Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization

Normalized exponential tilting is an extension of classical theories, including the Capital Asset Pricing Model (CAPM) and the Black–Merton–Scholes model, to price risks with general‐shaped distributions. The need for changing multivariate probability measures arises in pricing contingent claims on multiple underlying assets or liabilities. In this article, we apply it to valuation of mortality‐based securities written on mortality indices of several countries. We show how to use multivariate exponential tilting to price the first pure mortality security, the Swiss Re bond. The same technique can be applied in other mortality securitization pricing.     

Explaining Mortality Dynamics

Abstract

Using data for six OECD countries over the period 1950–2006, this paper studies the impact of macroeconomic fluctuations and cause of death trends on mortality dynamics in the Lee-Carter mortality forecasting model. The key results of this study are the following: (1) Periods can be identified in which the Lee-Carter mortality index k_t correlates significantly with macroeconomic fluctuations. (2) A few causes of death such as diseases of the circulatory system, influenza and pneumonia, and diabetes mellitus account for a large fraction of the variations in the Lee-Carter mortality index k_t . (3) Most cause-specific mortality rates show pronounced trends over the last few decades. These trends change the composition of deaths and alter how total mortality reacts to external factors such as macroeconomic fluctuations.     

Systematic Mortality Improvement Trends and Mortality Heterogeneity: Insights from Individual-Level HRS Data

Providers of life annuities and pensions need to consider both systematic mortality improvement trends and mortality heterogeneity. Although how mortality improvement varies with age and gender at the population level is well studied, how trends vary with risk factors remains relatively unexplored. This article assesses how systematic mortality improvement trends vary with individual risk characteristics using individual-level longitudinal data from the U.S. Health and Retirement Study between 1994 and 2009. Initially a Lee-Carter model is used to assess mortality improvement trends by grouping individuals with similar risk characteristics of gender, education, and race. We then fit a longitudinal mortality model to individual-level data allowing for heterogeneity and time trends in individual-level risk factors. Our results show how survey data can provide valuable insights into both mortality heterogeneity and improvement trends more effectively than commonly used aggregate models. We show how mortality improvement differs across individuals with different risk factors. Significantly, at an individual level, mortality improvement trends have been driven by changes in health history such as high blood pressure, cancer, and heart problems rather than risk factors such as education, marital status, body mass index, and smoker status.     

Jump Spillover in International Equity Markets

In this article we study jump spillover effects between a numberof country equity indexes. In order to identify the latent historicaljumps of each index, we use a Bayesian approach to estimatea jump-diffusion model on each index. We look at the simultaneousjump intensities of pairs of countries and the probabilitiesthat jumps in large countries cause jumps or unusually largereturns in other countries. In all cases, we find significantevidence of jump spillover. In addition, we find that jump spilloverseems to be particularly large between countries that belongto the same regions and have similar industry structures, whereas,interestingly, the sample correlations between the countrieshave difficulties in capturing the jump spillover effects.     

极端死亡率债券的运行机制与定价模型

极端死亡率债券是票息或面值与极端死亡概率相关的债券,能够将寿险公司所面临的极端死亡率风险转移到资本市场。本文阐述了极端死亡率债券的市场发展,包括发行规模、触发机制、债券期限、债券分层、债券评级等,分析了以 Tartan 债券为代表的本金赔付累积型极端死亡率债券的运行机制,并给出了考虑极端死亡率风险的跳跃性特征下的本金赔付累积型极端死亡率债券 Wang 转换定价的解析式。     

Mortality Inequality in Finland*

We study inequality in mortality in Finland using registry data that cover the whole population for years 1990–2018. We create municipality‐level indices of regional deprivation (poverty rate), and show how age‐specific mortality rates have evolved across regions and over time. The inequality in mortality has been remarkably low over the time period for most age groups. However, among young and prime‐age males, the mortality rates have been persistently higher in the poorer areas. For these age groups, the leading causes of death are deaths of despair (alcohol and suicides) and accidents. For the cohorts that were young during the deep recession of the early 1990s, we also document higher inequality in middle‐age mortality than for cohorts entering the labour market in recovery periods.     

A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration

In this article, we consider the evolution of the post‐age‐60 mortality curve in the United Kingdom and its impact on the pricing of the risk associated with aggregate mortality improvements over time: so‐called longevity risk. We introduce a two‐factor stochastic model for the development of this curve through time. The first factor affects mortality‐rate dynamics at all ages in the same way, whereas the second factor affects mortality‐rate dynamics at higher ages much more than at lower ages. The article then examines the pricing of longevity bonds with different terms to maturity referenced to different cohorts. We find that longevity risk over relatively short time horizons is very low, but at horizons in excess of ten years it begins to pick up very rapidly. A key component of the article is the proposal and development of a method for calculating the market risk‐adjusted price of a longevity bond. The proposed adjustment includes not just an allowance for the underlying stochastic mortality, but also makes an allowance for parameter risk. We utilize the pricing information contained in the November 2004 European Investment Bank longevity bond to make inferences about the likely market prices of the risks in the model. Based on these, we investigate how future issues might be priced to ensure an absence of arbitrage between bonds with different characteristics.     

Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee-Carter Framework

Longevity risk is a major issue for insurers and pension funds, especially in the selling of annuity products. In that respect, securitization of this risk could offer great opportunities for hedging. This article proposes to design survivor bonds which could be issued directly by insurers. In order to guaranty some transparency in the product, the survivor bond is based on a public mortality index. The classical Lee‐Carter model for mortality forecasting is used to price a risky coupon survivor bond based on this index.     

Global market integration: An alternative measure and its application

Global markets seem to be increasingly integrated but there is no well-accepted measure of integration. We show that the correlation across markets is a poor measure; perfectly integrated markets can exhibit weak correlation. We derive a new integration measure based on the explanatory power of a multi-factor model and use it empirically to investigate recent trends in global integration. For most countries, there has been a marked increase in measured integration over the past three decades, but this is not indicated by correlations among country indexes.     

Measuring Corporate Bond Mortality and Performance

This study develops an alternative way to measure default risk and suggests an appropriate method to assess the performance of fixed-income investors over the entire spectrum of credit-quality classes. The approach seeks to measure the expected mortality of bonds and the consequent loss rates in a manner similar to the way actuaries assess mortality of human beings. The results show that all bond ratings outperform riskless Treasuries over a ten-year horizon and that, despite relatively high mortality rates, B-rated and CCC-rated securities outperform all other rating categories for the first four years after issuance, with BB-rated securities outperforming all others thereafter.     

基于金融衍生工具视角的长寿风险管理

长寿风险已成为养老保障发展所面临的重要风险,而作为养老保障产品供给者的政府、年金和寿险公司等机构难以持续、有效地管理长寿风险。本文在分析长寿风险发展态势和现有管理方案的缺陷后,研究了最近的长寿风险管理工具创新及其发展动向,即死亡率巨灾债券、EIB/BNP长寿债券和远期等,并在此基础上分析了基于资本市场的长寿/死亡率风险相关衍生品设计与交易,包括长寿债券、死亡率互换、死亡率期货和死亡率期权,最后是长寿/死亡率衍生品交易市场建设的启示。     

The determinants of domestic and foreign bond bias

This paper studies the determinants of the domestic and the foreign bond biases and their evolution over time using aggregate bond allocation data from CPIS. Our results show that the home bias is prevalent across all countries, despite the decreasing of the domestic bias in most countries in the 1997–2009 period. We find that the domestic bond bias is lower in countries with higher economic development, higher restrictions on foreign capital transactions, more developed bond markets, higher familiarity, and higher efficiency of the judicial system. When investing overseas, investors also prefer to allocate their investments in countries with higher economic development, lower restrictions on capital flows, more developed bond markets, stronger judicial systems, and higher past returns. Additionally, we find that familiarity (i.e. geographic proximity, common language, and bilateral trade) is a major determinant to decrease the foreign bias. Finally, there is no evidence that investors’ bond allocations are explained by diversification opportunities as proxied by bond markets correlations.     

U.S. and Latin American stock market linkages

This paper examines to what extent the Latin American equity markets of Argentina, Brazil, Chile and Mexico have become more integrated with the US equity market. We empirically measure integration by finding the dynamic conditional correlation (DCC) between each market and that in the U.S. using a DCC multivariate GARCH model. We then track how these correlations evolve over time using a smooth transition model which not only shows when greater integration first occurred but also how long it took these correlations to transition to their new levels. Our sample period stretches from December 30th, 1988 to March 26th, 2004. Results show an increase in the degree of co-movement between these countries’ equity returns and those in the U.S. although the magnitude and speed of these increases greatly varies across these four countries.     

Correlations between stock returns and bond returns: income and substitution effects

We attempt to better understand the varying correlations between stock and bond returns across countries and over sample periods using international data. The observation is that there are two forces that affect the correlation between stock and bond returns. The force that drives a positive correlation is identified as the income effect. The force that drives a negative correlation is identified as the substitution effect. In combination, the two effects help determine the actual correlation between stock and bond returns. We contribute to the literature by proposing an empirical method, the structural vector autoregression (VAR) identification method, to identify the two—income and substitution—effects and to measure the relative importance of the two effects that determine the actual net relation between the two asset returns. We further provide some evidence that the income and substitution effects are related to, among other things, the size of the financial market, the growth and volatility (risk) of the economy, and the business cycle over time. In addition, the framework of the income and substitution effects helps us better understand the automatic stabilizing effects of the dynamic optimal asset allocation during business cycles.     

The impact of forced divestments on parent company stock prices: Buy on the rumor,sell on the news?

We measure how warnings of expropriation and forced divestments of private property affect the stock prices of parent companies. We use a unique database of 116 events in 12 countries from 2005 to 2013. Our results show that different types of warnings have significant negative effects on stock prices, and the largest effect is from a warning that takes the form of a transitory permit revocation. In the case of forced divestments, we find a significant negative impact when a permit is permanently revoked. However, nationalizations are associated with a positive market reaction.     

Securitization: The Transformation of Illiquid Financial Assets into Liquid Capital Market Securities Examples from the European Market

Since the benefits a firm can derive from securitization are universal, the discussion of a market bounded by national borders is somewhat artificial unless the focus is on constraints particular to the country which promote or inhibit the use of securitization. With the exception of the United Kingdom, regulatory constraints have been an important factor in slowing the development of a European market for asset and mortgage backed securities. In addition to the regulatory hurdles, securitization in Europe has been inhibited by segmented corporate bond markets and the relatively slow development of money market savings vehicles for households. Liquidity across credit spectrums has been enhanced since the introduction of the Euro, as has been the competition for savings. European companies are developing the ability to securitize even if the technique is not yet being widely exploited. What is the European market for mortgage and asset backed securities? Does it include the U.S. credit card banks, Citicorp, Chase, MBNA, and First USA that have refinanced U.S. credit card receivables in European currencies and in Euro? Does it include GMAC which has structured Swiss Franc and Euro ABS backed by its U.S. dealer floor plan loans? Does it include Japanese banks that have refinanced Yen denominated leases with Euro and Swiss Franc ABS? Does it include Barclays' issue of $1 billion of ABS backed by sterling credit card receivables? Of course the answer is yes. Markets are defined by both the supply and demand sides. Our analysis focuses on the supply side of the domestic European market.     

On the Modeling and Forecasting of Socioeconomic Mortality Differentials: An Application to Deprivation and Mortality in England

In any country, mortality rates and indices such as life expectancy usually differ across subpopulations, for example, defined by gender, geographic area, or socioeconomic variables (e.g., occupation, level of education, or income). These differentials, and in particular those related to socioeconomic circumstances, pose important challenges for the design of public policies for tackling social inequalities, as well as for the design of pension systems and the management of longevity risk in pension funds and annuity portfolios. We discuss the suitability for the modeling and forecasting of socioeconomic differences in mortality of several multiple population extensions of the Lee-Carter model, including a newly introduced relative model based on the modeling of the mortality in socioeconomic subpopulations alongside the mortality of a reference population. Using England mortality data for socioeconomic subpopulations defined using a deprivation index, we show that this new relative model exhibits the best results in terms of goodness of fit and ex post forecasting performance. We then use this model to derive projections of deprivation specific mortality rates and life expectancies at pensioner ages and analyze the impact of socioeconomic differences in mortality on the valuation of annuities.     

The Impact of Adopting International Accounting Standards on the Harmonization of Accounting Practices

Over the past few decades numerous organizations have been actively participating in the efforts to improve the comparability of financial reporting. Many studies have discussed the benefits and drawbacks of comparability. This study investigated the affect on the harmonization, or comparability, of accounting practices when a sample of companies choose to use international accounting standards (IASs) when preparing financial reports.This study analyzed trends in the I index, a measure of concentration for the use of a particular accounting practice introduced by van der Tas, to determine if the choice of accounting methods by a sample of Swiss companies became more aligned with a sample of companies from three other countries. The study included a control sample of Swiss companies that did not switch from reporting using local Swiss standards during the same time period, 1988 through 1995. Four accounting practices were included; depreciation, inventory, financial statement cost basis, and consolidation practices. The practices used were compared with a sample of companies from three countries; Japan, the UK, and the US.The results indicated that across the 8-year period, the majority of the I indices comparisons were positive and statistically significant. However, the results did not support that these increases were due primarily to the adoption of IASs.     

Mortality of Smoking by Gender

Exposure to cigarette smoke has had and will continue to have a huge effect on mortality. Significant differences in smoking prevalence rates by gender have contributed to varying levels and rates of improvement in mortality over the last several decades and are expected to continue to influence mortality improvement differently over the next several decades. The combined effect of greater historical smoking prevalence rates by males and their corresponding earlier and larger reduction has in part been responsible for the recent improvement in mortality rates for males compared to that for females in the United States. Similar patterns are evident in almost all economically developed countries, although their timing and levels differ. The patterns in less-developed countries will likely follow similar patterns as concerns emerge about the effect of smoking on the mortality of their citizens. The objective of this article is to compare smoking prevalence and cessation by gender and the effect on smoking-attributable and, in turn, all-cause mortality. A summary of mortality attribution approaches used to enhance the evaluation of the effect of smoking and projections of mortality rates by gender is also provided.     

Understanding Post‐Euro Law‐of‐One‐Price Deviations

We put together a unique panel of thousands of good‐level prices before and after the euro to compare the determinants and understand the evolution of goods price dispersion across Europe over time. We find that tradeability and nontraded inputs play a significantly smaller role for cross‐country price dispersion after the adoption of the euro, and for Eurozone economies as compared to European Union ones. We then compare the distributions of law‐of‐one‐price (LOP) deviations over time to understand how the degree of integration across European economies changed after the euro. Our tests reveal that the distributions after the euro are typically significantly different from those before, consistent with a greater degree of integration. Utilizing our unique panel data set to trace the location of individual goods in the distribution of LOP deviations, we ask how the price advantage or disadvantage evident in these price distributions evolves over time, and whether goods characteristics play a role for the persistence of these LOP deviations. LOP deviations for these goods are highly correlated over 5‐ or 10‐ year horizons, and correlations remain significantly high over longer horizons. These correlations are greater for homogeneous as compared to differentiated goods and vary across countries. Finally, for most of these European economies and goods, price advantage is typically revealed to be more persistent than price disadvantage.