Analysis of embedded options in individual pension schemes in Germany

Newly introduced government-subsidized pension products in Germany are required to contain a promise by the seller to provide a “money-back guarantee” at the end of the term. The client is also given the right to stop paying premiums at any time (paid-up option). In this case, the amount of all premiums paid must also be guaranteed by the seller at maturity, no matter when the client stopped paying the premiums. Previous analyses of guarantees in such government-subsidized pension products have ignored this additional option. Within a generalized Black/Scholes framework, we analyze the value of the paid-up option for different products, market scenarios, and client behavior. Our results indicate that the paid-up option significantly increases the value of the money-back guarantee. Furthermore, we find that reducing volatility by shifting the client’s assets from stocks to bonds as maturity approaches is a suitable means of reducing the risk arising from the “pure” money-back guarantee but much less effective in reducing the risk arising from the paid-up option. JEL Classification G13 · G23 · G28     

The Effect of House Prices on Household Consumption in Italy

This paper studies the effect of a change in real estate wealth on the consumption behaviour of Italian households, using the Bank of Italy’s Survey of Household Income and Wealth dataset. We relate annual household consumption to capital gains in housing, controlling for characteristics such as age. In line with the empirical predictions of our model, we find the oldest households—which are less affected by the higher costs of future rent—to be the most affected by increases in real net housing wealth. Younger households, on the other hand, are not significantly affected in their consumption decisions by house price increases. We also take into account the fact that benefiting from capital gains is conditional on owning housing wealth and estimate the different impacts of house price changes on the savings behaviours of both homeowners and renters. Our estimates suggest that house price increases raise consumption not only for homeowners but also for renters.     

Asset price bubbles from heterogeneous beliefs about mean reversion rates

Harrison and Kreps showed in 1978 how the heterogeneity of investor beliefs can drive speculation, leading the price of an asset to exceed its intrinsic value. By focusing on an extremely simple market model—a finite-state Markov chain—the analysis of Harrison and Kreps achieved great clarity but limited realism. Here we achieve similar clarity with greater realism, by considering an asset whose dividend rate is a mean-reverting stochastic process. Our investors agree on the volatility, but have different beliefs about the mean reversion rate. We determine the minimum equilibrium price explicitly; in addition, we characterize it as the unique classical solution of a certain linear differential equation. Our example shows, in a simple and transparent manner, how heterogeneous beliefs about the mean reversion rate can lead to everlasting speculation and a permanent “price bubble.”     

Solving an asset pricing model with hybrid internal and external habits,and autocorrelated Gaussian shocks

We derive an explicit formula for the price-dividend ratio of a generalized version of Abel’s asset pricing model. This model is generalized in two ways: first, consumption (dividend) growth is assumed to be an AR(1) process subject to Gaussian random shocks, and second, the investor’s preferences are allowed to be a convex combination of internal and external habits. With an internal habit weight, 50%, and a coefficient of risk aversion, 3.25, simulation results match the historic US equity premium and risk free interest rate.      

Factors driving aggregate mortality rates in postwar Germany

Using German data over the period 1956–2006, this study provides a comprehensive empirical analysis of factors driving aggregate mortality rates over time. It differs from previous contributions in this field by simultaneously considering an extensive set of macroeconomic, socioeconomic, and ecological factors as explanatory variables. Our regression analysis shows that sex- and age-specific mortality rates vary substantially in their response to external factors. Strongest associations are found with changes in real GDP, flu epidemics, and the two lifestyle variables—alcohol and cigarette consumption—in both univariate and multivariate setups. Further analysis indicates that these effects are primarily contemporary, whereas other indicators, such as weather conditions, exert lagged effects. We derive optimal multivariate models for every age group that provide a good fit to the observed variation in annual mortality rates, and thereby confirm the relevance of the identified factors.     

Institutional Monitoring and REIT CEO Compensation

Our objective in this paper is to investigate the relationship between institutional ownership and CEO compensation structure of REITs. Based on detailed analyses of data on institutional ownership, performance, CEO and board characteristics over the 10 year period 1998–2007, we find significant evidence that large institutions influence governance through CEO compensation—greater institutional ownership is associated with greater emphasis on incentive-based compensation (higher pay-performance sensitivity of CEO compensation), and higher cash and total compensation for CEOs. Further, we find that institutions are less active when managers are performing in a superior fashion. Two important conclusions emerge from the analysis. First, similar to unregulated firms, institutional owners do act as monitors in REITs. Broadly, this result suggests that governance is necessary for REITs. Second, institutional investors set a high pay-performance sensitivity for CEOs, but are willing to pay higher cash compensation to induce managers to take risk.     

Model misspecification analysis for bond options and Markovian hedging strategies

In this paper, we analyse the model misspecification risk of Markovian hedging strategies for discount bond options. We show how to decompose the Profit and Loss that results from model misspecification, and emphasize the importance of the position’s gamma in order to control it. We further provide mathematical results on the distribution of the forward Profit and Loss function for specific univariate term structure models. Finally, we run numerical simulations for options’ hedging strategies in order to examine the sensitivity of the forward Profit and Loss function with respect to the volatility of the forward rate curve, the frequency of the position rebalancing and the characteristics of the position being hedged.      

Evidence on Simulation Inference for Near Unit-Root Processes with Implications for Term Structure Estimation

The high persistence of interest rates has important implicationsfor the preferred method used to estimate term structure models.We study the finite-sample properties of two standard dynamicsimulation methods—efficient method of moments (EMM) andindirect inference—when they are applied to an first orderautoregressive (AR[1]) process with Gaussian innovations. Whensimulated data are as persistent as interest rates, the finite-sampleproperties of EMM differ both from their asymptotic propertiesand from the finite-sample properties of indirect inferenceand maximum likelihood. EMM produces larger confidence boundsthan indirect inference and maximum likelihood, yet is muchless likely to contain the true parameter value. This is primarilybecause the population variance of the data plays a much largerrole in the EMM conditions than in the moment conditions foreither indirect inference or maximum likelihood. These resultssuggest that, under Gaussian assumptions, indirect inference(if practical) is preferable to EMM when working with persistentdata such as interest rates. EMM's emphasis on the populationvariance strongly enforces stationarity on the underlying process,so this same reasoning suggests that EMM may be preferable insettings where stability and stationarity are important anddifficult to impose.     

An example of a stochastic equilibrium with incomplete markets

We prove existence and uniqueness of stochastic equilibria in a class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and general Markovian random endowments. The incompleteness featured in our setting—the source of which can be thought of as a credit event or a catastrophe—is genuine in the sense that not only the prices, but also the family of replicable claims itself are determined as a part of the equilibrium. Consequently, equilibrium allocations are not necessarily Pareto optimal and the related representative-agent techniques cannot be used. Instead, we follow a novel route based on new stability results for a class of semilinear partial differential equations related to the Hamilton–Jacobi–Bellman equation for the agents’ utility maximization problems. This approach leads to a reformulation of the problem where the Banach fixed-point theorem can be used not only to show existence and uniqueness, but also to provide a simple and efficient numerical procedure for its computation.     

Analysis of Consumers’ Perceptions of Buying Conditions for Houses

This paper examines the determinants of consumers’ buying attitudes for houses from January 1984 through June 2005. Data on buying attitudes are from responses to the Surveys of Consumer Attitudes conducted by the Survey Research Center, University of Michigan. The determinants considered include current and expected interest rates, wealth, expected real disposable income, expected change in financial status and house prices. The empirical estimates show that a long-run relationship exists between buying attitudes for houses and each of the above variables. Each of these determinants also Granger cause buying perceptions. Generalized impulse responses show that shocks to each of the above variables have a predictable and permanent impact on buying attitudes. Furthermore, generalized variance decompositions suggest that both current and expected interest rates explain a large proportion of the variation in consumers’ perceptions towards buying houses. Since consumers’ attitudes towards buying houses are likely to be translated into actual purchases, this study shows that in order of importance, interest rates—both current and future—have the maximum impact on decisions to purchase houses followed by expectations of real disposable income.

Leveraged Lévy processes as models for stock prices

Adopting a constant elasticity of variance formulation in the context of a general Lévy process as the driving uncertainty we show that the presence of the leverage effect? ?One explanation of the documented negative relation between market volatilities and the level of asset prices (the ‘smile’ or ‘skew’), we term the ‘leverage effect’, argues that this negative relation reflects greater risk taking by the management, induced by a fall in the asset price, with a view of maximizing the option value of equity shareholders. in this form has the implication that asset price processes satisfy a scaling hypothesis. We develop forward partial integro-differential equations under a general Markovian setup, and show in two examples (both continuous and pure-jump Lévy) how to use them for option pricing when stock prices follow our leveraged Lévy processes. Using calibrated models we then show an example of simulation-based pricing and report on the adequacy of using leveraged Lévy models to value equity structured products.     

Do Managerial Motives Impact Dividend Decisions in REITs?

Conflict of interest between shareholders (principal) and managers (agent) is a potential weakness of the modern corporate form. Various monitoring mechanisms—pay for performance compensation schemes, mix of cash compensation and long term compensation, the independence of the board of directors, the market for takeovers, and capital structure—have been developed to discipline management and motivate them to maximize shareholder wealth. We test the hypothesis that dividend payout levels reflect the quality of and motivation for managerial decision making and are a function of performance and monitoring effectiveness. Consistent with this hypothesis, our analyses indicate that dividend payout, and dividend yield are functions of corporate performance, board structure, CEO tenure, and CEO ownership of company shares.     

Squared Bessel Processes and Their Applications to the Square Root Interest Rate Model

We study the Bessel processes withtime-varying dimension and their applications to the extended Cox-Ingersoll-Rossmodel with time-varying parameters. It is known that the classical CIR model is amodified Bessel process with deterministic time and scale change. We show thatthis relation can be generalized for the extended CIR model with time-varyingparameters, if we consider Bessel process with time-varying dimension. Thisenables us to evaluate the arbitrage free prices of discounted bonds and theircontingent claims applying the basic properties of Bessel processes. Furthermorewe study a special class of extended CIR models which not only enables us to fitevery arbitrage free initial term structure, but also to give the extended CIRcall option pricing formula.     

New bond pricing models with applications to Japanese data

In this paper, the cross-sectional bond pricing model for individual bonds Kariya (1993) proposed by formulating stochastic discount function (term structure) is first applied to Japanese Government bond (JG-bond) data. The model performs very well as it stands. Second, we generalize the cross-sectional model to two types of time-dependent Markov models (TDM's) with the term structure of discount rates of each bond att being dependent on the one att−1, and apply them to the same data to find significantly improved results over those of the cross-sectional model. In fact, almost all the differences between actual prices and model values are less than 0.5 yen in each month over 12 years, implying that the error rate is less than 0.5%. On the basis of our analysis, we propose a TDM as a model for JG-bond trading.     

Limited attention and the earnings announcement returns of past stock market winners

We document that stocks with the strongest prior 12-month returns experience a significant average market-adjusted return of 1.58% during the five trading days before their earnings announcements and a significant average market-adjusted return of −1.86% in the five trading days afterward. These returns remain significant even after accounting for transactions costs. We empirically test a limited attention explanation for these anomalous returns—that stocks with sharp run-ups tend to attract individual investors’ attention and investment dollars, particularly before their earnings announcements. Our analysis suggests that the trading decisions of individual investors are at least partly responsible for the return pattern that we observe.     

How do investment patterns of independent and captive private equity funds differ? Evidence from Germany

Empirical literature emphasizes a positive contribution of private equity investors, which results from their combined provision of capital, monitoring, and management support. The aim of this study is to show that these previous results, which are based mostly on the analysis of US independent closed-end private equity funds, cannot be generalized since the private equity industry should not be treated as homogenous. We argue that it is necessary to distinguish between different types of private equity providers because their differing governance structures, strategic goals and experiences have a decisive influence on their value adding activities. The results of this study—which uses a data set of 179 German private equity-backed companies—are consistent with the conjecture that independent and corporate private equity providers tend to have a more pronounced role in corporate governance and monitoring of the companies they finance, than bank-dependent and governmental funds which often serve only as bridge investors.      

Interest Rate Term Structure Estimation with Exponential Splines: A Note

Vasicek and Fong 11 developed exponential spline functions as models of the interest rate term structure and claim such models are superior to polynomial spline models. It is found empirically that i) exponential spline term structure estimates are no more stable than estimates from a polynomial spline model, ii) data transformations implicit in the exponential spline model frequently condition the data so that it is difficult to obtain approximations in which one can place confidence, and iii) the asymptotic properties of the exponential spline model frequently are unrealistic. Estimation with exponential splines is no more convenient than estimation with polynomial splines and gives substantially identical estimates of the interest rate term structure as well.     

FHA vs. Subprime Mortgage Originations: Is FHA the Answer to Subprime Lending?

We analyze originations of mortgages guaranteed by the Federal Housing Administration (FHA) and of subprime mortgages—loans that dominate the non-prime mortgage market for riskier borrowers. Using home purchase and refinance loans data for 2005, we estimate that a sizeable number of borrowers who got subprime loans would have qualified for FHA loans, implying a potential net flow of borrowers from subprime to FHA, especially for refinance loans at a rate of about 30%. Also, consistent with the FHA’s modernization proposal to increase its loan limits, we find that increasing the limits on FHA loans could help to attract borrowers, mostly of home purchase loans, who are likely to be constrained by the lower-priced house limits. Our findings are generally in line with the recent increased flow of mortgages to FHA, and suggest that FHA loans could be the answer to the current subprime lending crisis.     

Price-volume Correlation in the Housing Market: Causality and Co-movements

Housing market cycles are featured by a positive correlation of prices and trading volume, which is conventionally attributed to a causal relationship between prices and volume. This paper analyzes the housing markets in 114 metropolitan statistical areas in the United States from 1990 to 2002, treats both prices and volume as endogenous variables, and studies whether and how exogenous shocks cause co-movements of prices and volume. At quarterly frequency, we find that, first, both home prices and trading volume are affected by conditions in labor markets, the mortgage market, and the stock market, and the effects differ between markets with low and high supply elasticity. Second, home prices Granger cause trading volume, but the effects are asymmetric—decreases in prices reduce trading volume, and increases in prices have no effect. Third, trading volume also Granger causes home prices, but only in markets with inelastic supply. Finally, we find a statistically significant positive price–volume correlation; which, however, is mainly explained by co-movements of prices and volume caused by exogenous shocks, instead of the Granger causality between prices and volume.