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Consider the strong subordination of a multivariate Lévy process with a multivariate subordinator. If the subordinate is a stack of independent Lévy processes and the components of the subordinator are indistinguishable within each stack, then strong subordination produces a Lévy process; otherwise it may not. Weak subordination was introduced to extend strong subordination, always producing a Lévy process even when strong subordination does not. Here we prove that strong and weak subordination are equal in law under the aforementioned condition. In addition, we prove that if strong subordination is a Lévy process then it is necessarily equal in law to weak subordination in two cases: firstly when the subordinator is deterministic, and secondly when it is pure-jump with finite activity.

The weak variance-alpha-gamma process is a multivariate Lévy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma subordinator. It generalises the variance-alpha-gamma process of Semeraro constructed by traditional subordination. We compare three calibration methods for the weak variance-alpha-gamma process, method of moments, maximum likelihood estimation (MLE) and digital moment estimation (DME). We derive a condition for Fourier invertibility needed to apply MLE and show in our simulations that MLE produces a better fit when this condition holds, while DME produces a better fit when it is violated. We also find that the weak variance-alpha-gamma process exhibits a wider range of dependence and produces a significantly better fit than the variance-alpha-gamma process on a S&P500-FTSE100 data set, and that DME produces the best fit in this situation.

'Investing with Confidence: Understanding Political Risk Management in the 21st Century' is the latest book in a series based on the MIGA–Georgetown University Symposium on International Political Risk Management. The most recent symposium brought together almost 200 senior practitioners from the political risk insurance (PRI) industry, including investors, insurers, brokers, lenders, academics, and members of the legal community. This volume addresses the key issues relevant for investors today, including arbitration, understanding and pricing for risk, and new developments in investments through timely assessments from 15 experts in the fields of international investment, finance, insurance, law, and academia. Contributors to this volume examine key political risk issues including claims and arbitration, perspectives on pricing from private, public and multilateral providers, and explore new frontiers in sovereign wealth funds and Islamic finance. The volume begins with a look back to the founding of International Center for the Settlement of Investment Disputes (ICSID) and MIGA and the respective visions for both of these important institutions. It continues with a review of new developments in global finance and risk management, including Islamic finance and sovereign wealth funds, and provides an investor perspective of what drives the decision making process on procuring political risk insurance. The volume then turns to consider methodologies of pricing from the private, public, and multilateral perspectives, and examines the expropriation and the pledge of shares. This section focuses on key legal questions such as understanding expropriation and the outcome of arbitration hearings, the latter being particularly relevant given the number of cases currently before arbitral panels. The volume concludes with an overview of the key thoughts raised by the authors and the implications for investors going forward. 'Investing with Confidence' offers valuable insights for practitioners and investors alike and is particularly relevant in today's uncertain markets.

Subordinating a multivariate Lévy process, the subordinate, with a univariate subordinator gives rise to a pathwise construction of a new Lévy process, provided the subordinator and the subordinate are independent processes. The variance-gamma model in finance was generated accordingly from a Brownian motion and a gamma process. Alternatively, multivariate subordination can be used to create Lévy processes, but this requires the subordinate to have independent components. In this paper, we show that there exists another operation acting on pairs (T, X) of Lévy processes which creates a Lévy process X ☉ T. Here, T is a subordinator, but X is an arbitrary Lévy process with possibly dependent components. We show that this method is an extension of both univariate and multivariate subordination and provide two applications. We illustrate our methods giving a weak formulation of the variance-α-gamma process that exhibits a wider range of dependence than using traditional subordination. Also, the variance generalised gamma convolution class of Lévy processes formed by subordinating Brownian motion with Thorin subordinators is further extended using weak subordination.

We present a Monte Carlo approach to pairs trading on mean-reverting spreads modeled by Lévy-driven Ornstein-Uhlenbeck processes. Specifically, we focus on using a variance gamma driving process, an infinite activity pure jump process to allow for more flexible models of the price spread than is available in the classical model. However, this generalization comes at the cost of not having analytic formulas, so we apply Monte Carlo methods to determine optimal trading levels and develop a variance reduction technique using control variates. Within this framework, we numerically examine how the optimal trading strategies are affected by the parameters of the model. In addition, we extend our method to bivariate spreads modeled using a weak variance alpha-gamma driving process, and explore the effect of correlation on these trades.

We empirically examined the return process of the emerging equity markets, and that of property indices in particular. We found that the emerging market property indices are more volatile than both the respective market indices and the real estate investment trust indices in the United States. In terms of predictability, contrary to the traditional wisdom, we did not find overwhelming evidence for autocorrelation in the majority number of these indices. We found certain diversification benefits to invest in the emerging market property indices, but we also found the unfavorable asymmetry in the correlation between emerging property indices and the U.S. NAREIT Index (i.e., correlations were higher during time of market volatility).

Consider a multivariate Lévy-driven Ornstein-Uhlenbeck process where the stationary distribution or background driving Lévy process is from a parametric family. We derive the likelihood function assuming that the innovation term is absolutely continuous. Two examples are studied in detail: the process where the stationary distribution or background driving Lévy process is given by a weak variance alpha-gamma process, which is a multivariate generalisation of the variance gamma process created using weak subordination. In the former case, we give an explicit representation of the background driving Lévy process, leading to an innovation term which is discrete and continuous mixture, allowing for the exact simulation of the process, and a separate likelihood function. In the latter case, we show the innovation term is absolutely continuous. The results of a simulation study demonstrate that maximum likelihood numerically computed using Fourier inversion can be applied to accurately estimate the parameters in both cases.

Consider the strong subordination of a multivariate Lévy process with a multivariate subordinator. If the subordinate is a stack of independent Lévy processes and the components of the subordinator are indistinguishable within each stack, then strong subordination produces a Lévy process, otherwise it may not. Weak subordination was introduced to extend strong subordination, always producing a Lévy process even when strong subordination does not. Here, we prove that strong and weak subordination are equal in law under the aforementioned condition. In addition, we prove that if strong subordination is a Lévy process, then it is necessarily equal in law to weak subordination in two cases: firstly, when the subordinator is deterministic and secondly, when it is pure-jump with finite activity.

The S‐shaped growth curves such as Gompertz, logistic, normal and Weibuli are widely used for forecasting technological substitutions. A family of data‐based transformed (DBT) models, which are linear in the regression parameters, including the above‐mentioned four models as special cases has been shown to be quite useful for short‐term forecasts. This paper explores modeling the technology penetration data directly with assumed S‐shaped growth curves. The resulting models, which are nonlinear in the regression parameters, also incorporate proper dependence structure and power transformation. It appears that the nonlinear modeling is a viable alternative to the DBT and other conventional forecasting models in forecasting technological substitutions. Hence, an appropriate strategy is to consider the nonlinear modeling approaches as possible alternatives and use the data at hand to select, via pseudo‐cross‐validation, the best model for forecasting purposes.