GUARANTEED MINIMUM BENEFITS EMBEDDED IN VARIABLE ANNUITIES: PRICING AND RISK ANALYSIS

The global economic turmoil of 2007–2008 exerted a profound impact on the banking sector while simultaneously exposing vulnerabilities within the insurance industry. Insurers faced substantial losses from misguided investment strategies, thereby underscoring the imperative of attaining a comprehensive understanding of the intricate risk landscape inherent in insurance products. This crisis served as a catalyst for the establishment of robust and adaptable regulatory frameworks capable of withstanding future financial upheavals and safeguarding the stability and resilience of the insurance sector. Notable examples of such regulatory mechanisms include Solvency II within the European Union (EU) and the life insurance regulatory framework in Canada overseen by the Office of the Superintendent of Financial Institutions (OSFI). Particularly noteworthy is OSFI's emphasis on the urgent necessity of devising a robust valuation methodology for guaranteed minimum benefits embedded within variable annuities. These guaranteed benefits assume a dual-purpose role within investors' retirement portfolios, offering both growth potential and downside protection. This emphasis underscores the critical significance of precise valuation techniques and a comprehensive grasp of the multifaceted risks associated with such guarantees, not only for insurers but also for regulators entrusted with ensuring sectoral stability and consumer welfare.\nThe primary aim of this thesis is to make substantive contributions toward advancing risk management protocols, fortifying regulatory frameworks, and safeguarding the interests of policyholders and beneficiaries of guaranteed minimum benefits associated with variable annuities and segregated funds. To fulfill this objective, the thesis comprises three distinct yet interrelated research endeavors, outlined as follows:\n(i) The initial research in this thesis centers on the valuation of guaranteed minimum accumulation benefit (GMAB) and guaranteed minimum maturity benefit (GMMB) within an integrated framework that incorporates three interlinked risk factors. Utilizing numerical illustrations, we elucidate the development of a computationally efficient method characterized by markedly enhanced calculation speed and accuracy compared to the benchmark Monte Carlo simulation method.\n(ii) The second research endeavor introduces a modelling structure for valuing the guaranteed minimum income benefit (GMIB), integrating correlated stochastic interest and mortality rates. Employing the numéraire transformation approach, we derive an analytical solution for the GMIB rider, considering two distinct Benefit Base function scenarios. Numerical demonstrations highlight the superiority of our proposed methodology over the standard Monte Carlo simulation as a benchmark in terms of computational accuracy and efficiency.\n(iii) The third research effort addresses the challenge of determining capital requirements for GMMB and GMIB riders. Two types of moment-based density approximation methods, namely the baseline-density-polynomial (BDP) density approximation method and the generalized Pearson family (GPF) probability density approximation method, are employed to estimate the distributions of GMMB and GMIB loss random variables. Subsequently, we compute numerical values for various risk measures based on the estimated loss distributions. These results are then compared against those obtained through the standard Monte Carlo simulation methodology, serving as a benchmark. Our findings confirm the superior accuracy of our proposed approach in the risk measurement of GMMB and GMIB.

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