This project is a continuation of two previous works, in 2009 and 2012, under DIME (“Un estudio sobre el requisito de rentabilidad mínima de los fondos de cesantías”, code 9986 , and “Un Estudio Actuarial sobre el Sistema de Retiro Programado”, code 15502), and a continuation of two master’s thesis (investigative modality) in Statistics.
The subject matter is in the area of the valuation of guarantees in certain annuities types, known as equity-indexed or equity-linked annuities (EIA, ELA), which has been extensively studied since some decades ago. Those types of annuities are financial products which has been introduced by some insurance companies and, as replacements of traditional life annuities, including the public pension system in some countries, are the subject of much debate and research.
In the previous work of Giraldo(2012), a first solution to the valuation problem of an interest rate guarantee was proposed using a methodology for risk-neutral valuation of contingent cash-flows proposed by Carriere. The model’s assumptions included an Ornstein-Uhlenbeck model for the portfolio of the annuity’s sponsor, assumed to be a balanced one, invested in stocks and bonds. And an individual account, protected by a collar-type interest rate derivative. The long position assumed by the annuity’s sponsor is justified by the fact that the collar’s costs are almost null. Then, no specific hedging strategy is needed.
In this project, we want to compare critically the model and the methodology proposed in Giraldo(2012) with some published articles on the same topic. And we want to explore more carefully the hypothesis made in the same work Giraldo(2012), of assuming the long-term rate in the Ornstein-Uhlenbeck to be equal to the technical interest rate for the life annuity, which was deemed unacceptable by a referee, in a specialized actuarial journal. What would be an acceptable assumption for the relation between the long-term rate and the technical interest rate?
As a first step in the investigation of this relation, we describe an empirical
The life annuity technical rate has to be defined each year. There exist now legal regulations about how to define and calculate it. For instance, the Chilean and Colombian regulations establish a formula which links this rate to the term structure of interest rates through the Nelson-Siegel model.
The inverse of the value of the life annuity is direct proportional with the 90-day passive interest rate (the rate given in savings accounts).
In some countries like UK, this inverse value of the life annuity is also provided by a specific market of life annuities. As Cannon and Tonks have demonstrated through several studies, this inverse value has negative correlation with the stock market returns. It is also well known that there exists a negative correlation between inflation and the stock market.
As a first step, a master thesis (professional modality) will be developed investigating the relationship between the (short) term structure of interest rates and the stock market index. The proposed model is a transfer model based on the cross correlation between the 90-day node and the index returns. There exists a direct relation between inflation and the term structure of interest rates which is important to explore. It is well known that there exists a negative correlation between inflation and the stock market.
The main objective being to understand the effect of the stock market and inflation on the technical rate of the drawdown pension scheme.
We finally examine another methodologies for valuation of interest rate guarantees in EIA, and alternative forms of these type of annuities which include guarantees for inflation and interest rate risks. |