CAPM and Option Pricing With Elliptically Contoured Distributions

This article offers an alternative proof of the capital asset pricing model (CAPM) when asset returns follow a multivariate elliptical distribution. Empirical studies continue to demonstrate the inappropriateness of the normality assumption for modeling asset returns. The class of elliptically contoured distributions, which includes the more familiar Normal distribution, provides flexibility in modeling the thickness of tails associated with the possibility that asset returns take extreme values with nonnegligible probabilities. As summarized in this article, this class preserves several properties of the Normal distribution. Within this framework, we prove a new version of Stein's lemma for this class of distributions and use this result to derive the CAPM when returns are elliptical. Furthermore, using the probability distortion function approach based on the dual utility theory of choice under uncertainty, we also derive an explicit form solution to call option prices when the underlying is log‐elliptically distributed. The Black–Scholes call option price is a special case of this general result when the underlying is log‐normally distributed.     

Optimal Capital Allocation Principles

This article develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimization argument, requiring that the weighted sum of measures for the deviations of the business unit's losses from their respective allocated capitals be minimized. The approach is fair insofar as it requires capital to be close to the risk that necessitates holding it. The approach is additionally very flexible in the sense that different forms of the objective function can reflect alternative definitions of corporate risk tolerance. Owing to this flexibility, the general framework reproduces several capital allocation methods that appear in the literature and allows for alternative interpretations and possible extensions.     

The Simple Analytics of a Pooled Annuity Fund

This article provides a formal analysis of payout adjustments from a longevity risk‐pooling fund, an arrangement we refer to as group self‐annuitization (GSA). The distinguishing risk diffusion characteristic of GSAs in the family of longevity insurance instruments is that the annuitants bear their systematic risk, but the pool shares idiosyncratic risk. This obviates the need for an insurance company, although such instruments could be sold through a corporate insurer. We begin by deriving the payout adjustment for a single entry group with a single annuity factor and constant expectations. We then show that under weak requirements a unique solution to payout paths exists when multiple cohorts combine into a single pool. This relies on the harmonic mean of the ratio of realized to expected survivorship rates across cohorts. The case of evolving expectations is also analyzed. In all cases, we demonstrate that the periodic‐benefit payment in a pooled annuity fund is determined based on the previous payment adjusted for any deviations in mortality and interest from expectations. GSA may have considerable appeal in countries which have adopted national defined contribution schemes and/or in which the life insurance industry is noncompetitive or poorly developed.     

Testing Adverse Selection With Two‐Dimensional Information: Evidence From the Singapore Auto Insurance Market

This article examines adverse selection in insurance markets with two‐dimensional information: policyholders’ riskiness and degree of risk aversion. We build a theoretical model to make equilibrium predictions on competitive insurance screening. We study several variations on the pattern of information asymmetry. The outcomes range from full separation to partial separation, and complete pooling of risk types. Next, we propose a copula approach to jointly examine policyholders’ coverage choice and accident occurrence in the Singapore automobile insurance market. Furthermore, we invoke the theory to identify subgroups of policyholders for whom one may expect the risk–coverage correlation and adverse selection to arise.     

Input–output interactions and optimal monetary policy

This paper deals with the implications of factor demand linkages for monetary policy design in a two-sector dynamic general equilibrium model. Part of the output of each sector serves as a production input in both sectors, in accordance with a realistic input–output structure. Strategic complementarities induced by factor demand linkages significantly alter the transmission of shocks and amplify the loss of social welfare under optimal monetary policy, compared to what is observed in standard two-sector models. The distinction between value added and gross output that naturally arises in this context is of key importance to explore the welfare properties of the model economy. A flexible inflation targeting regime is close to optimal only if the central bank balances inflation and value added variability. Otherwise, targeting gross output variability entails a substantial increase in the loss of welfare.     

Determinacy, stock market dynamics and monetary policy inertia

We study equilibrium determinacy in a New-Keynesian model where the Central Bank responds to asset prices growth. Unlike Taylor-type rules that react to asset prices, the proposed alternative does not harm dynamic stability and in certain cases promotes determinacy by inducing interest-rate inertia.     

Longitudinal modeling of insurance claim counts using jitters

Modeling insurance claim counts is a critical component in the ratemaking process for property and casualty insurance. This article explores the usefulness of copulas to model the number of insurance claims for an individual policyholder within a longitudinal context. To address the limitations of copulas commonly attributed to multivariate discrete data, we adopt a ‘jittering’ method to the claim counts which has the effect of continuitizing the data. Elliptical copulas are proposed to accommodate the intertemporal nature of the ‘jittered’ claim counts and the unobservable subject-specific heterogeneity on the frequency of claims. Observable subject-specific effects are accounted in the model by using available covariate information through a regression model. The predictive distribution together with the corresponding credibility of claim frequency can be derived from the model for ratemaking and risk classification purposes. For empirical illustration, we analyze an unbalanced longitudinal dataset of claim counts observed from a portfolio of automobile insurance policies of a general insurer in Singapore. We further establish the validity of the calibrated copula model, and demonstrate that the copula with ‘jittering’ method outperforms standard count regression models.     

Far away from a skill-biased change: falling educational wage premia in Italy

In this article we apply quantile regressions to investigate the evolution of Educational Wage Premia (EWP) in Italy from 1993 to 2004. Using the Survey of the Household Income and Wealth (SHIW, Bank of Italy) and different classifications for educational attainments, we show that, in the private sector, EWP have generally decreased over time, considering both continuous and categorical specifications for education, at all quantiles of the wage distribution. Different patterns are observed in the public sector, where EWP remain basically stable over time. A number of robustness checks and various econometric specifications are also applied in order to address sample selection issues. Our findings provide additional evidence in favour of the thesis that the increasing patterns in inequality and EWP, and the related interpretations concerning skill-biased changes, are much less pronounced in continental Europe than in Anglo-Saxon countries.     

Cereal price shocks and volatility in sub‐Saharan Africa: what really matters for farmers’ welfare?

The lack of information as well as some misperceptions about the distinction between the welfare consequences of higher versus more volatile cereal prices has limited the effectiveness of policy interventions during the recent food crises in many developing countries. This article proposes an integrated empirical strategy to investigate and compare the different effects of these two phenomena and tests it using nationally representative household survey data from four sub‐Saharan countries. Results show that the negative impacts of a cereal price increase substantially outweigh the effects of price volatility on household welfare across the entire income distribution. The amplitude and the distribution of those effects depend heavily on specific factors, such as: the weight of food consumption over total expenditure; the budget share devoted to cereals; the substitution effect among food groups; and the relative number of net sellers versus net buyers accessing the market. We also show that volatility mainly harms the poorest quintile of the population.     

The effects of exchange rate regimes on real exchange rate misalignment

The literature on exchange rate regimes has paid little attention to the effects of exchange rate policies on real exchange rate misalignments. This paper contributes to filling that gap by exploring such relation empirically. Because the underlying model is probably not linear and the treated individuals differ from non-treated individuals, we rely on Matching models rather than on standard regressions. Our main finding is that pegs are associated with more overvaluation. The results are robust to different exchange rate regime classifications, misalignment indexes, and matching estimators. The evidence presented suggests that policy-makers concerned with overvaluation should avoid sticking with rigid arrangements for too long.