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WORKING PAPERS 2017
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Boda Kang and Jonathan Ziveyi
February 2017

In this paper we analyse how the policyholder surrender behaviour is influenced by changes in various sources of risk impacting a variable annuity (VA) contract embedded with a guaranteed minimum maturity benefit rider that can be surrendered anytime prior to maturity. We model the underlying mutual fund dynamics by combining a Heston (1993) stochastic volatility model together with a Hull and White (1990) stochastic interest rate process. The model is able to capture the smile/skew often observed on equity option markets (Grzelak and Oosterlee, 2011) as well as the influence of the interest rates on the early surrender decisions as noted from our analysis. The annuity provider charges management fees which are proportional to the level of the mutual fund as a way of funding the VA contract. To determine the optimal surrender decisions, we present the problem as a 4-dimensional free-boundary partial differential equation (PDE) which is then solved efficiently by the method of lines (MOL) approach. The MOL algorithm facilitates simultaneous computation of the prices, fair management fees, optimal surrender boundaries and hedge ratios of the variable annuity contract as part of the solution at no additional computational cost. A comprehensive analysis on the impact of various risk factors in influencing the policyholder’s surrender behaviour is carried out, highlighting the significance of both stochastic volatility and interest rate parameters in influencing the policyholder’s surrender behaviour.

 
Nikolay Gudkov, Katja Ignatieva and Jonathan Ziveyi
February 2017

This paper values Guaranteed Minimum Withdrawal Benefit (GMWB) riders embedded in variable annuities assuming that the underlying fund dynamics evolve under the influence of stochastic interest rates, stochastic volatility, stochastic mortality and equity risk. The valuation problem is formulated as a partial differential equation (PDE) which is solved numerically by employing the operator splitting method. Sensitivity analysis of the fair guarantee fee is performed with respect to various model parameters. We find that (i) the fair insurance fee charged by the product provider is an increasing function of the guarantee rate; (ii) the GMWB price is higher when stochastic interest rates and volatility are incorporated in the model, compared to the case involving static interest rates and volatility; (iii) the GMWB price behaves non-monotonically with changing volatility of variance parameter; (iv) the fair fee increases with increasing volatility of interest rates parameter, and increasing correlation between the underlying fund and the interest rates; (v) the fair fee increases when the speed of mean-reversion of stochastic volatility or the average long-term volatility increase; (vi) the GMWB fee decreases when the speed of mean-reversion of stochastic interest rates or the average long-term interest rates increase. We investigate both, static and dynamic (optimal) policyholder’s withdrawal behaviours and present the optimal withdrawal schedule as a function of the withdrawal account and the investment account for varying volatility and interest rates. When incorporating stochastic mortality we find that its impact on the fair guarantee fee is rather small. Our results demonstrate the importance of correct quantification of risks embedded in GMWB riders, and provide guidance to product providers on optimal hedging of various risks associated with the contract.

 
Rafal Chomik, John Piggott and Peter McDonald
February 2017

APEC economies encompass a wide range of socio-economic profiles – poor to rich, young to old, regulated to free market. These differences can be instructive for those seeking international policy lessons. They also create new opportunities for cooperation that have the potential to improve wellbeing across member economies. How economies and regions manage demographic change will define their success in what will be an ‘ageing century’. To write an overview paper on the role of demographic change on labour force and economic growth in APEC requires some unifying framework to organise the issues. Here we apply a supply-side, GDP accounting framework to decompose the contribution of population, participation, and productivity to GDP per capita (the 3P’s). We use this modelling to examine historic and projected demographic and macro-economic trends to inform policy discussions and decisions. Section 2 presents this framework and the central projections. Sections 3, 4, and 5 discuss each of the abovementioned three contributors to growth in turn. Section 6 concludes by summarising the findings and policy responses.

 
Jennifer Alonso Garcia, Oliver Wood and Jonathan Ziveyi
February 2017

This paper extends the Fourier-cosine (COS) method to the pricing and hedging of variable annuities embedded with guaranteed minimum withdrawal benefit (GMWB) riders. The COS method facilitates efficient computation of prices and hedge ratios of the GMWB riders when the underlying fund dynamics evolve under the influence of the general class of Levy processes. Formulae are derived to value the contract at each withdrawal date using a backward recursive dynamic programming algorithm. Numerical comparisons are performed with results presented in Bacinello et al. (2014) and Luo and Shevchenko (2014) to confirm the accuracy of the method. The efficiency of the proposed method is assessed by making comparisons with the approach presented in Bacinello et al. (2014). We find that the COS method presents highly accurate results with notably fast computational times. The valuation framework forms the basis for GMWB hedging. A local risk minimisation approach to hedging inter-withdrawal date risks is developed. A variety of risk measures are considered for minimisation in the general Levy framework. While the second moment and variance have been considered in existing literature, we show that the value-at-risk may also be of interest as a risk measure to minimise risk in variable annuities portfolios.

 
Elena Capatina
January 2017

Approximately one in four workers aged 25-40 who lacked private health insurance in 2010 in the US did not enroll in employer-provided health insurance (EPHI) that was available to them. In this paper, I study selection in EPHI among eligible employees using data from the Medical Expenditures Panel Survey from 2001 to 2010 and from the National Longitudinal Survey of Youth ’97 in 2010. Controlling for firm and job characteristics that proxy for the choice of plans and premiums faced by workers, I find that individuals aged 25-40 who decline EPHI and remain privately uninsured have significantly worse health and health behaviors than those who enroll. No correlation between health and insurance take up is found in the 41-64 age group. The advantageous selection among young employees is in part explained by education and family income, short expected job tenure, and by Medicaid crowding out EPHI for low socioeconomic status workers who have higher health risk. Preferences for health risk contribute very little and preferences for financial risk do not play a significant role. The results shed light on the characteristics of uninsured workers in the US and on the interaction between private and public health insurance, with implications for the design of health care reform.