Mathematical and Statistical Methods for Actuarial Sciences and Finance

This paper investigates liquidity shocks on the US corporate bond market around credit rating change announcements. These shocks may be induced by the information content of the announcement itself, and abnormal trading activity can be triggered by the release of information after any upgrade or downgrade. Our findings show that: (1) the market anticipates rating changes, since trends liquidity proxies prelude the event, and additionally, large volume transactions are detected the day before the downgrade; (2) the concrete materialization of the announcement is not fully anticipated, since we only observe price overreaction immediately after downgrades; (3) a clear asymmetric reaction to positive and negative rating events is observed; (4) different agency-specific and rating-specific features are able to explain liquidity behavior around rating events; (5) financial distress periods exacerbate liquidity responses derived from downgrades and upgrades.

Peer review is still used as the main tool for research evaluation, but its costly and time-consuming nature triggers a debate about the necessity to use, alternatively or jointly with it, bibliometric indicators. In this contribution we introduce an approach based on generalised linear models that jointly uses former peer-review and bibliometric indicators to predict the outcome of UK’s Research Excellence Framework (REF) 2014. We use the outcomes of the Research Assessment Exercise (RAE) 2008 as peer-review indicators and the departmental h-indices for the period 2008–2014 as bibliometric indicators. The results show that a joint use of bibliometric and peer-review indicators can be an effective tool to predict the research evaluation made by REF.

In this paper we introduce a hierarchical Lee-Carter model (LC) specification to forecast the death rates of a set of demographically related countries. We assume that the latent mortality factor of LC is common for all of them, given the linkage among them. On the other hand, hierarchical modeling is usually conducted by Bayesian approach, which has the disadvantage that assumptions on the prior distributions are needed, which are not usually known or obtainable, introducing thus subjectivity in the model when setting these prior distributions. An option to overcome this limitation is provided by Data Cloning, a novel technique raised in the Ecology field that allows approximating maximum likelihood estimates in hierarchical settings. Even though this technique works with MCMC algorithms, it constitutes a frequentist approach, and the results are invariant to the prior distributions. Finally, we apply the methodology to a set of linked countries, getting a very satisfactory forecasting, concluding that it can be used in both private insurance companies and public pensions systems in order to forecast mortality and mitigate longevity risk.

This paper is devoted to show duality in the estimation of Markov Switching (MS) GARCH processes. It is well-known that MS GARCH models suffer of path dependence which makes the estimation step unfeasible with usual Maximum Likelihood procedure. However, by rewriting the model in a suitable state space representation, we are able to give a unique framework to reconcile the estimation obtained by filtering procedure with that coming from some auxiliary models proposed in the literature. Estimation on short-term interest rates shows the feasibility of the proposed approach.

In the context of portfolio theory, the evaluation of risk is of paramount relevance. In this respect, the connections among the risky assets of the portfolio should be carefully explored. This paper elaborates on this topic. We define a portfolio through a network, whose nodes are the assets composing it. The weights on the nodes and the arcs represent the share of capital invested on the assets and the dependence among them, respectively. The risk profile of the portfolio will be given through a suitably defined risk measure on the portfolio-network. The standard Markowitz theory will be rewritten in this particular setting. Surprisingly, we will note that the resulting decision problem is not consistent with an adapted version of the axiomatization of the standard expected utility theory.

In this paper we consider a simple trading system (TS) based on a set of Technical Analysis (TA) indicators. Their peculiarity is the dependence on the time-window widths used to calculate them. To attempt to improve the performances of the TS, we optimize these parameters (that is the time-window widths) by the Particle Swarm Optimization (PSO), which is a metaheuristic used to solve global optimization problems. The use of PSO is necessary since the involved optimization problem is nonlinear, nondifferentiable and integer: in summary, it is complex. In such a case, the use of exact solution methods would be excessively time-consuming, in particular for practical purposes. The proposed TS is tested using the daily closing prices from January 2, 2001, to June 30, 2016, of eight Italian stocks of different economic sectors. As benchmark, we consider the same TS but with standard time-window lengths. Irrespective of their signs, both in-sample and out-of-sample performances achieved by the TS with optimized parameters are better than those achieved by the benchmark, highlighting that parameter optimization can play an important role in TA-based TSs.

In previous works we developed the formulas of the prediction error in generalized linear model (GLM) for the future payments by calendar years assuming the logarithmic link and the parametric family of error distributions named power family. In the particular case of assuming (overdispersed) Poisson and logarithmic link the GLM gives the same provision estimations as those of the Chain-Ladder deterministic method. Now, we are studying the possibility to use distance-based generalized linear models (DB-GLM) to solve the problem of claim reserving in the same way as GLM is used in this context. DB-GLM can be fitted by using the function dbglm of the dbstats package for R. In this study we calculate the prediction error associated to the accident years future payments and total payment, and also to the calendar years future payments using DB-GLM in the general case of the power families of error distributions and link functions. We make an application with the well known run-off triangle of Taylor and Ashe.

Combining insurer’s profitability with products’ attractiveness in terms of marketing competitiveness is a critical issue within the risk/profit management of an insurance business. In particular life insurance products are characterized by the presence of financial and demographic risk sources, whose combined effect requires suitable management strategies. This paper deals with the impact of the load factor on life annuity portfolio performance from the insurers point of view. The aim is to build a performance indicator that clearly points out the role of the load factor in the performance making, giving to it a central role in the company management strategy. Such index is characterized by a simple mathematical structure and fits to the purpose: in fact it provides clear indications to the manager about the influence of the load factor on the performance of the life annuity business line.

The financial industry has extensively used quantile-based risk measures relying on the Value-at-Risk (V aR). They need to be estimated from relevant historical data sets. Consequently, they contain uncertainty due to the finiteness of observations in practice. We propose an alternative quantile-based risk measure (the Spectrum Stress V aR) to capture the uncertainty in the historical V aR approach. This one provides flexibility to the risk manager to implement prudential regulatory framework. It can be a V aR based stressed risk measure. In the end we propose a stress testing application for it.

The bias between the expected realized variance under the historical measure and the risk neutral probability introduces the concept of the variance risk premium (VRP). Our work introduced a probabilistic modeling of the VRP via a parametric class of stochastic volatility models which incorporates the nonlinear class.

The covered call writing, which entails selling a call option on one’s underlying stock holdings, is perceived by investors as a strategy with limited risk. It is a very popular strategy used by individual, professional and institutional investors. Previous studies analyze behavioral aspects of the covered call strategy, indicating that hedonic framing and risk aversion may explain the preference of such a strategy with respect to other designs. In this contribution, following this line of research, we extend the analysis and apply Cumulative Prospect Theory in its continuous version to the evaluation of the covered call strategy and study the effects of alternative framing.

The description of Cumulative Prospect Theory (CPT) includes three important parts: a value function over outcomes, v(⋅ ); a weighting function over cumulative probabilities, w(⋅ ); CPT-utility as unconditional expectation of the value function v under probability distortion w. In this paper we consider the problem of choosing an CPT-investor’s portfolio in the case of complete market. The problem of finding the optimal portfolio for CPT-investor is to maximize the unconditional expectation of the value function v under probability distortion w over terminal consumption, subject to budget constraint on initial wealth. We find the optimal payoffs for CPT-investor for the classic Black-Scholes environment assuming that there are a single lognormally distributed stock and a risk free bond. We compare the optimal payoffs of CPT-investor with the optimal payoffs of the investor that maximizes expected power utility over terminal payoffs, subject to budget constraint on initial wealth.