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The implied volatility function and the implied volatility surface are both key tools for analyzing financial and derivative markets and various approaches were proposed to estimate theses quantities. On the other hand, theoretical, practical, and also computational pitfalls occur in most of them. An innovative estimation method based on an idea of a sparse estimation and an atomic pursuit approach is introduced to overcome some of these limits: the quantile LASSO estimation implies robustness with respect to common market anomalies; the panel data structure allows for a time dependent modeling; changepoints introduce some additional flexibility in order to capture some sudden changes in the market and linear constraints ensure the arbitrage-free validity; last but not least, the interpolated implied volatility concept overcomes the problem of consecutive maturities when observing the implied volatility over time. Some theoretical backgrounds for the quantile LASSO estimation method are presented, the idea of the interpolated volatilities is introduced, and the proposed estimation approach is applied to estimate the implied volatility of the Erste Group Bank AG call options quoted in EUREX Deutschland Market.

The main goal of a pension fund manager is sustainability. We propose an Asset and Liability Management model structured as a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. Among other constraints, we consider the second-order stochastic dominance with respect to a benchmark portfolio. To protect the pension fund from shocks, we test the inclusion of hedge financial contracts in the form of put options and, moreover, we stress the portfolio introducing a new scenario tree contamination technique, namely the nodal contamination. Numerical results show that we can efficiently manage the pension fund satisfying several targets such as liquidity, returns, sponsor’s extraordinary contribution and funding gap. Moreover, we test the sensitivity with respect to put option strikes and to the stochastic dominance constraints. Finally, we demonstrate the effect of the scenario tree contamination.

In this paper we develop an analysis of the efficiency of the expansion strategies to be followed to attain the emissions targets established by the European Commission in the Energy Roadmap 2050. A multi-stage investment model in generating and storage capacity from the point of view of a central planner is presented, considering long-term uncertainties in the decision-making process, such as the demand growth and the investment and fuel costs, and short-term variability. To evaluate the wellness of the expansion strategies according to the CO2 emissions generated and the total cost, second-order stochastic dominance constraints are introduced in the model. This approach allows to obtain better expansion strategies enforcing acceptable distributions of CO2 emissions. The numerical study is carried out considering the case of the European power system. The predictions and suggestions made by the European Commission towards 2050 are the basis to define the benchmark solutions, whose outcomes are analysed. The results obtained from this study highlight that a renewable capacity of at least 2900 GW is needed to attain a net zero CO2 emission European power system. The strategy based on carbon capture and storage does not reduce effectively CO2 emissions while it represents an expensive alternative. Including stochastic dominance in the optimization model allows to obtain less expensive alternative expansion strategies with comparatively lower CO2 emissions in the worst scenarios.

Renewable sources are increasing their presence in power systems to achieve the goal of decarbonizing the generation of electricity. However, the variability of these resources introduces high uncertainty in the operation of a power system and, hence, fast generating and storage units must be incorporated in the system. To obtain economically and technically efficient solutions in the capacity expansion problem, an adequate representation of the variability of the renewable resource is crucial, but this may increase the size of the problem up to computational intractability. The most suitable representation is often selected through clustering techniques. The clustering algorithms proposed in the literature suffer from a significant trade-off between their ability to capture the inter-temporal correlation of the clustered elements and the representativeness of the clusters when only very few are needed. This paper proposes an innovative clustering technique that overcomes this trade-off. A case study based on the European power system is solved. The outcomes given by the new clustering algorithm and other well-known techniques are investigated through in-sample and out-of-sample analyses applied to multiple cases that differ in to the number of clusters and the minimum renewable production.

This paper considers an extension of the common asset universe of a pension fund to investment certificates. Investment certificates are a class of structured products particularly interesting for their special payoff structures and they are acquiring relevancy in the worldwide markets. In fact, some subclasses of certificates offer loss protection and show high liquidity and, thus, they can be very appreciated by pension fund managers. We consider the problem of a pension fund manager who has to implement an Asset and Liability Management model trying to achieve a long-term sustainability. Therefore, we formulate a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. We propose a technique to price highly structured products such as investment certificates on a discrete scenario tree. Finally, we solve the investment problem considering some investment certificate types both in term of payoff structure and protection level, and we test whether they are preferred or not to standard hedging contract such as put options. Moreover, we test the inclusion of first-order and second-order stochastic dominance constraints on multiple stages with respect to a benchmark portfolio. Numerical results show that the portfolio composition reacts to the inclusion of the stochastic dominance constraints, and that the optimal portfolio is efficiently able to reach several targets such as liquidity, returns, sponsor’s extraordinary contribution and funding gap.

This paper focuses on classical portfolio strategies applied to five countries, which are Brazil, Russia, India, China and South Africa. These five countries form the so-called BRICS group. In particular, the authors investigate their corporate and sovereign bond market and evaluate whether these markets can represent a profitable investment for non-satiable and risk-averse investors. Two-step optimization is proposed to control price risk and market risk. For price risk management, classical immunization strategies and are obtained funds of bond are obtained that share the same risk measure. For market risk control, the previously found funds are used and a performance measure optimization commonly used in stock markets is applied to define the best portfolio of funds. Therefore, the resulting optimal portfolio controls the price risk and jointly maximizes a desired performance measure that includes the market risk. Finally, the authors propose an empirical analysis to evaluate the profitability of the suggested two-step optimization for the five BRICS countries and compare the ex-post sample paths of the obtained portfolios for testing the stochastic dominance relations.

Multistage stochastic optimization is used to solve many real-life problems where decisions are taken at multiple times. Such problems need the representation of stochastic processes, which are usually approximated by scenario trees. In this article, we implement seven scenario reduction algorithms: three based on random extraction, named Random, and four based on specific distance measures, named Distance-based. Three of the latter are well known in literature while the fourth is a new approach, namely nodal clustering. We compare all the algorithms in terms of computational cost and information cost. The computational cost is measured by the time needed for the reduction, while the information cost is measured by the nested distance between the original and the reduced tree. Moreover, we also formulate and solve a multistage stochastic portfolio selection problem to measure the distance between the optimal solutions and between the optimal objective values of the original and the reduced tree.

Internationalization of higher education is a rapidly rising phenomenon and it has become a priority in the European education policy. At the same time, research in this area is expanding with the aim of understanding motivations and potential benefits of international students’ mobility. Within this context, the purpose of our contribution is to analyse students’ motivations and the fulfillment of their expectations about the mobility experience abroad. To this aim, we have conducted an online survey addressed to a sample of about 1300 Italian students enrolled in a medium size university (the University of Bergamo) with outward mobility experiences during the six academic years from 2008/2009 to 2013/2014. To assess the results of the survey, we propose a mapping of the answer variables using the VOSviewer software.

The practical adoption of the Solvency II regulatory framework in 2016, together with increasing property and casualty (PC) claims in recent years and an overall reduction of treasury yields across more developed financial markets have profoundly affected traditional risk management approaches by insurance institutions. The adoption of firm-wide risk capital methodologies to monitor the companies’ overall risk exposure has further consolidated the introduction of risk-adjusted performance measures to guide the management medium and long-term strategies. Relying on a dynamic stochastic programming formulation of a 10 year asset-liability management (ALM) problem of a PC company, we analyse in this article the implications on capital allocation and risk-return trade-offs of an optimization problem developed for a global insurance company based on a pair of risk-adjusted return functions. The analysis is relevant for any institutional investor seeking a high risk-adjusted performance as for regulators in their structuring of stress-tests and effective regulatory frameworks. The introduction of the concept of risk capital, or economic capital, in the definition of medium and long term insurance strategies poses a set of modeling and methodological issues tackled in this article. Of particular interest is the study of optimal ALM policies under different assets’ correlation assumptions. From a computational viewpoint it turns out that, depending on the assumed correlation matrix, the stochastic program is linear or of second order conic type. A case study from a real-world company development is presented to highlight the effectiveness of applied stochastic programming in capturing complex risk and return dynamics arising in modern corporate finance and lead to an efficient long-term financial allocation process.

We present an asset-liability management (ALM) model designed to support optimal strategic planning by a defined benefit (DB) occupational pension fund (PF) manager. PF ALM problems are by nature long-term decision problems with stochastic elements affecting both assets and liabilities. Increasingly PFs operating in the second pillar of modern pension systems are subject to mark-to-market accounting standards and constrained to monitor their risk capital exposure over time. The ALM problem is formulated as a multi-stage stochastic program (MSP) with an underlying scenario tree structure in which decision stages are combined with non-decision annual stages aimed at mapping carefully the evolution of PF’s liabilities. We present a case-study of an underfunded PF with an initial liquidity shortage and show how a dynamic policy, relying on a set of specific decision criteria, is able to gain a long-term equilibrium solvency condition over a 20 year horizon.

This paper deals with implied volatility (IV) estimation using no-arbitrage techniques. The current market practice is to obtain IV of liquid options as based on Black–Scholes (BS type hereafter) models. Such volatility is subsequently used to price illiquid or even exotic options. Therefore, it follows that the BS model can be related simultaneously to the whole set of IVs as given by maturity/moneyness relation of tradable options. Then, it is possible to get IV curve or surface (a so called smile or smirk). Since the moneyness and maturity of IV often do not match the data of valuated options, some sort of estimating and local smoothing is necessary. However, it can lead to arbitrage opportunity if no-arbitrage conditions on state price density (SPD) are ignored. In this paper, using option data on DAX index, we aim to analyse the behavior of IV and SPD with respect to different choices of bandwidth parameter h, time to maturity and kernel function. A set of bandwidths which violates no-arbitrage conditions is identified. We document that the change of h implies interesting changes in the violation interval of moneyness. We also perform the analysis after removing outliers, in order to show that not only outliers cause the violation of no-arbitrage conditions. Moreover, we propose a new measure of arbitrage which can be considered either for the SPD curve (arbitrage area measure) or for the SPD surface (arbitrage volume measure). We highlight the impact of h on the proposed measures considering the options on a German stock index. Finally, we propose an extension of the IV and SPD estimation for the case of options on a dividend-paying stock.

Homogeneous self-dual algorithms for stochastic semidefinite programs with finite event space have been proposed by Jin et al. in [17]. Alzalg [8] has adopted their work to derive homogeneous selfdual algorithms for stochastic second-order programs with finite event space. In this paper, we generalize these to derive homogeneous selfdual algorithms for stochastic programs with finite event space over the much wider class of all symmetric cones. They include among others, stochastic semidefinite programs and stochastic second-order cone programs.

The aim of this paper is to analyse the pricing of highly structured convertible bonds by taking a real world case. To this end we examine the Cashes (Convertible And Subordinated Hybrid Equity-linked Securities), which are characterised by both voluntary and mandatory conversion that depend on different triggering events, as well as floating coupons whose payment hinges on dividends and earning of the issuer. Our results highlight that prices are very sensitive to the modelling of the sources of uncertainty, both market and credit risk, and underscore the relevance of the time horizon chosen for the estimation.