Pricing pension buy-outs under stochastic interest and mortality rates

Pension buy-out is a special financial asset issued to offload the pension liabilities holistically in exchange for an upfront premium. In this paper, we concentrate on the pricing of pension buy-outs under dependence between interest and mortality rates risks with an explicit correlation structure in a continuous time framework. Change of measure technique is invoked to simplify the valuation. We also present how to obtain the buy-out price for a hypothetical benefit pension scheme using stochastic models to govern the dynamics of interest and mortality rates. Besides employing a non-mean reverting specification of the Ornstein–Uhlenbeck process and a continuous version of Lee–Carter setting for modeling mortality rates, we prefer Vasicek and Cox–Ingersoll–Ross models for short rates. We provide numerical results under various scenarios along with the confidence intervals using Monte Carlo simulations.     

Stochastic mortality under measure changes

We provide a self-contained analysis of a class of continuous-time stochastic mortality models that have gained popularity in the last few years. We describe some of their advantages and limitations, examining whether their features survive equivalent changes of measures. This is important when using the same model for both market-consistent valuation and risk management of life insurance liabilities. We provide a numerical example based on the calibration to the French annuity market of a risk-neutral version of the model proposed by Lee & Carter (1992).     

Modelling and management of mortality risk: a review

In the first part of the paper, we consider the wide range of extrapolative stochastic mortality models that have been proposed over the last 15–20 years. A number of models that we consider are framed in discrete time and place emphasis on the statistical aspects of modelling and forecasting. We discuss how these models can be evaluated, compared and contrasted. We also discuss a discrete-time market model that facilitates valuation of mortality-linked contracts with embedded options. We then review several approaches to modelling mortality in continuous time. These models tend to be simpler in nature, but make it possible to examine the potential for dynamic hedging of mortality risk. Finally, we review a range of financial instruments (traded and over-the-counter) that could be used to hedge mortality risk. Some of these, such as mortality swaps, already exist, while others anticipate future developments in the market.     

Computing finite-time survival probabilities using multinomial approximations of risk models

We consider the problem of computing finite-time survival probabilities for various risk models. We develop an approximating discrete-time multinomial lattice that mimics the evolution of the corresponding continuous risk process. A simple recursive algorithm to compute survival probabilities is described. Numerical results show that the proposed scheme yields accurate values in all the considered cases.     

Estimation of DSGE models when the data are persistent

Dynamic stochastic general equilibrium (DSGE) models are often solved and estimated under specific assumptions as to whether the exogenous variables are difference or trend stationary. However, even mild departures of the data generating process from these assumptions can severely bias the estimates of the model parameters. This paper proposes new estimators that do not require researchers to take a stand on whether shocks have permanent or transitory effects. These procedures have two key features. First, the same filter is applied to both the data and the model variables. Second, the filtered variables are stationary when evaluated at the true parameter vector. The estimators are approximately normally distributed not only when the shocks are mildly persistent, but also when they have near or exact unit roots. Simulations show that these robust estimators perform well especially when the shocks are highly persistent yet stationary. In such cases, linear detrending and first differencing are shown to yield biased or imprecise estimates.     

A transactions data analysis of intraday betas

Using a sample of 27 stocks from the Dow Jones Industrial Average for the years 1986–1992, we examine the equality of beta for individual firms during the trading day. Both alphas and betas are found to differ through the trading day. Evidence suggests these changes are systematic for individual stocks. Using the midday beta as the base, the number of rejections of beta equality follow a U-shaped pattern through the trading day, indicating the differing distributions (U-shaped patterns) for intraday returns are reflected in similar changes in beta. These results have implications for further developing and testing market microstructure models.     

On the Distribution of the Deficit at Ruin when Claims are Phase-type

We consider the distribution of the deficit at ruin in the Sparre Andersen renewal risk model given that ruin occurs. We show that if the individual claim amounts have a phase-type distribution, then there is a simple phase-type representation for the distribution of the deficit. We illustrate the application of this result with several examples.     

商业银行信用风险评估的生存分析模型及实证研究

企业发生财务危机，不能归还到期贷款是商业银行信贷资产的主要风险来源，商业银行如何构建恰当的信用风险评估模型来预测企业的财务危机，从而避免这类信用风险的出现就显得尤为重要。本文以我国上市公司为研究对象，结合杜邦分析法建立了基于生存分析的信用风险评估模型，模型对于随机选取的预测样本，其提前1年、2年和3年的预测准确率分别达到86％、72％和68％。通过与Ahman模型、Ohlson模型预测结果的比较和鲁棒性检验的结果发现，该模型同时具有可以使用时间序列、无需样本配对、中远期预测能力强和高鲁棒性的特点．这些特点特别对于商业银行中长期信贷风险管理具有较高的应用价值．     

商业银行信用风险评估的生存分析模型及实证研究

企业发生财务危机,不能归还到期贷款是商业银行信贷资产的主要风险来源,商业银行如何构建恰当的信用风险评估模型来预测企业的财务危机,从而避免这类信用风险的出现就显得尤为重要。本文以我国上市公司为研究对象,结合杜邦分析法建立了基于生存分析的信用风险评估模型,模型对于随机选取的预测样本,其提前1年、2年和3年的预测准确率分别达到86%、72%和68%。通过与Altman模型、Ohlson模型预测结果的比较和鲁棒性检验的结果发现,该模型同时具有可以使用时间序列、无需样本配对、中远期预测能力强和高鲁棒性的特点,这些特点特别对于商业银行中长期信贷风险管理具有较高的应用价值。     

Change analysis of a dynamic copula for measuring dependence in multivariate financial data

This paper proposes a new approach to measure dependencies in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes within the dependence structure. Recently, two methods have been proposed using copulas to analyse such changes. The first approach investigates changes within the parameters of the copula. The second determines the sequence of copulas using moving windows. In this paper we take into account the non-stationarity of the data and analyse the impact of (1) time-varying parameters for a copula family, and (2) the sequence of copulas, on the computations of the VaR and ES measures. We propose tests based on conditional copulas and the goodness-of-fit to decide the type of change, and further give the corresponding change analysis. We illustrate our approach using the Standard & Poor 500 and Nasdaq indices in order to compute risk measures using the two previous methods.