基于Wang两因素模型的台风巨灾债券定价——利用广东省台风数据的实证研究北大核心

我国是世界上自然灾害发生较为频繁的国家之一,由于自然灾害的偶发性和不可预测性,往往会带来较大的经济损失和社会危害。巨灾债券作为巨灾风险证券化产品,能够有效弥补巨灾保险的不足,分散巨灾风险,降低巨灾造成的损害,在我国有着广阔的市场前景。巨灾债券进行市场化运营的关键在于定价是否准确。本文利用广东省1983年至2017年间的台风损失数据和1951年至2017年间的台风登陆次数数据,基于非寿险精算和蒙特卡洛模拟方法进行巨灾损失分布和发生次数的拟合,运用Wang两因素模型对台风巨灾债券定价进行实证分析。研究结果表明,巨灾债券价格随着触发概率的下降而上升,保障型债券比无保障型债券价格更高。由上述研究结论带来的启示:第一,建立健全巨灾损失数据库,为巨灾债券定价提供数据支撑;第二,加大财政支持力度,建立巨灾债券融资担保制度;第三,完善相关法律法规和监管制度,为巨灾债券提供制度保障。     

考虑多风险因素的我国巨灾债券定价研究

巨灾债券是巨灾风险转移资本市场上交易最活跃、使用最广泛的金融创新产品。本文创新性的引入资产、负债和利率模型,结合我国地震损失程度和频率分布对我国巨灾债券定价进行了实证研究,并在资产负债管理视角下首次对多风险因素作用下的我国巨灾债券定价进行了量化研究。研究结果表明违约风险、道德风险、基差风险对巨灾债券价格具有显著的影响且其共同作用使巨灾债券价格进一步降低,有效的资产负债管理可以分散上述风险。本文研究对保险公司发行巨灾债券具有精算定价参考作用,同时表明保险公司在发行巨灾债券时应当加强其资产负债管理,以达到规避风险、保障偿付能力的目的。     

基于资产负债管理的我国巨灾再保险定价研究

我国是自然灾害种类多、频率高、损失大的国家。对巨灾保险需求很大,但是由于巨灾的特性,给保险公司带来的风险极大,因此对巨灾再保险有很大需求。通过建立资产、负债和利率模型,根据我国洪水、暴雨损失程度和频率拟合关系式,采用蒙特卡罗模拟分别计算有无违约风险和发行巨灾债券的巨灾再保险费率。通过计算结果看出,发行巨灾债券能够降低违约风险,提高巨灾再保险费率,增加巨灾再保险合同的价值。同时,还考虑了资产负债比、免赔额、债券价值与负债占比对巨灾再保险费率的影响并得到合理结果。本文根据我国洪水、暴雨实际发生情况,从资产负债管理视角研究巨灾再保险定价问题,对于开展适合中国国情的巨灾再保险具有理论指导意义。     

洪水巨灾债券及其定价的实证研究——基于Wang两因素模型对我国洪水债券定价的分析

近年来,巨灾频发,巨灾债券已成为国际公认而又行之有效的巨灾风险转移工具。我国自然灾害多发,全国有2／3的国土面积遭受洪水威胁。因此,在我国发行巨灾债券特别是洪水巨灾债券意义重大。而发行巨灾债券的难点便在于债券的合理定价。本文收集了1961年至2009年我国洪水灾害数据,运用Wang两因素模型对其经验估计分布进行了调整,得出了中国市场上一年期洪水巨灾债券的价格。以期对我国臣灾债券的合理定价有所借鉴。最后,文章针对中国发行洪水巨灾债券的细节方面提出了建议。     

我国农业慈善巨灾债券定价研究——以河南省洪灾慈善巨灾债券为例

我国农业巨灾损失的规模往往大大超过来自内部和外部的救灾资金,农业慈善巨灾债券给低概率高损失的农业巨灾风险分散到资本市场提供了机会。在探讨农业慈善巨灾债券的背景、性质和作用基础上,运用修正的Wang两因素模型,以河南省洪灾为例对农业慈善巨灾债券的定价问题进行了研究,认为农业慈善巨灾债券可以成为我国农业巨灾风险分散的一种有效替代工具。     

巨灾风险证券化及我国地震巨灾债券的初步设计

巨灾风险证券化作为一种金融创新产品,能够有效地转移和分散巨灾风险。本文首先阐释了传统风险管理技术——再保险的微观运作机制,并指出其在面对巨灾风险时具有明显的局限性,进而推演出引入巨灾保险风险证券化的必要性。本文以1978～2010年间中国发生的214起地震灾害事故为样本,根据地震损失分布特点并利用资本资产定价模型(CAPM)和债券定价原理推算了地震巨灾债券的收益率及价格,从而对我国地震巨灾债券进行了初步设计。最后结合我国保险业和资本市场的发展现状提出了相应的建议。     

巨灾债券的运作原理及在我国的应用

随着保险公司承担越来越多的风险,巨灾债券逐渐发展成为其分散风险的又一种工具。本文将巨灾债券的运作过程分为三个阶段,对其运作原理进行了分析,并介绍了巨灾债券的定价模型,为巨灾债券的定价提供一种方案：一种金融产品能否顺利发行取决于其发展的前景。本文最后分析了我国发行巨灾债券的必要性和可行性,并提出构建我国巨灾债券的相关建议。     

复合触发机制下地震巨灾债券定价研究——考虑风险反馈的影响

本文基于均衡定价理论,利用CIR随机利率模型模拟无风险利率的变化情况,使用Copula函数建立复合触发机制下的联合分布函数,计算得出1～5年期的地震巨灾债券的价格。研究表明:风险触发反馈条件越严格,有效期越短,则风险暴露的程度越低,巨灾债券的价格就会越高;风险补偿能够提高巨灾债券的价格,使巨灾债券满足不同投资人的需求。相应的政策建议为确定相应的风险指数以有利于债券定价、发行多种类型的巨灾债券等。     

尖峰厚尾巨灾损失数据的组合分布模型

具有尖峰厚尾特征的巨灾损失数据,通常的损失分布模型很难对其进行拟合,这给巨灾风险管理带来了极大挑战。近几年,关于组合分布模型的研究为巨灾损失数据的拟合提供了一种新的建模思路。组合分布模型是两个普通损失分布的平滑组合。本文将逆威布尔分布分别与帕累托分布和广义帕累托分布进行组合,构建了三个新的组合分布模型,即固定权重的逆威布尔-帕累托组合分布模型、可变权重的逆威布尔-帕累托组合分布模型以及可变权重的逆威布尔-广义帕累托组合分布模型。与现有的组合分布模型相比,这三个组合分布模型结构更加简洁,为拟合尖峰厚尾的巨灾损失数据提供了新的备选模型。     

国债期货定价与交割期权关系实证研究

本文研究我国国债期货中交割期权对期货定价的影响。通过加入对交割期权的考虑,建立期货价格与远期价格的关系,并建立了国债期货定价的线性回归模型。模型认为,国债期货的价格除了和利率有关,还和不同可交割债券对利率变化的敏感性有关,正是这种不同的利率敏感性导致交割期权价值的不同。本文采用期货仿真交易数据和银行间市场的可交割债券实盘数据进行实证研究。分析结果显示存在很强的证据表明交割期权对国债期货定价有显著的影响。     

Catastrophe Risk Bonds

Abstract

This article examines the pricing of catastrophe risk bonds. Catastrophe risk cannot be hedged by traditional securities. Therefore, the pricing of catastrophe risk bonds requires an incomplete markets setting, and this creates special difficulties in the pricing methodology. The authors briefly discuss the theory of equilibrium pricing and its relationship to the standard arbitrage-free valuation framework. Equilibrium pricing theory is used to develop a pricing method based on a model of the term structure of interest rates and a probability structure for the catastrophe risk. This pricing methodology can be used to assess the default spread on catastrophe risk bonds relative to traditional defaultable securities.     

The Optimal Write-Down Coefficients in a Percentage for a Catastrophe Bond

Catastrophe bonds, also known as CAT bonds, are insurance-linked securities that help to transfer catastrophe risks from insurance industry to bond holders. When the aggregate catastrophe loss exceeds a specified amount by the maturity, the CAT bond is triggered and the future bond payments are reduced. This article first presents a general pricing formula for a CAT bond with coupon payments, which can be adapted to various assumptions for a catastrophe loss process. Next, it gives formulas for the optimal write-down coefficients in a percentage, implemented by Monte Carlo simulations, which maximize two measurements of risk reduction, hedge effectiveness rate (HER) and hedge effectiveness (HE), respectively, and examines how the optimal write-down coefficients in a percentage help reinsurance or insurance companies to mitigate extreme catastrophe losses. Last, it demonstrates how the number of coupon payments, loss share, retention level, strike price, maturity, frequency, and severity parameters of the catastrophe loss process and different interest rate models affect the optimal write-down coefficients in a percentage with numerical examples for illustrations.     

A simple robust model for Cat bond valuation

This note provides a simple closed form solution for valuing Cat bonds. The formula is consistent with any arbitrage-free model for the evolution of the Libor term structure of interest rates. The crucial inputs to the valuation formula are the likelihood of the catastrophe event, per unit time, and the percentage loss rate realized if an event occurs. The pricing methodology is based on the reduced form models used to price credit derivatives.     

Interest Rate Futures Options and Interest Rate Options

This paper derives pricing models of interest rate options and interest rate futures options. The models utilize the arbitrage-free interest rate movements model of Ho and Lee. In their model, they take the initial term structure as given, and for the subsequent periods, they only require that the bond prices move relative to each other in an arbitrage-free manner. Viewing the interest rate options as contingent claims to the underlying bonds, we derive the closed-form solutions to the options. Since these models are sufficiently simple, they can be used to investigate empirically the pricing of bond options. We also empirically examine the pricing of Eurodollar futures options. The results show that the model has significant explanatory power and, on average, has smaller estimation errors than Black's model. The results suggest that the model can be used to price options relative to each other, even though they may have different expiration dates and strike prices.     

A contingent claims analysis of the interest rate risk characteristics of corporate liabilities

This paper provides a contingent claims analysis of the interest rate risk characteristics of corporate liabilities by identifying Merton's (1973) option pricing model with Vasicek's (1977) mean reverting term structure model. Only a non-zero positive range of duration values for the firms' assets is shown to be consistent with the previous empirical evidence on the interest rate sensitivity of corporate stocks and bonds. Chance's (1990) duration measure is shown to be biased downward under empirically realistic conditions. Theoretical conditions are derived under which the duration of a default-prone zero coupon bond can be either higher or lower than the duration of the corresponding default-free bond. The duration of the default-prone bond of a firm with high (low) interest rate sensitive assets is shown to be an increasing (decreasing) function of the bond's default-risk.     

Return generating process and the determinants of term premiums

This paper examines asset pricing theories for treasury bonds using longer maturities than previous studies and employing a simple multi-factor model. We allow bond factor loadings to vary over time according to term structure variables. The model examines not only the time variation in the expected returns of bonds but also their unexpected returns. This allows us to explicitly test some asset pricing restrictions which are difficult to study under existing frameworks. We confirm that the pure expectation theory of the term structure of interest rates is rejected by the data. Our empirical study of a two-factor model finds substantial evidence of time-varying term-premiums and factor loadings. The fact that factor loadings vary with long-term interest rates and yield spreads suggest that bond return volatilities are sensitive to interest rate levels.     

Bond and option pricing for interest rate model with clustering effects

This paper analyzes an interest rate model with self-exciting jumps, in which a jump in the interest rate model increases the intensity of jumps in the same model. This self-exciting property leads to clustering effects in the interest rate model. We obtain a closed-form expression for the conditional moment-generating function when the model coefficients have affine structures. Based on the Girsanov-type measure transformation for general jump-diffusion processes, we derive the evolution of the interest rate under the equivalent martingale measure and an explicit expression of the zero-coupon bond pricing formula. Furthermore, we give a pricing formula for the European call option written on zero-coupon bonds. Finally, we provide an interpretation for the clustering effects in the interest rate model within a simple framework of general equilibrium. Indeed, we construct an interest rate model, the equilibrium state of which coincides with the interest rate model with clustering effects proposed in this paper.     

A Simple Approach to Valuing Risky Fixed and Floating Rate Debt

We develop a simple approach to valuing risky corporate debt that incorporates both default and interest rate risk. We use this approach to derive simple closed-form valuation expressions for fixed and floating rate debt. The model provides a number of interesting new insights about pricing and hedging corporate debt securities. For example, we find that the correlation between default risk and the interest rate has a significant effect on the properties of the credit spread. Using Moody's corporate bond yield data, we find that credit spreads are negatively related to interest rates and that durations of risky bonds depend on the correlation with interest rates. This empirical evidence is consistent with the implications of the valuation model.     

Pricing Contingent Claims under Interest Rate and Asset Price Risk

This paper presents a general framework for pricing contingent claims under interest rate and asset price uncertainty. The framework extends Ho and Lee's (1986) valuation framework by allowing not only future interest rates but also future asset prices to depend on the current term structure of interest rates. The approach is shown to provide risk-neutral valuation relationships that are consistent with the initial term structure of interest rates and can be applied to valuation of a broad class of assets including stock options, convertible bonds, and junk bonds.     

Pricing catastrophe risk in life (re)insurance

What is the catastrophe risk a life insurance company faces? What is the correct price of a catastrophe cover? During a review of the current standard model, due to Strickler, we found that this model has some serious shortcomings. We therefore present a new model for the pricing of catastrophe excess of loss cover (Cat XL). The new model for annual claim cost C is based on a compound Poisson process of catastrophe costs. To evaluate the distribution of the cost of each catastrophe, we use the Peaks Over Threshold model for the total number of lost lives in each catastrophe and the beta binomial model for the proportion of these corresponding to customers of the insurance company. To be able to estimate the parameters of the model, international and Swedish data were collected and compiled, listing accidents claiming at least twenty and four lives, respectively. Fitting the new model to data, we find the fit to be good. Finally we give the price of a Cat XL contract and perform a sensitivity analysis of how some of the parameters affect the expected value and standard deviation of the cost and thus the price.