuing a reinsurance contract and examines how a reinsurance company can increase the value of a reinsurance contract and reduce its default risk by issuing catastrophe (CAT) bonds. The results also show how the changes in contract values and default risk premium are related to basis risk, trigger level, catastrophe risk, interest rate risk, and the reinsurer’s capital position.     

基于贝叶斯分析的中国商业银行内部欺诈分析

内部欺诈事件类型是中国商业银行最严重的操作风险类型。但由于操作风险本质特征和中国商业银行内部欺诈损失数据收集年度较短,数据匮乏,小样本数据容易导致参数结果不稳定。为了在小样本数据下进行更准确的度量,本文采用贝叶斯马尔科夫蒙特卡洛模拟方法,在损失分布法框架下,假设损失频率服从泊松-伽马分布,而损失强度服从广义帕累托-混合伽马分布,分析后验分布的形式,获得中国商业银行不同业务线的内部欺诈损失频率和损失强度的后验分布估计,并进行蒙特卡罗模拟获得不同业务线内部欺诈的风险联合分布。结果表明,拟合结果很好,与传统极值分析法相比,基于利用贝叶斯的分析获得的后验分布可以作为未来的先验分布,有利于在较小样本下获得较真实的参数估计,本方法有助于银行降低监管资本要求。     

基于风险网络的大型工程项目风险度量方法研究

风险度量是风险管理的基础,提出适合大型工程项目风险的风险度量方法.针对大型工程项目风险因素、风险信息、风险损失之间的复杂联系,构建大型工程项目风险网络,分别采用贝叶斯网络推理和网络层次分析法获得风险发生概率和风险量的估计,从而提出基于风险网络的大型工程项目风险度量方法.方法将风险损失量和风险损失发生概率进行了明确合理的结合,既可用于度量客观风险,也可用于度量主观风险.最后以槽菁头隧道施工风险管理为例说明该方法的具体应用步骤和效果.     

Reexamining the feasibility of diversification and transfer instruments on smoothing catastrophe risk

The present study discusses the effects of diversification and transfer of risk by global insurers on smoothing the peak of catastrophic claims. Empirical experiments indicate that the occurrence frequency of natural catastrophes (NatCat) has a serially dependent trend and that the Cox–Ingersoll–Ross square-root model for global insured losses is best fit than any other static distributions. The results are used to develop a NatCat risk insurance model that sets up a NatCat premium formula, uses the serially dependent dynamics of insured loss and establishes the cash flow of all involved parties while considering corporate income tax and no additional risk premium. The simulation results based on this model shows that fluctuation reserves, catastrophe bonds and catastrophe funds with payback schemes are feasible options for smoothing risk because they can benefit all long-term involved parties, including insurance company shareholders, the insured, bondholders, the fund and the government (i.e. taxpayers).     

防洪风险分析中改进的组合分布模型研究

洪水变量分布的选择是防洪风险分析中的一个重要工作 ,目前常用 P- 分布来描述洪水的随机特性 .建立在组合分布模型的基础上 ,本文提出了改进的组合分布模型 ,给出了不同情况下求最优分界点的模型 .实例计算表明 ,改进的组合分布模型在理论和应用上都优于原始分布 ,它能较好地反映洪水的风险     

Valuation of contingent convertible catastrophe bonds — The case for equity conversion

Within the context of banking-related literature on contingent convertible bonds, we comprehensively formalise the design and features of a relatively new type of insurance-linked security, called a contingent convertible catastrophe bond (CocoCat). We begin with a discussion on its design and compare its relative merits to catastrophe bonds and catastrophe-equity puts. Subsequently, we derive analytical valuation formulae for index-linked CocoCats under the assumption of independence between natural catastrophe and financial market risks. We model natural catastrophe losses by a time-inhomogeneous compound Poisson process, with the interest-rate process governed by the Longstaff model. By using an exponential change of measure on the loss process, as well as a Girsanov-like transformation to synthetically remove the correlation between the share and interest-rate processes, we obtain these analytical formulae. Using selected parameter values in line with earlier research, we numerically analyse our valuation formulae for index-linked CocoCats. An analysis of the results reveals that the CocoCat prices are most sensitive to changing interest-rates, conversion fractions and the threshold levels defining the trigger times.     

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In this paper, we investigate a competing risks model based on exponentiated Weibull distribution under Type-I progressively hybrid censoring scheme. To estimate the unknown parameters and reliability function, the maximum likelihood estimators and asymptotic confidence intervals are derived. Since Bayesian posterior density functions cannot be given in closed forms, we adopt Markov chain Monte Carlo method to calculate approximate Bayes estimators and highest posterior density credible intervals. To illustrate the estimation methods, a simulation study is carried out with numerical results. It is concluded that the maximum likelihood estimation and Bayesian estimation can be used for statistical inference in competing risks model under Type-I progressively hybrid censoring scheme.     

Robust Bayesian Inference for Seemingly Unrelated Regressions with Elliptical Errors

Bayesian inference is considered for the seemingly unrelated regressions with an elliptically contoured error distribution. We show that the posterior distribution of the regression parameters and the predictive distribution of future observations under elliptical errors assumption are identical to those obtained under independently distributed normal errors when an improper prior is used. This gives inference robustness with respect to departures from the reference case of independent sampling from the normal distribution.     

基于贝叶斯极值估计的商业银行内部欺诈风险度量研究

内部欺诈风险是我国商业银行面临的一个重大风险来源。本文针对内部欺诈具有的低频率高损失的特点,采用不同分布分段刻画其损失统计分布规律,对于低于和高于门限值的样本点,采用Box-Cox变换和全Paretian分布模型进行分析,然后采用贝叶斯估计对全Paretian分布模型的参数进行估计,接着在此基础上对建立了一个内部欺诈风险度量模型,然后使用所构建的风险度量模型对操作风险在险风险值、经济资本和最大可能损失进行了测算,最后提出了防范操作风险的政策建议。     

Shape mixtures of multivariate skew-normal distributions

Classes of shape mixtures of independent and dependent multivariate skew-normal distributions are considered and some of their main properties are studied. If interpreted from a Bayesian point of view, the results obtained in this paper bring tractability to the problem of inference for the shape parameter, that is, the posterior distribution can be written in analytic form. Robust inference for location and scale parameters is also obtained under particular conditions.     

Economical sampling plans with warranty based on truncated data from Burr type XII distribution

Economical sampling plans to ensure the qualities of Burr type XII distributed lifetimes were established using a truncated life test. The Bayesian inference method was used to address the lot-to-lot variation of products. The sampling plan was characterized by the sample size and the acceptance number to minimize the expected total cost. A simple empirical Bayesian estimation method was provided to estimate the hyperparameters of prior distribution, and simulation studies were conducted to validate the proposed empirical Bayesian estimation method. Lastly, the application of this proposed method was illustrated using two examples.     

A stochastic approach to the flood control problem

We propose a stochastic model in conjunction with reliability analysis concepts to improve estimates for the protection volume that should be allocated in a reservoir to control a flood wave. In this approach, the inflow that reaches the reservoir during a flood is considered to be a load, and the reservoir capacity to control this flood is considered to be the resistance that the reservoir offers against the propagation of the flood. Here, the load and the resistance are modeled as a diffusion stochastic process, and the protection volume is determined via Itô's formula. In this scenario, an explicit formula for the failure risk is derived. The parameter inference is carried out by a Bayesian approach for a time discrete version of the load, and the estimates are obtained by using Monte Carlo Markov Chain Algorithms (MCMC). The maximum likelihood estimators are used in the comparison. The record utilized comprises nine years of daily inflow rates during flood periods that come to the Chavantes hydroelectric power plant (CHPP) in Southeast Brazil. The protection volumes estimated through the proposed model are compared to the volumes obtained by other existing methods.     

Extreme values of the stationary distribution of random walks on directed graphs

We examine the stationary distribution of random walks on directed graphs. In particular, we focus on the principal ratio, which is the ratio of maximum to minimum values of vertices in the stationary distribution. We give an upper bound for this ratio over all strongly connected graphs on n vertices. We characterize all graphs achieving the upper bound and we give explicit constructions for these extremal graphs. Additionally, we show that under certain conditions, the principal ratio is tightly bounded. We also provide counterexamples to show the principal ratio cannot be tightly bounded under weaker conditions.     

Reliability analysis for Weibull distribution with homogeneous heavily censored data based on Bayesian and least-squares methods

The reliability for Weibull distribution with homogeneous heavily censored data is analyzed in this study. The universal model of heavily censored data and existing methods, including maximum likelihood, least-squares, E-Bayesian estimation, and hierarchical Bayesian methods, are introduced. An improved method is proposed based on Bayesian inference and least-squares method. In this method, the Bayes estimations of failure probabilities are focused on for all the samples. The conjugate prior distribution of failure probability is set, and an optimization model is developed by maximizing the information entropy of prior distribution to determine the hyper-parameters. By integrating the likelihood function, the posterior distribution of failure probability is then derived to yield the Bayes estimation of failure probability. The estimations of reliability parameters are obtained by fitting distribution curve using least-squares method. The four existing methods are compared with the proposed method in terms of applicability, precision, efficiency, robustness, and simplicity. Specifically, the closed form expressions concerning E-Bayesian estimation and hierarchical Bayesian methods are derived and used. The comparisons demonstrate that the improved method is superior. Finally, three illustrative examples are presented to show the application of the proposed method.     

Securitization of motor insurance loss rate risks

In an attempt to transfer the loss rate risks in motor insurance to the capital market, we use the tranche technique to hedge the motor insurance risks. This paper illustrates AXA and their securitization of French motor insurance in 2005 as an example. Though this application is new, this transaction is based on a concept similar to CDOs. Tranches of bonds are constructed on the basis of the expected loss ratio from motor insurance policy holders’ groups. As a consequence we develop motor loss rate bonds using the structure of synthetic CDOs. The coupon payments of each tranche depend on the level of the loss rates of the underlying motor insurance pool. We show the integral formulas for the loss tranche contract where the loss distribution is modelled with discounted compound Poisson process. Esscher transform is chosen for a risk adjusted measure change and Fourier inversion method is used to calculate the price of the motor claim rate securities. The pricing methods of the tranches are illustrated, and possible suggestions to improve the pricing method and the design of these new securities follow.     

以截尾伽玛分布为先验分布的产品失效率的贝叶斯估计

本文研究了基于泊松分布的产品失效率估计问题.利用贝叶斯统计推断方法,获得了以截尾伽玛分布为先验分布时,产品失效率的贝叶斯估计和相关性质,推广了以伽玛分布为先验分布的贝叶斯估计结果.     

Arc refractor methods for adaptive importance sampling on large Bayesian networks under evidential reasoning

Approximate Bayesian inference by importance sampling derives probabilistic statements from a Bayesian network, an essential part of evidential reasoning with the network and an important aspect of many Bayesian methods. A critical problem in importance sampling on Bayesian networks is the selection of a good importance function to sample a network’s prior and posterior probability distribution. The initially optimal importance functions eventually start deviating from the optimal function when sampling a network’s posterior distribution given evidence, even when adaptive methods are used that adjust an importance function to the evidence by learning. In this article we propose a new family of Refractor Importance Sampling (RIS) algorithms for adaptive importance sampling under evidential reasoning. RIS applies “arc refractors” to a Bayesian network by adding new arcs and refining the conditional probability tables. The goal of RIS is to optimize the importance function for the posterior distribution and reduce the error variance of sampling. Our experimental results show a significant improvement of RIS over state-of-the-art adaptive importance sampling algorithms.