This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractIn the light of the growing importance of the Variable Annuities market, in this paper we introduce a theoretical model for the pricing and valuation of Guaranteed Lifelong Withdrawal Benefit Options (GLWB) embedded in Variable Annuity products. As the name suggests, this option offers a lifelong withdrawal guarantee; therefore, there is no limit on the total amount that is withdrawn over the term of the policy, because if the account value becomes zero while the insured is still alive he continues to receive the guaranteed amount annually until death. Any remaining account value at the time of death is paid to the beneficiary as a death benefit We offer a specific framework to value the GLWB in a market consistent manner under the hypothesis of a static withdrawal strategy, according to which the withdrawal amount is always equal to the guaranteed amount. The valuation approach is based on the decomposition of the product into living and death benefits. The model makes use of the standard no-arbitrage models of mathematical finance, that extend the BlackScholes framework to insurance contracts, assuming the fund follows a Geometric Brownian Motion and the insurance fee is paid, on an ongoing basis, as a proportion of the assets. We develop a sensitivity analysis, which shows how the value of the product varies with the key parameters, including the age of the policyholder at the inception of the contract, the guaranteed rate, the risk free rate and the fund volatility. We calculate the fair fee, using Monte Carlo simulations under different scenarios. We give special attention to the impact of mortality risk on the value of the option, using a flexible model of mortality dynamics, which allows for the possible perturbations by mortality shock of the standard mortality tables used by practitioners. Moreover, we evaluate the introduction of roll-up and step-up options and the effect of the decision to delay withdrawing. Empirical analyses are performed and numerical results are provided.

Several approaches have been developed for forecasting mortality using the stochastic model. In particular, the Lee-Carter model has become widely used and there have been various extensions and modifications proposed to attain a broader interpretation and to capture the main features of the dynamics of the mortality intensity. Hyndman-Ullah show a particular version of the Lee-Carter methodology, the so-called Functional Demographic Model, which is one of the most accurate approaches as regards some mortality data, particularly for longer forecast horizons where the benefit of a damped trend forecast is greater. The paper objective is properly to single out the most suitable model between the basic Lee-Carter and the Functional Demographic Model to the Italian mortality data. A comparative assessment is made and the empirical results are presented using a range of graphical analyses. This is an electronic reprint of the original article published by the Institute of Mathematical Statistics in The Annals of Applied Statistics, 2011, Vol. 5, No. 2A, 705-724. This reprint differs from the original in pagination and typographic detail. 1 2 V. D'AMATO, G. PISCOPO AND M. RUSSOLILLOits expected values. These changes clearly affect pricing and reserve allocation for life annuities and represent one of the major threats to a social security system that has been planned on the basis of a more modest life expectancy. The risk is of using mortality tables that do not take these trends into account, thus underestimating the survival probability and determining inappropriate premiums. To face this risk, it is necessary to build projected tables including this trend. Thus, reasonable mortality forecasting techniques have to be used to consistently predict the trends [Brouhns, Denuit and Vermunt (2002)]. In that respect, over the years a number of approaches have been proposed for forecasting mortality using the stochastic model, however, the Lee-Carter model [Lee and Carter (1992)] unquestionably represents a milestone in the literature. This methodology has become widely used and there have been various extensions and modifications proposed to attain a broader interpretation and to capture the main features of the dynamics of the mortality intensity [e.g., Booth, Maindonald and Smith (2002); Haberman and Renshaw (2003, 2008); Hyndman and Ullah (2007); Renshaw and Haberman (2003a, 2003b)].The main statistical tool of LC is least-squares estimation via singular value decomposition of the matrix of the log age-specific observed death rates. In fact, the mortality data (death counts and exposures-to-risk) have to fill a rectangular matrix. Henceforth, we will denote with m x,t the observed death rates at age x during calendar year t, obtained by the ratio between the number of deaths, D x,t , recorded at age x during year t, from an exposure-to-risk E x,t , that is, the number of person years from which D x,t occurred. As regards the Italian population data set on the basis of the death rates, classified by gender and individual ...

No abstract

No abstract

This paper follows the recent literature on real estate price prediction and proposes to take advantage of machine learning techniques to better explain which variables are more important in describing the real estate market evolution. We apply the random forest algorithm on London real estate data and analyze the local variables that influence the interaction between housing demand, supply and price. The variables choice is based on an urban point of view, where the main force driving the market is the interaction between local factors like population growth, net migration, new buildings and net supply.