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Recently, Stein et al. (2016) studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE). In this paper, the authors extend the model to a wider class of memory kernels and then propose a bond and bond option valuation model based on the extension of the generalized Langevin process of Stein et al. (2016).

Bond and bond option pricing based on the proposed interest rate models presents new difficulties as the standard partial differential equation method of stochastic calculus for bond pricing cannot be used directly. The authors obtain bond and bond option prices by finding the closed form expression of the conditional characteristic function of the integrated short rate process driven by a general Lévy noise.

The authors obtain zero-coupon default-free bond and bond option prices for short rate models driven by a variety of Lévy processes, which include Vasicek model and the short rate model obtained by solving a second-order Langevin stochastic differential equation (SDE) as special cases.

Bond and bond option pricing plays an important role in capital markets and risk management. In this paper, the authors derive closed form expressions for bond and bond option prices for a wider class of interest rate models including second-order SDE models. Closed form expressions may be especially instrumental in facilitating parameter estimation in these models.

The purpose of this paper is to research the optimal portfolio proportion for the optimal investment model and the optimal consumption investment strategies for the optimal consumption investment model under compound‐jump processes.

Traditionally, the price of risky security or asset is often modeled as geometric Brownian motion. However, the analysis of stock price evolution reveals sudden and rare breaks logically accounted for by exogenous events on information. It is natural to model such behavior by means of a point process, or, more simply, by a Poisson process, which has jumps of constant size occurring at rare and unpredictable intervals. Assume that the price of risky security stock is modeled by a compound‐jump process, the renew process theory is chosen to solve the optimal investment model, the HJB equation is chosen for the optimal consumption investment model.

Derive the analytical optimal portfolio proportion for the reduction model of optimal investment. The optimal consumption investment strategies are given by some equations for the optimal consumption investment model.

Accessibility and availability of data are the main limitations which model will be applied.

The results obtained in this paper could be used as a guide to actual portfolio management.

The new approach for the optimal portfolio model under compound‐jump processes. The paper is aimed at actual portfolio managers.

The purpose of this research is to investigate sustainable strategies for skills development that is specific to the youth of South Africa. International and South African data are statistically analysed and quantified to provide inputs for the systems dynamics (SD)-based predictive skills model. The skills model simulates the impact of barriers and drivers on youth skills development towards identification of focus areas for improvement.

The research adopts a mixed-methods approach. The study begins with an explorative literature study on skills development, with the findings applied in developing (1) South African specific research instruments for small, medium and micro enterprises (SMMEs) and skills programme grant recipients and (2) a conceptual framework of the SD predictive skills model. The responses to the South African specific instruments are analysed via confirmatory factor analysis (CFA), which quantifies the input coefficients to the system dynamics model. To quantify the global inputs for the SD model, an in-depth literature review of the global skills development initiatives is conducted. The SD model output on skills, for the South African inputs, is comparatively evaluated against global inputs.

The paper details the results of the literature analysis, instrument analyses, CFA and SD model. The instrument results rank experience, skills and interactions with experts and work-based learning as most important. South African and global learners identify networking as the primary medium for identifying training and employment opportunities. South African and global learners also identify qualifications and work-based experience as key to finding employment. The quantified results of the SA and global analysis are used as inputs in the SD model to deliver a forecasting tool. The SD model finds that the global data provide for better development of the skills base than the South African inputs. The key focus areas identified for improvement in South Africa include networking, work-based experience and a reduction in administrative requirements.

The research's originality resides in the ability to predict the impact of drivers and barriers on skills development. This research sought to transform qualitative global and South African inputs into a consolidated, predictive systems-based model. The SD model can be adopted as an indicator of drivers and barriers focused towards the optimisation of skills development.

The purpose of this study was to test the effectiveness of purposeful attempts to cope with stress by senior educational administrators in an Australian state education department of over 2,000 schools and employing teaching and administrative staff in excess of 60,000. At the time of the study this department was undergoing the initial stages of large‐scale restructuring, moving from a centralized system of management to a school‐centred, decentralized structure. This provided a unique opportunity to examine the ways in which senior executives respond in a time of discontinuous change. Presents general findings of a self‐report coping strategies questionnaire and reveals some significant relationships between general wellbeing, personality type and coping strategies.

This paper derives the analytic solutions of the pure discount bond price under the various types of -stable Levy process. It is well-known that only a few cases in-stable Levy process have the moment generating function. This paper extends the model to damped-stable Levy processes, which have artificial stable process with the moment generating function. This paper also extends models to stochastic volatility by time change method of Levy process.

The purpose of the paper is to back-test value-at-risk (VaR) models for conditional distributions belonging to a Generalized Hyperbolic (GH) family of Lévy processes – Variance Gamma, Normal Inverse Gaussian, Hyperbolic distribution and GH – and compare their risk-management features with a traditional unconditional extreme value (EV) approach using data from future contracts return data of S&P500, FTSE100, DAX, HangSeng and Nikkei 225 indices.

The authors apply tail-based and Lévy-based calibration to estimate the parameters of the models as part of the initial data analysis. While the authors utilize the peaks-over-threshold approach for generalized Pareto distribution, the conditional maximum likelihood method is followed in case of Lévy models. As the Lévy models do not have closed form expressions for VaR, the authors follow a bootstrap method to determine the VaR and the confidence intervals. Finally, for back-testing, they use both static calibration (on the entire data) and dynamic calibration (on a four-year rolling window) to test the unconditional, independence and conditional coverage hypotheses implemented with 95 and 99 per cent VaRs.

Both EV and Lévy models provide the authors with a conservative proportion of violation for VaR forecasts. A model targeting tail or fitting the entire distribution has little effect on either VaR calculation or a VaR model’s back-testing performance.

To the best of the authors’ knowledge, this is the first study to explore the back-testing performance of Lévy-based VaR models. The authors conduct various calibration and bootstrap techniques to test the unconditional, independence and conditional coverage hypotheses for the VaRs.

August 9, 1966 Harrogate, Yorkshire Assessment to levy‐reduction in scope of trade of appellants ‐number of employees reduced — calculation of levy — whether fact that appellants will not benefit from scheme valid ground for resisting assessment — Industrial Training Levy (Wool) Order 1965.

This paper discusses theoretical extensions of the implied volatility method of Dupire (1994) when the stock prices follow the Geometric Levy process. For the extensions of Kolmogorov forward equation for Levy process, this paper uses adjoint operator in L² spaces. This paper obtains similar results of Dupire (1994) and Andersen and Andreasan (2001). However, our results can be applied to more general semi-martingale processes such as well-known VG (Variance Gamma) model and NIG (Normal Inverse Gaussian) model with diffusion processes. This paper also applies the approach to the case of stochastic time changed Levy process, which generates the stochastic volatility models.

Knight's Industrial Law Reports goes into a new style and format as Managerial Law This issue of KILR is restyled Managerial Law and it now appears on a continuous updating basis rather than as a monthly routine affair.

We study an efficient numerical method for pricing European options when the dynamics of the underlying asset are described by Levy processes. In this case. we can write a characteristic function solution for a specific Levy option model and then take its inversion numerically. Specifically we use Variance Gamma process as an example of Levy option model and consider various characteristic function representation forms of European option price such as Carr and Madan (1999), Bakshi and Madan (2000). and Lewis (2001). Fast Fourier Transform method is applied to solve the numerical inversion problem with parameters for the KOSPI 200 options data. After analysing the problems in the FFT method, we propose alternative numerical inversion method, Gaussian Quadrature. This paper reports that Gaussian Quadrature numerical inversion method with the representation form of Bakshi & Madan (2000) is more efficient and accurate than other alternatives considered in this paper.