Proposta de modelos de apreçamento de opções embutidas em produtos de previdência no Brasil.

Abstract

This work, which consists of quantitative research within operations management, presents the development of mathematical models for pricing options embedded in Brazilian insurance retirement-related products. The problem studied refers to the financial option that an insurance company writes to its clients who purchase open ended retirement plans. Such option allows the participant to purchase, in the date of his or her retirement, an annuity under terms and conditions defined at the date the participant adheres to the plan. Models presented intend to calculate the value and sensibilities of the liability incurred, considering the financial risks involved. The problem is approached in two steps. Firstly, risks acquired by the insurance company are modeled and the characteristics of the option written to the participant are identified. This allows, under certain assumptions for investment choices and mortality behavior, the use of option pricing models traditional in Finance Theory to determine the value of liabilities. Secondly, the use of portfolio optimization models to hedge the insurance company against changes in the value of liabilities is analyzed. Moreover, the pricing model is applied to calculate the adequate fee to be applied to each contribution an individual makes to the plan (known as taxa de carregamento). Changes to such adequate fees resulting from changes in interest rate and volatility levels are also analyzed. Finally, the models presented are applied to a real problem of an insurance company. Results achieved indicate that, although the current value of liabilities is relatively small, the significant sensitivity to decreases in interest rates and hedge difficulties stemming from the long maturity of liabilities make the problem relevant from the perspective of the insurance company.