Modeling Mortality With Jumps: Applications to Mortality Securitization

In this article, we incorporate a jump process into the original Lee–Carter model, and use it to forecast mortality rates and analyze mortality securitization. We explore alternative models with transitory versus permanent jump effects and find that modeling mortality via transitory jump effects may be more appropriate in mortality securitization. We use the Swiss Re mortality bond in 2003 as an example to show how to apply our model together with the distortion measure approach to value mortality-linked securities. Pricing the Swiss Re mortality bond is challenging because the mortality index is correlated across countries and over time. Cox, Lin, and Wang (2006) employ the normalized multivariate exponential tilting to take into account correlations across countries, but the problem of correlation over time remains unsolved. We show in this article how to account for the correlations of the mortality index over time by simulating the mortality index and changing the measure on paths.     

Non‐additivity in Accounting Valuation: Theory and Applications

This paper has three objectives. First, to introduce a theoretical solution to the issue of non‐additivity between assets in place, relying on an accounting‐based valuation approach. Second, to explain how such an approach can be implemented empirically by measuring synergies between assets. Third, to present the properties of this non‐additive valuation technique. We use Choquet capacities, that is, non‐additive aggregation operators, to measure the interactions between assets and apply our methodology to a sample of US firms from the capital goods industry. To operationalize our approach we examine the relationships between synergies—captured by Choquet capacities—and the market‐to‐book ratio (proxying for growth options), and show how interactions between assets are consistently linked to a firm’s market‐to‐book ratio. We also measure firm‐specific productive efficiency relative to the industry and firm size. For large firms, efficiency, as defined by our approach, is positively associated with higher future operating cash flows. For small firms, efficiency is positively associated with higher future sales growth. We document that the non‐additive approach appears to be better able to identify expected relationships between efficiency and future performance than a simpler approach based on the market‐to‐book ratio.     

Longevity/Mortality Risk Modeling and Securities Pricing

Securitizing longevity/mortality risk can transfer longevity/mortality risk to capital markets. Modeling and forecasting mortality rate is key to pricing mortality‐linked securities. Catastrophic mortality and longevity jumps occur in historical data and have an important impact on security pricing. This article introduces a stochastic diffusion model with a double‐exponential jump diffusion process that captures both asymmetric rate jumps up and down and also cohort effect in mortality trends. The model exhibits calibration advantages and mathematical tractability while better fitting the data. The model provides a closed‐form pricing solution for J.P. Morgan’s q‐forward contract usable as a building block for hedging.     

Bond Option Valuation for Non‐Markovian Interest Rate Processes

The standard method for valuing a European option on a bond portfolio is developed by Jamshidian. He shows that under certain circumstances the payoff from a bond option can be expressed as a portfolio of payoffs on discount bond options, allowing the option to be valued as a portfolio of options. A limitation of this approach is that it cannot be applied to non‐Markovian interest rate processes. This paper develops a method for the valuation of a European option on a bond portfolio that can be applied to both Markovian and non‐Markovian interest rate processes.     

Modeling and Pricing Longevity Derivatives Using Stochastic Mortality Rates and the Esscher Transform

The Lee-Carter mortality model provides a structure for stochastically modeling mortality rates incorporating both time (year) and age mortality dynamics. Their model is constructed by modeling the mortality rate as a function of both an age and a year effect. Recently the MBMM model (Mitchell et al. 2013) showed the Lee Carter model can be improved by fitting with the growth rates of mortality rates over time and age rather than the mortality rates themselves. The MBMM modification of the Lee-Carter model performs better than the original and many of the subsequent variants. In order to model the mortality rate under the martingale measure and to apply it for pricing the longevity derivatives, we adapt the MBMM structure and introduce a Lévy stochastic process with a normal inverse Gaussian (NIG) distribution in our model. The model has two advantages in addition to better fit: first, it can mimic the jumps in the mortality rates since the NIG distribution is fat-tailed with high kurtosis, and, second, this mortality model lends itself to pricing of longevity derivatives based on the assumed mortality model. Using the Esscher transformation we show how to find a related martingale measure, allowing martingale pricing for mortality/longevity risk–related derivatives. Finally, we apply our model to pricing a q-forward longevity derivative utilizing the structure proposed by Life and Longevity Markets Association.     

我国随机死亡率的长寿风险建模和衍生品定价

长寿风险近年来对各国保险业、养老金体系、社会保障体系造成大规模影响,成为保险和风险管理学术界关注和研究的重点。采用国际前沿的研究方法,系统深入地采用中国数据研究这一问题。在Lee-Carter模型的基础上,通过双指数跳跃扩散模型对Lee-Carter模型中的时间序列因子进行拟合,较好地刻画了中国人口死亡率的长寿跳跃和死亡跳跃;引用Swiss Re死亡债券度量长寿风险的市场价格,预估未来中国人口死亡率,并得出了寿险衍生品Q型远期的中国定价。     

The CBD Mortality Indexes: Modeling and Applications

Most extrapolative stochastic mortality models are constructed in a similar manner. Specifically, when they are fitted to historical data, one or more series of time-varying parameters are identified. By extrapolating these parameters to the future, we can obtain a forecast of death probabilities and consequently cash flows arising from life contingent liabilities. In this article, we first argue that, among various time-varying model parameters, those encompassed in the Cairns-Blake-Dowd (CBD) model (also known as Model M5) are most suitably used as indexes to indicate levels of longevity risk at different time points. We then investigate how these indexes can be jointly modeled with a more general class of multivariate time-series models, instead of a simple random walk that takes no account of cross-correlations. Finally, we study the joint prediction region for the mortality indexes. Such a region, as we demonstrate, can serve as a graphical longevity risk metric, allowing practitioners to compare the longevity risk exposures of different portfolios readily.     

Valuation of Catastrophe Equity Puts With Markov‐Modulated Poisson Processes

We derive the pricing formula for catastrophe equity put options (CatEPuts) by assuming catastrophic events follow a Markov Modulated Poisson process (MMPP) whose intensity varies according to the change of the Atlantic Multidecadal Oscillation (AMO) signal. U.S. hurricanes events from 1960 to 2007 show that the CatEPuts pricing errors under the MMPP(2) are smaller than the PP by 30 percent to 66 percent. The scenario analysis indicates that the MMPP outperforms the exponential growth pattern (EG) if the hurricane intensity is the AMO signal, whereas the EG may outperform the MMPP if the future climate is warming rapidly.     

Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II

Recently Cairns et al. introduced a general framework for modeling the dynamics of mortality rates of two related populations simultaneously. Their method ensures that the resulting forecasts do not diverge over the long run by modeling the difference in the stochastic factors between the two populations with a mean-reverting autoregressive process. In this article, we investigate how the modeling of the stochastic factors may be improved by using a vector error correction model. This extension is highly intuitive, allowing us to visualize the cross-correlations and the long-term equilibrium relation between the two populations. Another key benefit is that this extension does not require the user to assume which one of the two populations is dominant. This benefit is important because, as we demonstrate, it is not always easy to identify the dominant population, even if one population is much larger than the other. We illustrate our proposed extension with data from a pair of populations and apply it to the calculation of Solvency II risk capital.     

The Impact of the Disclosure of Non‐GAAP Earnings in Australian Annual Reports on Non‐Sophisticated Users

The disclosure of non‐GAAP earnings in Australian annual reports has risen steadily in recent years. These non‐statutory earnings measures are generally disclosed in the unaudited section of the annual report and are not consistent with statutory profit as defined under generally accepted Australian accounting standards (GAAP). Recent research conducted in the United States (US) has provided evidence that non‐sophisticated investor decisions are influenced by the presence and prominence of non‐GAAP earnings information. Further evidence suggests that investor perception changed after non‐GAAP earnings disclosures became subject to regulation in that jurisdiction. Australia has high investor participation rates by international standards, including investors operating self‐managed superannuation funds, resulting in a significant number of active individual investors. This study employs an experimental design to investigate the impact on non‐sophisticated investors of the reporting of non‐GAAP earnings information in addition to GAAP earnings information in Australian annual reports. The results of this study show a positive association between the prominent disclosure of non‐GAAP earnings information and non‐sophisticated investor reliance on this information. These results provide important evidence to Australian regulators as these narrative disclosures are not subject to regulation, in contrast to the US where mandatory regulation has been in place since 2003.     

On the Life Cycle Dynamics of Venture‐Capital‐ and Non‐Venture‐Capital‐Financed Firms

We use data over 25 years to understand the life cycle dynamics of VC‐ and non‐VC‐financed firms. We find successful and failed VC‐financed firms achieve larger scale but are not more profitable at exit than matched non‐VC‐financed firms. Cumulative failure rates of VC‐financed firms are lower, with the difference driven largely by lower failure rates in the initial years after receiving VC. Our results are not driven by VCs disguising failures as acquisitions or by certain types of VCs. The performance difference between VC‐ and non‐VC‐financed firms narrows in the post‐internet bubble years, but does not disappear.     

Disclosure Prominence and the Quality of Non‐GAAP Earnings

The SEC prohibits the presentation of non‐GAAP measures before corresponding GAAP measures; however, a large proportion of non‐GAAP reporters present non‐GAAP EPS before GAAP EPS in their earnings announcements. This noncompliance raises questions about whether firms use prominence to highlight higher or lower quality non‐GAAP information. For firms reporting non‐GAAP EPS between 2003 and 2016, prominent non‐GAAP EPS is associated with higher quality non‐GAAP reporting. Further tests reveal that nonregulatory incentives, rather than regulatory costs, explain this relation. Specifically, prominence is associated with higher quality non‐GAAP reporting in settings where prominence is not regulated, investors ignore prominence when non‐GAAP reporting quality is lower, and the minority of firms using prominence to mislead exhibit characteristics associated with weaker investor monitoring. Overall, we provide evidence that regulatory noncompliance can reflect an intent to inform, and that most firms use prominence to highlight higher quality non‐GAAP information despite prohibitive regulation.     

也谈企业价值评估中折现率确定及方法模型——与高波先生商榷

本人拜读了高波先生2003年第2期发表于本刊的一篇题为《企业价值评估中折现率确定及方法模型》(以下简称“高文”)的文章。高文提出了一个很有创意的思路,找到了一个相对科学合理,符合中国现有资本市场实际的方法,对在企业价值评估中涉及的折现率的确定问题作出了回答,对本人有很大的启发。根据高先生的见解,企业价值评估中折现率的确定方法思路为:以行业平均收益率(主要是净资产报酬率)为基础,将企业管理会计中的企业经营杠杆系数、财务杠杆系数及综合杠杆系数等概念引入资产评估理论,以上述三个系数作为企业风险的衡量指标,考虑委估企业相…     

Non‐operating earnings and firm risk*

We find that non‐operating earnings reduce total earnings volatility, stock price volatility, idiosyncratic risk, and crash risk. The risk‐reducing effects of non‐operating earnings are higher than those of operating earnings for risk measures based on stock market data. Non‐operating earnings serve to mitigate risks among firms with operating losses, high financial leverage, high growth uncertainty, and low‐ability managers.