考虑银行破产外部效应的存款保险定价模型

运用存款保险的期望损失定价方法和Shapley值法,建立了考虑银行违约/破产外部效应的存款保险定价模型。模型中度量的破产成本不仅考虑了银行破产清算过程中其自身资产价值的损失,还考虑了银行违约/破产的负外部效应——可能增加其他银行的破产损失,据此确定的存款保险保费反映了各银行对系统总破产成本的边际贡献。为验证模型效果,构造了三种情景进行模拟分析,结果表明:存款保险保费与银行系统对破产银行资产的收购能力负相关,且负相关程度随经济形势的恶化而加剧;保费与整个银行系统参保银行数目之间也呈负相关关系。     

Credit spreads, endogenous bankruptcy and liquidity risk

In this paper, we consider a bond valuation model with both credit risk and liquidity risk to show that credit spreads are not negligible for short maturities. We adopt the structural approach to model credit risk, where the default triggering barrier is determined endogenously by maximizing equity value. As for liquidity risk, we assume that bondholders may encounter liquidity shocks during the lifetime of corporate bonds, and have to sell the bond immediately at the price, which is assumed to be a fraction of the price in a perfectly liquid market. Under this framework, we derive explicit expressions for corporate bond, firm value and bankruptcy trigger. Finally, numerical illustrations are presented.     

Optimal financing and dividend control of the insurance company with proportional reinsurance policy

We consider the optimal control problem of the insurance company with proportional reinsurance policy. The management of the company controls the reinsurance rate, dividends payout as well as the equity issuance processes to maximize the expected present value of the dividends minus the equity issuance until the time of bankruptcy. This is the first time that the financing process in an insurance model has been considered, which is more realistic. To find the solution of the mixed singular-regular control problem, we firstly construct two categories of suboptimal models, one is the classical model without equity issuance, the other never goes bankrupt by equity issuance. Then we identify the value functions and the optimal strategies corresponding to the suboptimal models depending on the relationships between the coefficients.     

基于KMV模型的农业上市公司信用风险测度研究

通过构建改进后的KMV模型,设定三种不同违约情境,对2010-2012年我国农业上市公司的信用风险进行测度与比较研究,并确定其隶属的风险类型,以揭示现阶段农业上市公司的信用状况.研究结果表明:不同农业上市公司的资产价值均高于股权价值,其未来发展具有较好的价值增值空间;农业上市公司的资产价值波动率总体呈下降趋势;农业上市公司信用状况相对较差,且风险类型主要集中于"∩"型和↘型".由此得出农业上市公司未来的发展,应在推进"股权分置"改革、建立可量化的风险管理机制、实现风险管理与业务流程融合等方面采取措施,从而有效降低我国农业上市公司的信用风险.     

Predicting default of a small business using different definitions of financial distress

The paper introduces a number of risk-rating models for UK small businesses applying an accounting-based approach, which uses financial ratios to predict corporate bankruptcy. An enhancement to these models is considered through features typical to retail credit risk modelling. A common problem of default prediction consists in the relatively small number of bankruptcies or real defaults available for model-building. In order to expand the ‘default’ group beyond bankrupt companies, the paper considers adopting four different definitions of ‘a failing business’ by investigating combinations of financial distress levels. The impact of each default definition on the choice of predictor variables and on the model's predictive accuracy is explored. In addition, the paper examines the value of categorizing financial ratios used as predictor variables.     

The effects of asset liquidity on dynamic sell-out and bankruptcy decisions

We develop a dynamic bankruptcy model with asset illiquidity. In the model, a distressed firm chooses between sell-out and default, as well as its timing under the assumption that sell-out is feasible only at Poisson jump times, where the arrival rate of acquirers stands for asset liquidity. With lower asset liquidity, the firm increases the sell-out region to mitigate the risk of not finding an acquirer until bankruptcy. Despite the larger sell-out region, lower asset liquidity increases the default probability and decreases the equity, debt, and firm values. In the optimal capital structure, with lower asset liquidity, the firm reduces leverage, but the cautious capital structure does not fully offset the increased default risk. The stock price reaction caused by sell-out depends on the sell-out timing. When the firm’s asset value is not sufficiently high, the stock price jump size is an inverted U-shape with the economic state variable. Lower asset liquidity increases the jump size due to greater surprise. These results fit empirical observations.     

Optimal mean–variance investment and reinsurance problems for the risk model with common shock dependence

In this paper, we study the optimal investment–reinsurance problems in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. Under the criterion of mean–variance, two cases are considered: One is the optimal mean–variance problem with bankruptcy prohibition, i.e., the wealth process of the insurer is not allowed to be below zero at any time, which is solved by standard martingale approach, and the closed form solutions are derived; The other is the optimal mean–variance problem without bankruptcy prohibition, which is discussed by a very different method—stochastic linear–quadratic control theory, and the explicit expressions of the optimal results are obtained either. In the end, a numerical example is given to illustrate the results and compare the values in the two cases.     

基于障碍期权的贷款保险定价研究

现有的贷款保险定价模型通常忽略了违约门槛和提前违约对贷款损失的影响。本文基于障碍期权中的向下敲入看跌期权,将这两个重要因素纳入到了新的贷款保险定价模型中。进一步,本文通过蒙特卡洛模拟的方法,给出了贷款保险敲入概率和敲入时间点的估计过程。此外,本文将新构建的贷款保险定价模型应用于实际中,并进行了实证分析。结果表明,违约门槛的上升会提高贷款保险的定价水平和敲入概率,并导致更早的敲入时间点。而银行降低对企业违约情况的观察频率会引起贷款保险的价值损失。     

Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs

We consider the optimal financing and dividend control problem of the insurance company with fixed and proportional transaction costs. The management of the company controls the reinsurance rate, dividends payout as well as the equity issuance process to maximize the expected present value of the dividends payout minus the equity issuance until the time of bankruptcy. This is the first time that the financing process in an insurance model with two kinds of transaction costs, which come from real financial market has been considered. We solve the mixed classical-impulse control problem by constructing two categories of suboptimal models, one is the classical model without equity issuance, the other never goes bankrupt by equity issuance.     

The informational content of subordinated debt and equity prices in the presence of bankruptcy costs

The paper extends the contingent valuation framework of Black and Cox [J. Finance 31(2) (1976) 351] to value subordinated debt by explicitly incorporating bankruptcy costs in the model. We show that the information from subordinated debt prices is complementary to the information from the equity prices only when the bankruptcy costs are taken into account. In fact, the joint use of equity and subordinated debt prices can provide information on magnitude of expected bankruptcy costs. Knowing the magnitude of expected bankruptcy costs is necessary for calculating variables underlying policy objectives. In particular, it is illustrated that the value of expected liability of a deposit insurer would be underestimated if the bankruptcy costs were not taken into account.     

Omega diffusion risk model with surplus-dependent tax and capital injections

In this paper, we propose and study an Omega risk model with a constant bankruptcy function, surplus-dependent tax payments and capital injections in a time-homogeneous diffusion setting. The surplus value process is both refracted (paying tax) at its running maximum and reflected (injecting capital) at a lower constant boundary. The new model incorporates practical features from the Omega risk model (Albrecher et al., 2011), the risk model with tax (Albrecher and Hipp, 2007), and the risk model with capital injections (Albrecher and Ivanovs, 2014). The study of this new risk model is closely related to the Azéma–Yor process, which is a process refracted by its running maximum. We explicitly characterize the Laplace transform of the occupation time of an Azéma–Yor process below a constant level until the first passage time of another Azéma–Yor process or until an independent exponential time. We also consider the case when the process has a lower reflecting boundary. This result unifies and extends recent results of Li and Zhou (2013) and Zhang (2015). We explicitly characterize the Laplace transform of the time of bankruptcy in the Omega risk model with tax and capital injections up to eigen-functions, and determine the expected present value of tax payments until default. We also discuss a further extension to occupation functionals through stochastic time-change, which handles the case of a non-constant bankruptcy function. Finally we present examples using a Brownian motion with drift, and discuss the pricing of quantile options written on the Azéma–Yor process.     

A latent process model for the pricing of corporate securities

We propose a structural model with a joint process of tangible assets (marker) and firm status for the pricing of corporate securities. The firm status is assumed to be latent or unobservable, and default occurs when the firm status process reaches a default threshold at the first time. The marker process is observable and assumed to be correlated with the latent firm status. The recovery upon default is a fraction of tangible assets at the time of default. Our model can evaluate both the corporate debt and equity to fit their market prices in a unified framework. When the two processes are perfectly correlated, our model is reduced to the seminal Black–Cox model. Numerical examples are given to support the usefulness of our model. A previous version of this paper was presented at the Tsukuba–Stanford workshop held at Stanford University on March 2006. The authors are grateful to participants of the workshop for helpful discussions.     

On the regulator–insurer interaction in a structural model

In this paper, we provide a new insight to the previous work of Briys and de Varenne [E. Briys, F. de Varenne, Life insurance in a contingent claim framework: Pricing and regulatory implications, Geneva Papers on Risk and Insurance Theory 19 (1) (1994) 53–72], Grosen and Jørgensen [A. Grosen, P.L. Jørgensen, Life insurance liabilities at market value: An analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework, Journal of Risk and Insurance 69 (1) (2002) 63–91] and Chen and Suchanecki [A. Chen, M. Suchanecki, Default risk, bankruptcy procedures and the market value of life insurance liabilities, Insurance: Mathematics and Economics 40 (2007) 231–255]. We show that the particular risk management strategy followed by the insurance company can significantly change the risk exposure of the company, and that it should thus be taken into account by regulators. We first study how the regulator establishes regulation intervention levels in order to control for instance the default probability of the insurance company. This part of the analysis is based on a constant volatility. Given that the insurance company is informed of regulatory rules, we study how results can be significantly different when the insurance company follows a risk management strategy with non-constant volatilities. We thus highlight some limits of the prior literature and believe that the risk management strategy of the company should be taken into account in the estimation of the risk exposure as well as in that of the market value of liabilities.     

基于权益再融资与策略性债务支付的公司财务困境纾解研究

为了应对公司财务困境问题,在兼顾股东与债权人利益的基础上,采用激励相容理论,构建了基于权益再融资和策略性债务支付的公司定价模型,厘清了权益再融资、债务重组、财务困境及其伴生的再谈判之间的关系,据此提出了一种公司财务困境纾解方案。特别地,给出了策略性债务支付下进行权益再融资的可行性依据,并辅以再谈判手段及股东、债权人双方利益最大化目标,确定了最优重组边界及最优减记息票。分析结果表明:①将策略性债务支付置于财务困境之后、兼容权益再融资的综合方案,可在一定程度上避免策略性债务支付行为的投机性所导致的对公司定价的高估,产生了在一定条件下增加债务价值、放缓信用价差增长速度的效果;②权益再融资成本与信用价差之间呈现倒U型关系;③基于纳什均衡博弈的策略性债务支付减记息票不受流动性及权益再融资的影响,并可保证其处于公司的支付能力之内。     

Optimal dividend-equity issuance strategy in a dual model with fixed and proportional transaction costs

In this paper, we consider the problem of optimal dividend payout and equity issuance for a company whose liquid asset is modeled by the dual of classical risk model with diffusion. We assume that there exist both proportional and fixed transaction costs when issuing new equity. Our objective is to maximize the expected cumulative present value of the dividend payout minus the equity issuance until the time of bankruptcy,which is defined as the first time when the company’s capital reserve falls below zero. The solution to the mixed impulse-singular control problem relies on two auxiliary subproblems: one is the classical dividend problem without equity issuance, and the other one assumes that the company never goes bankrupt by equity issuance.We first provide closed-form expressions of the value functions and the optimal strategies for both auxiliary subproblems. We then identify the solution to the original problem with either of the auxiliary problems. Our results show that the optimal strategy should either allow for bankruptcy or keep the company’s reserve above zero by issuing new equity, depending on the model’s parameters. We also present some economic interpretations and sensitivity analysis for our results by theoretical analysis and numerical examples.     

Government-provided annuities under insolvency risk

This paper seeks to determine whether governments should intervene in the private annuity market by directly providing public insurance in the form of annuities when both the government and the insurance companies could default. It is found that, although the government could default, intervening by means of an annuity can improve social welfare if the insurance companies could default and the expected return on the public annuity is greater than the rate of return on a risk-free bond. We also find that, under actuarially fair pricing, the government should provide more in terms of a public annuity than the optimal amount of the annuity that the individual purchases in the private market if the government is less likely to default on the public annuity than an insurance company would in the case of a private annuity.     

Government-provided annuities under insolvency risk

This paper seeks to determine whether governments should intervene in the private annuity market by directly providing public insurance in the form of annuities when both the government and the insurance companies could default. It is found that, although the government could default, intervening by means of an annuity can improve social welfare if the insurance companies could default and the expected return on the public annuity is greater than the rate of return on a risk-free bond. We also find that, under actuarially fair pricing, the government should provide more in terms of a public annuity than the optimal amount of the annuity that the individual purchases in the private market if the government is less likely to default on the public annuity than an insurance company would in the case of a private annuity.     

Calibrating affine stochastic mortality models using term assurance premiums

In this paper, we focus on the calibration of affine stochastic mortality models using term assurance premiums. We view term assurance contracts as a “swap” in which policyholders exchange cash flows (premiums vs. benefits) with an insurer analogous to a generic interest rate swap or credit default swap. Using a simple bootstrapping procedure, we derive the term structure of mortality rates from a stream of contract quotes with different maturities. This term structure is used to calibrate the parameters of affine stochastic mortality models where the survival probability is expressed in closed form. The Vasicek, Cox-Ingersoll-Ross, and jump-extended Vasicek models are considered for fitting the survival probabilities term structure. An evaluation of the performance of these models is provided with respect to premiums of three Italian insurance companies.     

Catastrophe equity put options with target variance

In this study, we consider a new class of catastrophe equity put options, whose payoff depends on the ratio of the realized variance of the stock over the life of the option and the target variance, which represents the insurance company’s expectation of the future realized variance. This kind of options could help insurance companies raise more equity capital when a large number of catastrophic events occur during the life of the option. We employ a compound doubly stochastic Poisson process with lognormal intensity to describe accumulated catastrophe losses and assume the volatility varies stochastically. Finally, numerical results are presented to investigate the values of this class of options.     

Analytical pricing of defaultable discrete coupon bonds in unified two-factor model of structural and reduced form models

Pricing formulae for defaultable corporate bonds with discrete coupons (under consideration of the government taxes) in the united two-factor model of structural and reduced form models are provided. The aim of this paper is to generalize the two-factor structural model for defaultable corporate discrete coupon bonds (considered in [1]) into the unified model of structural and reduced form models. In our model the bond holders receive the stochastic coupon (which is the discounted value of a predetermined value at the maturity) at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered. The expected default event occurs when the equity value is not sufficient to pay coupon or debt at the coupon dates or maturity and the unexpected default event can occur at the first jump time of a Poisson process with the given default intensity provided by a step function of time variable. We provide the model and pricing formula for equity value and using it calculate expected default barrier. Then we provide pricing model and formula for defaultable corporate bonds with discrete coupons and consider its duration.