A flexible lattice framework for valuing options on assets paying discrete dividends and variable annuities embedding GMWB riders

In a market where a stochastic interest rate component characterizes asset dynamics, we propose a flexible lattice framework to evaluate and manage options on equities paying discrete dividends and variable annuities presenting some provisions, like a guaranteed minimum withdrawal benefit. The framework is flexible in that it allows to combine financial and demographic risk, to embed in the contract early exercise features, and to choose the dynamics for interest rates and traded assets. A computational problem arises when each dividend (when valuing an option) or withdrawal (when valuing a variable annuity) is paid, because the lattice lacks its recombining structure. The proposed model overcomes this problem associating with each node of the lattice a set of representative values of the underlying asset (when valuing an option) or of the personal subaccount (when valuing a variable annuity) chosen among all the possible ones realized at that node. Extensive numerical experiments confirm the model accuracy and efficiency.

     

Robust stochastic frontier analysis: a Student’s t-half normal model with application to highway maintenance costs in England

The presence of outliers in the data has implications for stochastic frontier analysis, and indeed any performance analysis methodology, because they may lead to imprecise parameter estimates and, crucially, lead to an exaggerated spread of efficiency predictions. In this paper we replace the normal distribution for the noise term in the standard stochastic frontier model with a Student’s t distribution, which generalises the normal distribution by adding a shape parameter governing the degree of kurtosis. This has the advantages of introducing flexibility in the heaviness of the tails, which can be determined by the data, as well as containing the normal distribution as a limiting case, and we outline how to test against the standard model. Monte Carlo simulation results for the maximum simulated likelihood estimator confirm that the model recovers appropriate frontier and distributional parameter estimates under various values of the true shape parameter. The simulation results also indicate the influence of a phenomenon we term ‘wrong kurtosis’ in the case of small samples, which is analogous to the issue of ‘wrong skewness’ previously identified in the literature. We apply a Student’s t-half normal cost frontier to data for highways authorities in England, and this formulation is found to be preferred by statistical testing to the comparator normal-half normal cost frontier model. The model yields a significantly narrower range of efficiency predictions, which are non-monotonic at the tails of the residual distribution.

     

Integral stochastic optimal design criteria in linear models

Within the framework of classical linear regression model integral optimal design criteria of stochastic nature are considered and their properties are established. Their limit behaviour generalizes that of the distance stochastic optimality criterion. As an example a line fit model is taken. Acknowledgement. I would like to thank the referees for their constructive comments which improved the paper.     

Modeling dependence in two-tier stochastic frontier models

The two-tier stochastic frontier model has seen widespread application across a range of social science domains. It is particularly useful in examining bilateral exchanges where unobserved side-specific information exists on both sides of the transaction. These buyer and seller specific informational aspects offer opportunities to extract surplus from the other side of the market, in combination also with uneven relative bargaining power. Currently, this model is hindered by the fact that identification and estimation relies on the potentially restrictive assumption that these factors are statistically independent. We present three different models for empirical application that allow for varying degrees of dependence across these latent informational/bargaining factors.

     

Debt Service Capacity Revisited

Abstract

Debt Service Capacity (DSC) is revisited within a new framework, i.e., Neural Networks (NN), an established method in the field of artificial intelligence (AI). A select group of traditional models that have been used to predict DSC is also reviewed and the logit approach is chosen for comparison with NN.

Ten measures (indices) are constructed as determinants of DSC. To keep the comparison simple, empirical applications of the two models are controlled by employing the same data sample and the same holdout and estimation groups in both models. A few drawbacks of the traditional approaches, especially the presence of multicollinearity, are pointed out. It is shown that when multicollinearity is present, the exponential of the coefficients cannot be explained as the odds ratio.

A number of tests and sensitivity analyses are performed to exhibit the attributes and the performance of the two models.     

A stochastic frontier model with correction for sample selection

Heckman’s (Ann Econ Soc Meas 4(5), 475–492, 1976; Econometrica 47, 153–161, 1979) sample selection model has been employed in three decades of applications of linear regression studies. This paper builds on this framework to obtain a sample selection correction for the stochastic frontier model. We first show a surprisingly simple way to estimate the familiar normal-half normal stochastic frontier model using maximum simulated likelihood. We then extend the technique to a stochastic frontier model with sample selection. In an application that seems superficially obvious, the method is used to revisit the World Health Organization data (WHO in The World Health Report, WHO, Geneva 2000; Tandon et al. in Measuring the overall health system performance for 191 countries, World Health Organization, 2000) where the sample partitioning is based on OECD membership. The original study pooled all 191 countries. The OECD members appear to be discretely different from the rest of the sample. We examine the difference in a sample selection framework.     

Kernel-based nonlinear canonical analysis and time reversibility

We consider a kernel-based approach to nonlinear canonical correlation analysis and its implementation for time series. We deduce a test procedure of the reversibility hypothesis. The method is applied to the analysis of stochastic differential equation from high-frequency data on stock returns.     

Optimal Dividend Payment Strategy under Stochastic Interest Force

This paper attempts to study the optimal dividend barrier strategy in risk analysis of an insurance company under stochastic discount interest. Based on stochastic perturbation methodology, we first describe the random of interest by Wiener Process and Poisson process and yield some theoretical results satisfied by optimal dividend barrier. In the case of an exponential individual claim distribution, a group of barrier values are obtained. Meanwhile we also discuss the effect of stochastic interest on the barrier by data analysis and direct interpretations about interest models. It is found that the barrier is more sensitive to constant interest force than other parameters in interest model and the effect of diffusion coefficient on barrier is less sensitive than that of Poisson coefficient. These all provide insights into the effect of stochastic interest on the optimal barrier, and show the importance of introducing stochastic interest. Finally, we propose several meaningful and follow-up problems, for example, changing the criterion of finding the optimal barrier and discussing under more extended risk models.     

The relationship between private investors and small firms: an agency theory approach

Many small firms in Sweden are characterized by a lack of equity capital. For several years measures to increase the equity capital have been discussed. In this discussion the private investors' market has received virtually no attention. This study presents some preliminary results of the private investors in Sweden.

The research in small firms financing is characterized by a lack of theoretical framework. One basic assumption in the study is that agency theory can provide an essential framework to explain the interaction between the private investor and entrepreneur. Twenty-five hypotheses generated from agency theory are formulated and tested on 62 small unlisted firms in Sweden. Multiple regression analysis is used for the causal analyses.

The empirical results in the study show inter alia that the geographic distance and the private investor's knowledge about the portfolio firm's transformation process seem to be the most influential factors for determining the private investor's involvement in the portfolio firms. It is also interesting to notice that none of the variables, frequency of contacts and the private investor's operational work in the portfolio firm affect the performance of the firm. Contrary to conventional wisdom, private investors do not add value to their portfolio firms through their interaction with the entrepreneurs.

The theoretical conclusion is that agency theory does not provide any satisfactory framework to explain the private investor - entrepreneur relationship. Some of the basic assumptions in agency theory seem to be invalid. A model for the relationship between private investors and entrepreneurs is developed in which four interaction strategies are identified. The model gives implications on two levels: the portfolio level and the individual case level.     

Estimating production frontiers and efficiency when output is a discretely distributed economic bad

This article studies the estimation of production frontiers and efficiency scores when the commodity of interest is an economic bad with a discrete distribution. Existing parametric econometric techniques (stochastic frontier methods) assume that output is a continuous random variable but, if output is discretely distributed, then one faces a scenario of model misspecification. Therefore a new class of econometric models has been developed to overcome this problem. The Delaporte subclass of models is studied in detail, and tests of hypotheses are proposed to discriminate among parametric models. In particular, Pearson’s chi-squared test is adapted to construct a new kernel-based consistent Pearson test. A Monte Carlo experiment evaluates the merits of the new model and methods, and these are used to estimate the frontier and efficiency scores of the production of infant deaths in England. Extensions to the model are discussed.     

Markovian lifts of positive semidefinite affine Volterra-type processes

We consider stochastic partial differential equations appearing as Markovian lifts of matrix-valued (affine) Volterra-type processes from the point of view of the generalized Feller property (see, e.g., Dörsek and Teichmann in A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). We introduce in particular Volterra Wishart processes with fractional kernels and values in the cone of positive semidefinite matrices. They are constructed from matrix products of infinite dimensional Ornstein–Uhlenbeck processes whose state space is the set of matrix-valued measures. Parallel to that we also consider positive definite Volterra pure jump processes, giving rise to multivariate Hawkes-type processes. We apply these affine covariance processes for multivariate (rough) volatility modeling and introduce a (rough) multivariate Volterra Heston-type model.

     

Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia

This study estimates the technical efficiency measures of maize producing farm households in Ethiopia using stochastic frontier (SF) panel models that take different approaches to model firm heterogeneity. The efficiency measures are found to vary depending on how the estimation model treats both unobserved and observed firm heterogeneity. Estimates from the ‘true’ random effects (TRE) models that treat firm effects as heterogeneity are found to be identical to those from pooled SF models. Those results differ from the ones generated from the basic random effects (RE) models that treat firm effects as part of overall technical inefficiency. The more flexible generalised ‘true’ random effects (GTRE) model that splits the error term into firm effects, persistent inefficiency, transient inefficiency, and a random noise component indicates the presence of higher levels of persistent inefficiency than transient inefficiency. The basic truncated-normal RE model and heteroscedastic RE model yields similar efficiency estimates. The GTRE model predict persistent efficiency measures similar to those from the basic RE and flexible RE model with environmental variables incorporated in the variance function as well as in the deterministic production frontier. These results imply that the RE and GTRE panel models provide reliable efficiency estimates for our data compared to the TRE models. All the estimated SF models generate comparable production function parameters in terms of magnitude and sign. Overall, the results underscore the importance of scrutinising stochastic frontier models for their reliability of analytical results before drawing policy inferences.

     

Option Pricing under the Double Exponential Jump-Diffusion Model with Stochastic Volatility and Interest Rate

This paper proposes an efficient option pricing model that incorporates stochastic interest rate (SIR), stochastic volatility (SV), and double exponential jump into the jump-diffusion settings. The model comprehensively considers the leptokurtosis and heteroscedasticity of the underlying asset’s returns, rare events, and an SIR. Using the model, we deduce the pricing characteristic function and pricing formula of a European option. Then, we develop the Markov chain Monte Carlo method with latent variable to solve the problem of parameter estimation under the double exponential jump-diffusion model with SIR and SV. For verification purposes, we conduct time efficiency analysis, goodness of fit analysis, and jump/drift term analysis of the proposed model. In addition, we compare the pricing accuracy of the proposed model with those of the Black–Scholes and the Kou (2002) models. The empirical results show that the proposed option pricing model has high time efficiency, and the goodness of fit and pricing accuracy are significantly higher than those of the other two models.     

Teoria dell'utilita'«SSB» e scelta tra distribuzioni di probabilita'

Summary In this paper we apply the SSB theory to the problem of choice among probability distributions. We propose a criterion of choice based on the SSB model and establish a necessary and sufficient condition for it.Finally, a comparison with the usual first order stochastic dominance rule is made.

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Lavoro eseguito nell'ambito del Contributo C.N.R. n. 85.001164.10     

Dynamic correlation multivariate stochastic volatility with latent factors

Modeling the correlation structure of returns is essential in many financial applications. Considerable evidence from empirical studies has shown that the correlation among asset returns is not stable over time. A recent development in the multivariate stochastic volatility literature is the application of inverse Wishart processes to characterize the evolution of return correlation matrices. Within the inverse Wishart multivariate stochastic volatility framework, we propose a flexible correlated latent factor model to achieve dimension reduction and capture the stylized fact of ‘correlation breakdown’ simultaneously. The parameter estimation is based on existing Markov chain Monte Carlo methods. We illustrate the proposed model with several empirical studies. In particular, we use high‐dimensional stock return data to compare our model with competing models based on multiple performance metrics and tests. The results show that the proposed model not only describes historic stylized facts reasonably but also provides the best overall performance.     

Maximum likelihood estimation of stochastic frontier models by the Fourier transform

The paper is concerned with several kinds of stochastic frontier models whose likelihood function is not available in closed form. First, with output-oriented stochastic frontier models whose one-sided errors have a distribution other than the standard ones (exponential or half-normal). The gamma and beta distributions are leading examples. Second, with input-oriented stochastic frontier models which are common in theoretical discussions but not in econometric applications. Third, with two-tiered stochastic frontier models when the one-sided error components follow gamma distributions. Fourth, with latent class models with gamma distributed one-sided error terms. Fifth, with models whose two-sided error component is distributed as stable Paretian and the one-sided error is gamma. The principal aim is to propose approximations to the density of the composed error based on the inversion of the characteristic function (which turns out to be manageable) using the Fourier transform. Procedures that are based on the asymptotic normal form of the log-likelihood function and have arbitrary degrees of asymptotic efficiency are also proposed, implemented and evaluated in connection with output-oriented stochastic frontiers. The new methods are illustrated using data for US commercial banks, electric utilities, and a sample from the National Youth Longitudinal Survey.     

Timing and duration effects in residence histories and other longitudinal data: I. Stochastic and statistical models

A framework for studying the timing of events in migration histories and other micro-level longitudinal data is presented. The framework derives from a general stochastic model of the histories in which moves depend on the past history of the process, time varying individual characteristics, and exogenous constraints and opportunities. The semi-Markov model plays a distinguished role. The framework emphasizes the range of stochastic models available, the different types of time intervals and observational schemes that can be considered, distributions that can be used to characterize intervals, and statistical methodology. The use and crucial importance of the framework in empirical research is illustrated in the sequel.     

Employment Growth in Italian Local Labour Systems: Issues of Model Specification and Sectoral Aggregation

Abstract

In this paper we construct a model to estimate local employment growth in Italian local labour markets for the period 1991–2001. The model is constructed in a similar manner to the original models of Glaeser et al. (1992), Henderson et al. (1995) and Combes (2000). Our objective is to identify the extent to which the results estimated by these types of models are themselves sensitive to the model specification. In order to do this we extend the basic models by successively incorporating new explanatory variables into the model framework. In addition, and for the first time, we also estimate these same models at two different levels of sectoral aggregation, for the same spatial structure. Our results indicate that these models are highly sensitive to sectoral aggregation and classification and our results therefore strongly support the use of highly disaggregated data.     

Irreversible Investment in Stochastically Cyclical Markets

This paper studies entry and exit decisions in markets whose demand alternates between growth and decline phases at uncertain times. We introduce a stochastic process that captures these features of random market evolution, and we provide key mathematical results related to first passage times which make the characterization of entry and exit behavior quite simple and straightforward (even when the process is subject to an endogenously determined upper or lower barrier). We characterize entry and exit patterns in a dynamic competitive equilibrium, and we show why our results differ from those obtained if demand follows a diffusion process (e.g., a Geometric Brownian Motion). Despite the stochastic process of the underlying variable has a continuous sample path in both cases, we demonstrate in our setting that positive rates of entry and exit discontinuously fall to zero owing to informational overshooting. Another advantage of our framework is that it can explain discontinuities in firm values even if sample paths are continuous. Our framework is also amenable to empirical implementations (as we show using Corts’ 2008 offshore oil drilling application), and to an intuitive interpretation of optimal (dis) investment rules based on Bernanke’s (1983) “bad news principle of irreversible investment.”     

A new class of multidimensional Wishart-based hybrid models

In this article, we present a new class of pricing models that extend the application of Wishart processes to the so-called stochastic local volatility (or hybrid) pricing paradigm. This approach combines the advantages of local and stochastic volatility models. Despite the growing interest on the topic, however, it seems that no particular attention has been paid to the use of multidimensional specifications for the stochastic volatility component. Our work tries to fill the gap: we introduce two hybrid models in which the stochastic volatility dynamics is described by means of a Wishart process. The proposed parametrizations not only preserve the desirable features of existing Wishart-based models but significantly enhance the ability of reproducing market prices of vanilla options.