Stochastic dominance analysis of CTA funds

In this paper, we employ the stochastic dominance (SD) approach to rank the performance of commodity trading advisors (CTA) funds. An advantage of this approach is that it alleviates the problems that can arise if CTA returns are not normally distributed by utilizing the entire returns distribution. We find both first-order and higher-order SD relationships amongst the CTA funds and conclude that investors are better off investing in the first-order dominant funds to maximize their expected utilities and expected wealth. However, for higher-order dominant CTAs, risk-averse investors can maximize their expected utilities but not their expected wealth. In addition to the advantages of the SD approach in the case of non-normal returns, the paper concludes that the approach is more appropriate compared with traditional approaches as a filter in the CTA selection process as it provides meaningful economic interpretation of the results.     

The Recovery Theorem

We can only estimate the distribution of stock returns, but from option prices we observe the distribution of state prices. State prices are the product of risk aversion—the pricing kernel—and the natural probability distribution. The Recovery Theorem enables us to separate these to determine the market's forecast of returns and risk aversion from state prices alone. Among other things, this allows us to recover the pricing kernel, market risk premium, and probability of a catastrophe and to construct model‐free tests of the efficient market hypothesis.     

Do we need higher-order comoments to enhance mean-variance portfolios? Evidence from a simplified jump process

We consider a joint distribution that decomposes asset returns into two independent components: an elliptical innovation (Gaussian) and a systematic non-elliptical latent process. The paper provides a tractable approach to estimate the underlying parameters and, hence, the assets’ exposures to the latent non-elliptical factor. Additionally, the framework incorporates higher-order moments, such as skewness and kurtosis, for portfolio selection. Taking into account estimation risk, we investigate the economic contribution of the non-elliptical term. Overall, we find weak empirical evidence to support the inclusion of the non-elliptical term and, hence, the higher-order comoments. Nonetheless, our findings support the mean–variance (MV) decision rule that incorporates the elliptical term alone. Excluding the non-elliptical term results in more robust mean–variance estimates and, thus, enhanced out-of-sample performance. This evidence is significant among stocks that exhibit a strong deviation from the Gaussian property. Moreover, it is most pronounced during market turmoils, when exposures to the latent factor are highest.     

Stochastic dominance analysis of Asian hedge funds

We employ the stochastic dominance approach that utilizes the entire return distribution to rank the performance of Asian hedge funds as traditional mean-variance and CAPM approaches could be inappropriate given the nature of non-normal returns. We find both first-order and higher-order stochastic dominance relationships amongst the funds and conclude that investors would be better off by investing in the first-order dominant funds to maximize their expected wealth. By investing in higher-order dominant funds, risk-averse investors can maximize their expected utilities but not their wealth. In addition, we find the common characteristic for most pairs of funds is that one fund is preferred to another in the negative domain whereas the preference reverses in the positive domain. We conclude that the stochastic dominance approach is more appropriate compared with traditional approaches as a filter in hedge fund selection. Compared with traditional approaches, the SD approach, not only is assumption free, but also provides greater insights to the performance and risk inherent in a hedge fund's track record.     

What Determines Collection Rates of Debt Collection Agencies?

We contribute to the literature on debt collection agencies in two ways: First, we present an estimation of the collection rates. The distribution of collection rates exhibits a mean of about 65% and a strong bimodality with peaks at the very ends of the distribution. Second, we investigate potential determinants of the collection success. We find that collection rates are positively related to the exposure at default and to prior debtor‐specific collection rates. In contrast, the age of the account and—if applicable—prior experience with the debtor have a negative impact on collection rates.     

The effect of learning by hiring on productivity

This article focuses on the phenomenon of interfirm labor mobility as a potential channel for knowledge transfer. Using data from the Danish employer‐employee register covering the period 1995–2005, we investigate how knowledge carriers—technicians and highly educated workers recruited from a donor firm—contribute to knowledge diffusion and enhanced productivity in the hiring (recipient) firm. Structural estimation of the hiring firms' production functions shows that the impact of the recruitment of knowledge carriers on a firm's value added is an increase of 1%–2%. Several robustness checks confirm this finding.     

A multivariate stochastic volatility model with applications in the foreign exchange market

The main objective of this paper is to study the behavior of a daily calibration of a multivariate stochastic volatility model, namely the principal component stochastic volatility (PCSV) model, to market data of plain vanilla options on foreign exchange rates. To this end, a general setting describing a foreign exchange market is introduced. Two adequate models—PCSV and a simpler multivariate Heston model—are adjusted to suit the foreign exchange setting. For both models, characteristic functions are found which allow for an almost instantaneous calculation of option prices using Fourier techniques. After presenting the general calibration procedure, both the multivariate Heston and the PCSV models are calibrated to a time series of option data on three exchange rates—USD-SEK, EUR-SEK, and EUR-USD—spanning more than 11 years. Finally, the benefits of the PCSV model which we find to be superior to the multivariate extension of the Heston model in replicating the dynamics of these options are highlighted.     

Recursive marginal quantization of higher-order schemes

Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large derivative books. Recursive marginal quantization (RMQ) of the Euler scheme has recently been proposed as an efficient numerical method for evaluating functionals of solutions of stochastic differential equations. This method involves recursively quantizing the conditional marginals of the discrete-time Euler approximation of the underlying process. By generalizing this approach, we show that it is possible to perform RMQ for two higher-order schemes: the Milstein scheme and a simplified weak order 2.0 scheme. We further extend the applicability of RMQ by showing how absorption and reflection at the zero boundary may be incorporated, when necessary. To illustrate the improved accuracy of the higher-order schemes, various computations are performed using geometric Brownian motion and the constant elasticity of variance model. For both models, we provide evidence of improved weak order convergence and computational efficiency. By pricing European, Bermudan and barrier options, further evidence of improved accuracy of the higher-order schemes is demonstrated.     

The impact of the COVID-19 pandemic and Russia-Ukraine war on multiscale spillovers in green finance markets: Evidence from lower and higher order moments

This study analyzes the impact of the COVID-19 pandemic and the Russia-Ukraine war on the connectedness of lower-order moments (returns and volatility) and higher-order moments (skewness and kurtosis) in the markets of green bonds, clean energy, wind, solar, and sustainability indexes. To compare the spillover effects of these moments, we use the Diebold and Yilmaz and Barunik and Krehlik methods. Our findings show that the total spillover effect of lower-order moments is higher than that of higher-order moments in the time domain. In the frequency domain, the total return and skewness spillover are primarily concentrated in the short term, whereas the total volatility spillover is mainly concentrated in the long term. Furthermore, we observe that the spillover effect of the Russia-Ukraine war on the green finance market is mild, while the COVID-19 pandemic has a significant and unprecedented influence on the spillover of both lower- and higher-order moments in this market. Additionally, we note that before the COVID-19 outbreak, the total kurtosis spillover was irregular, but it became concentrated in the long term after the outbreak. Moreover, the continuation of COVID-19 has had an unprecedented and long-lasting impact on the kurtosis and skewness of the green bond market.     

International asset allocation under regime switching, skew, and kurtosis preferences

This paper investigates the international asset allocation effectsof time-variations in higher-order moments of stock returnssuch as skewness and kurtosis. In the context of a four-momentInternational Capital Asset Pricing Model (ICAPM) specificationthat relates stock returns in five regions to returns on a globalmarket portfolio and allows for time-varying prices of covariance,co-skewness, and co-kurtosis risk, we find evidence of distinctbull and bear regimes. Ignoring such regimes, an unhedged USinvestor's optimal portfolio is strongly diversified internationally.The presence of regimes in the return distribution leads toa substantial increase in the investor's optimal holdings ofUS stocks, as does the introduction of skewness and kurtosispreferences.     

A simple approach to standardized-residuals-based higher-moment tests

We propose a new approach to the higher-moment tests for evaluating the standardized error distribution hypothesis of a conditional mean-and-variance model (such as a GARCH-type model). Our key idea is to purge the effect of estimating the conditional mean-and-variance parameters on the estimated higher moments by suitably using the first and second moments of the standardized residuals. The resulting higher-moment tests have a simple invariant form for various conditional mean-and-variance models, and are also applicable to the symmetry or independence hypothesis that does not involve a complete standardized error distribution. Thus, our tests are simple and flexible. Using our approach, we establish a class of skewness–kurtosis tests, characteristic-function-based moment tests, and Value-at-Risk tests for exploring the standardized error distribution and higher-order dependence structures. We also conduct a simulation to show the validity of our approach in purging the estimation effect, and provide an empirical example to show the usefulness of our tests in exploring conditional non-normality.     

On a Sparre Andersen risk model perturbed by a spectrally negative Lévy process

In this paper, we consider a Sparre Andersen risk model perturbed by a spectrally negative Lévy process (SNLP). Assuming that the interclaim times follow a Coxian distribution, we show that the Laplace transforms and defective renewal equations for the Gerber–Shiu functions can be obtained by employing the roots of a generalized Lundberg equation. When the SNLP is a combination of a Brownian motion and a compound Poisson process with exponential jumps, explicit expressions and asymptotic formulas for the Gerber–Shiu functions are obtained for exponential claim size distribution and heavy-tailed claim size distribution, respectively.     

Wertorientierte Steuerung von Lebensversicherungsunternehmen mittels stochastischer Prozesse

In this paper we present the concept for value based management of life insurance companies using stochastic process methods. The stochastic processes are used for modelling the random parameters determining the value. Stochastic processes in discrete and continuous time as well as with discrete and continuous state space are considered. As shown in the article this results in distribution functions for the corporate value which lie approximately or even exactly in the class of normal distribution functions.     

Effects of intervaling on high-frequency realized higher-order moments

In high-frequency finance, the statistical terms ‘realized skewness’ and ‘realized kurtosis’ refer to the realized third- and fourth-order moments of high-frequency returns data normalized (or divided) by ‘realized variance’. In particular, before any computations of these two normalized realized moments are carried out, one often predetermines the holding-interval and sampling-interval and thus implicitly influencing the actual magnitudes of the computed values of the normalized realized higher-order moments i.e. they have been found to be interval-variant. To-date, little theoretical or empirical studies have been undertaken in the high-frequency finance literature to properly investigate and understand the effects of these two types of intervalings on the behaviour of the ensuring measures of realized skewness and realized kurtosis. This paper fills this gap by theoretically and empirically analyzing as to why and how these two normalized realized higher-order moments of market returns are influenced by the selected holding-interval and sampling-interval. Using simulated and price index data from the G7 countries, we then proceed to illustrate via count-based signature plots, the theoretical and empirical relationships between the realized higher-order moments and the sampling-intervals and holding-intervals.     

Insurance contracts portfolios with heterogenous parametric life distributions

In this paper we consider two portfolios: one of m endowment insurance contracts and one of m whole life insurance contracts. We introduce the majorization order, Schur functions, and parametric families of distribution functions. We assume that the owners of the portfolios are exposed to different members of a known parametric family of distributions and study the effect of this stochastic heterogeneity on the premiums and death benefits of the insurance contracts. We show that the premiums paid in both contracts are Schur concave and that the death benefit awarded in the whole life contract is Schur convex. We provide upper and lower bounds for the premiums and for the death benefit, and compute the bounds for four parametric families of distribution functions used frequently in the Actuarial Sciences.     

New solvable stochastic volatility models for pricing volatility derivatives

In this paper we discuss a new approach to extend a class of solvable stochastic volatility models (SVM). Usually, classical SVM adopt a CEV process for instantaneous variance where the CEV parameter γ takes just few values: 0—the Ornstein–Uhlenbeck process, 1/2—the Heston (or square root) process, 1—GARCH, and 3/2—the 3/2 model. Some other models, e.g. with γ = 2 were discovered in Henry-Labordére (Analysis, geometry, and modeling in finance: advanced methods in option pricing. Chapman & Hall/CRC Financial Mathematics Series, London, 2009) by making connection between stochastic volatility and solvable diffusion processes in quantum mechanics. In particular, he used to build a bridge between solvable superpotentials (the Natanzon superpotentials, which allow reduction of a Schrödinger equation to a Gauss confluent hypergeometric equation) and existing SVM. Here we propose some new models with ${\gamma \in \mathbb{R}}$ and demonstrate that using Lie’s symmetries they could be priced in closed form in terms of hypergeometric functions. Thus obtained new models could be useful for pricing volatility derivatives (variance and volatility swaps, moment swaps).     

Independent boards and innovation

Much research has suggested that independent boards of directors are more effective in reducing agency costs and improving firm governance. How they influence innovation is less clear. Relying on regulatory changes, we show that firms that transition to independent boards focus on more crowded and familiar areas of technology. They patent and claim more and receive more total future citations to their patents. However, the citation increase comes mainly from incremental patents in the middle of the citation distribution; the numbers of uncited and highly cited patents—arguably associated with riskier innovation strategies—do not change significantly.     

Asian option pricing with orthogonal polynomials

In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black–Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any special functions are involved. We provide sufficient conditions to guarantee convergence of the series. The moment indeterminacy of the log-normal distribution introduces an asymptotic bias in the series, however we show numerically that the bias can safely be ignored in practice.     

On an inverse Gaussian process

Abstract

Tweedie [11] investigated properties of the Inverse Gaussian distribution. We define in this paper the Inverse Gaussian process. For the discrete case we find the density function of the functions of Inverse Gaussian variates. We look for covariance function and stochastic integral as well as conditional density functions of an Inverse Gaussian process.     

On series expansions for scale functions and other ruin-related quantities

ABSTRACT

In this note, we consider a nonstandard analytic approach to the examination of scale functions in some special cases of spectrally negative Lévy processes. In particular, we consider the compound Poisson risk process with or without perturbation from an independent Brownian motion. New explicit expressions for the first and second scale functions are derived which complement existing results in the literature. We specifically consider cases where the claim size distribution is gamma, uniform or inverse Gaussian. Some ruin-related quantities will also be re-examined in light of the aforementioned results.