Avaliação de opções e garantias embutidas em seguros ligados a fundos de investimento

Mestrado em Ciências ActuariaisA avaliação de opções contratuais e garantias financeiras encontra-se no centro das atenções do sector segurador e tem despertado um forte interesse académico nos anos recentes. Tal decorre, por um lado, das tendências evolutivas ao nível dos seguros comercializados no ramo Vida, com características cada vez mais complexas e ligadas a uma vertente financeira e, por outro, do desenvolvimento de importantes projectos internacionais, tal como o Solvência II. Em linhas gerais, o presente trabalho visa estudar a aplicação da teoria das opções financeiras à avaliação de contratos de seguros ligados a fundos de investimento com determinadas opções contratuais e garantias financeiras, tendo por base o princípio de avaliação market-consistent. Para alcançar esse objectivo, uma parte importante da análise centra-se no processo de calibragem de modelos estocásticos para certos riscos de mercado, designadamente o risco de taxa de juro e o risco accionista, de forma o mais consistente possível com a informação disponível nos mercados financeiros, com o propósito de gerar cenários económicos futuros num ambiente neutro face ao risco. Posteriormente, o valor de certas garantias financeiras e da opção de resgate total de um contrato é determinado através da aplicação de metodologias baseadas na simulação de Monte Carlo.The valuation of contractual options and financial guarantees is at the center of attention of the insurance sector and has drawn a strong academic interest in recent years. This is due, on one hand, to the evolutionary trends in Life insurance products, with features that are increasingly complex and connected to the financial market and, on the other hand, to the development of important international projects, such as Solvency II. In general, this paper aims to study the application of financial options theory to the valuation of unit-linked contracts with some contractual options and financial guarantees. The study is based on the principle of market-consistent valuation. To achieve this purpose, an important part of the analysis focuses on the calibration process of stochastic models for certain market risks, namely the interest rate risk and the equity risk, in a way as consistent as possible with the information available in the financial markets, with the aim of generating future economic scenarios in a risk-neutral world. Afterwards, the value of some financial guarantees and of the surrender option is determined by means of methodologies based on the Monte Carlo simulation method

Four Essays in Equity-Linked Life and Pension Insurance : Financial Analysis of Surrender Guarantees, Pension Guarantee Funds and Pension Retirement Plans

In this dissertation we study three very important types of insurance, equity-linked life insurance with surrender guarantees, pension insurance and the insurance provided by (pension) insurance guarantee funds. In chapter 2 we study the market consistent valuation of equity linked life insurance contracts, particularly the valuation of a surrender option. In our model the policyholder can surrender exogenously and endogenously. More importantly, we model the realistic perspective that the surrender option value depends on the state of the economy. The state of the economy can represent financial market regimes, macroeconomic regimes or business cycles. The consideration of economic states is an important contribution since equity-linked life insurance contracts are long-dated and in the long run there can occur several structural changes in the economic conditions which considerably affect both the value of the underlying financial portfolio and most importantly the surrender behavior of the policyholder. Chapter 3 and chapter 4 are concerned with the (re)insurance of pension guarantee funds (PGF). These government imposed pension schemes provide (re)insurance to defined benefit (DB) plan holders in terms of paying pension benefits if the corresponding sponsoring company and the pension fund are insolvent. We study and model solution concepts for pension guarantee funds to better protect policyholders by reducing the risk exposure of their financial guarantee. We model two solution concepts. In chapter 3 we provide a formal model to compute a risk-based premium paid to the PGF under distress termination, the conventional type of termination, where a pension fund is closed due to the insolvency of the sponsoring company. We incorporate several realistic perspectives and compare our theoretical pricing formula for a sample of the largest US DB plan sponsors. In chapter 4 we study the other type of termination, involuntary termination. Under involuntary termination the PGF terminates a substantially underfunded DB plan. In that case the crucial question is when the PGF should optimally intervene. We determine an optimal timing of intervention in terms of a critical funding ratio of the insured DB pension fund. The basic idea of our model is that the PGF acts in the interest of the beneficiaries and maximizes their expected utility. In addition the PGF protects its financial guarantee by controlling two solvency requirements, the shortfall probability and the expected shortfall of the DB plan. In chapter 4 the DB plan is modeled more specifically and compared to the other main pension retirement plan, the defined contribution plan (DC plan). The analysis is conducted in an expected utility framework under different preferences by taking an essential tradeoff into account. Specifically, the policyholder faces salary risk in both retirement plans, he faces investment risk only in the DC plan and portability risk, the risk of losing benefits when changing the employer is mostly present in the DB plan. As a means of comparison we take the critical job switching intensity or more intuitively the average number of job moves after which the DC plan is preferred in expected utility terms

Fee Structure and Surrender Incentives in Variable Annuities

Variable annuities (VAs) are investment products similar to mutual funds, but they also protect policyholders against poor market performance and other risks. They have become very popular in the past twenty years, and the guarantees they offer have grown increasingly complex. Variable annuities, also called segregated funds in Canada, can represent a challenge for insurers in terms of pricing, hedging and risk management. Simple financial guarantees expose the insurer to a variety of risks, ranging from poor market performance to changes in mortality rates and unexpected lapses. Most guarantees included in VA contracts are financed by a fixed fee, paid regularly as a fixed percentage of the value of the VA account. This fee structure is not ideal from a risk management perspective since the resulting amount paid out of the fund increases as most guarantees lose their value. In fact, when the account value increases, most financial guarantees fall out of the money, while the fixed percentage fee rate causes the fee amount to grow. The fixed fee rate can also become an incentive to surrender the variable annuity contract, since the policyholder pays more when the value of the guarantee is low. This incentive deserves our attention because unexpected surrenders have been shown to be an important component of the risk faced by insurers that sell variable annuities (see Kling, Ruez and Russ (2014) ). For this reason, it is important that the surrender behaviour be taken into account when developing a risk management strategy for variable annuity contracts. However, this behaviour can be hard to model. In this thesis, we analyse the surrender incentive caused by the fixed percentage fee rate and explore different fee structures that reduce the incentive to optimally surrender variable annuity contracts. We introduce a "state-dependent" fee, paid only when the VA account value is below a certain threshold. Integral representations are presented for the price of different guarantees under the state-dependent fee structure, and partial differential equations are solved numerically to analyse the resulting impact on the surrender incentive. From a theoretical point of view, we study certain conditions that eliminate the incentive to surrender the VA contract optimally. We show that the fee structure can be modified to design contracts whose optimal hedging strategy is simpler and robust to different surrender behaviours. The last part of this thesis analyzes a different problem. Group self-annuitization schemes are similar to life annuities, but part, or all, of the investment and longevity risk is borne by the annuitant through periodic adjustments to annuity payments. While they may decrease the price of the annuity, these adjustments increase the volatility of the payment patterns, making the product risky for the annuitant. In the last chapter of this thesis, we analyse optimal investment strategies in the presence of group self-annuitization schemes. We show that the optimal strategies obtained by maximizing the utility of the retiree's consumption may not be optimal when they are analysed using different metrics

Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science