Sebastiano Vitali

Individual optimal pension allocation under stochastic dominance constraints

An individual investor has to decide how to allocate his/her savings from a retirement perspective. This problem covers a long-term horizon. In this paper we consider a 40-year horizon formulating a multi-criteria multistage program with stochastic dominance constraints in an intermediate stage and in the final stage. As we are dealing with a real problem and we have formulated the model in cooperation with a commercial Italian bank, the intermediate stage corresponds to a possible withdrawal allowed by the Italian pension system. The sources of uncertainty considered are: the financial returns, the interest rate evolution, the investor’s salary process and a considerable withdrawal event. We include a set of portfolio constraints according to the pension plan regulation. The objective of the model is to minimize the Average Value at Risk Deviation measure and to satisfy wealth goals. Three different wealth target formulations are considered: a deterministic wealth target (i.e. a comparison between the accumulated average wealth and a fixed threshold) and two stochastic dominance relations—the first order and the second order—introducing a benchmark portfolio and then requiring the optimal portfolio to dominate the benchmark. In particular, we prove that solutions obtained under stochastic dominance constraints ensure a safer allocation while still guaranteeing good returns. Moreover, we show how the withdrawal event affects the solution in terms of allocation in each of the three frameworks. Finally, the sensitivity and convergence of the stochastic solutions and computational issues are investigated.

Portfolio selection strategy for fixed income markets with immunization on average

In this paper, we develop a portfolio optimization method to maximize the performance of a fixed income portfolio. To achieve this aim, we define a two-step optimization problem where we firstly manage the immunization risk and then we maximize the portfolio wealth in a reward–risk framework. In the first optimization step, we create funds of bonds with constant immunization measure over time, and we propose an innovative immunization measure for bond portfolio management that leads to a more flexible immunization approach and a better trade-off between reward and risk. In the second optimization step, maximizing two performance measures on these baskets of bonds we obtain portfolio strategies that consider different investors’ profiles. An empirical application to the US fixed income market during 2002–2012 period is provided. Applying the portfolio optimization method to different bond classes, we compare the results with an equity index. This ex-post analysis indicates the benefits of the proposed portfolio strategy in outperforming the benchmark and proves that capital flows to safer markets during crisis periods.

Optimal pension fund composition for an Italian private pension plan sponsor

We address the problem of a private pension plan sponsor who has to find the best pension funds for its members. Starting from a descriptive analysis of the pension plan members we identify a set of representative subscribers. Then, the optimal allocation for each representative will become a pension fund of the pension plan. For each representative, we propose a multistage stochastic program (MSP) which includes a multi-criteria objective function. The optimal choice is the portfolio allocation that minimizes the average value at risk deviation of the final wealth and satisfies a wealth target in the final stage and other constraints regarding pension plan regulations. Stochasticity arises from the investor’s salary process and from asset returns. Numerical results show the optimal dynamic portfolios with respect to the investor’s preferences and then the best pension funds the sponsor might offer.

Optimal Multistage Defined-Benefit Pension Fund Management

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.

The pricing of convertible bonds in the presence of structured conversion clauses: the case of Cashes

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.

Motivations and Expectations of Students’ Mobility Abroad: A Mapping Technique

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.

Implied volatility and state price density estimation: arbitrage analysis

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.