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Improvements on the equity indexed annuity market
Sachelarie, Vlad

2002, Doctor of Philosophy, Ohio State University, Mathematics.
Equity indexed annuities (EIA's) were introduced to the market in the early 1995 and ever since then they have been producing a lot of interest and excitement in the option market. An EIA is an equity linked annuity whose return is based on the performance of an equity mutual fund or a stock index. These annuities have some really nice features such as: minimum guaranteed return, tax-deferral, and locking in of a credited interest rate, and also each EIA customer takes part in some way in the stock market. A typical example of an EIA is a point-to-point design. If S&P 500 has a realized 5-year return of 8% and the participation rate is set at 90%, then the actual interest rate credited to the policy will be 8%*90%=7.2% if this is bigger than the minimum guaranteed rate (usually around 3%). There are also some other classic designs like annual reset and continuous lookback that we discuss in Chapter 2. The problem the EIA market is facing today is the increased volatility of the market as well as an abrupt stop in the phenomenal growth of the stock market. Insurers aren't able to offer the same participation rates as they used to in the late 90's, and lower participation rates mean lower sale numbers. The need for some new designs or models of EIA's is clear and that's what this thesis will answer. We will show how to improve the classic EIA designs using a multibarrier approach and we will also introduce a few other new designs that perform much better then the classic ones in today's volatile market. These last designs are based on a path-dependence approach where we look at the value of the respective index throughout the period of the policy or just on an arbitrary period. So we introduced 5 new types of EIA's and derived closed form formulae for the price of these new designs. We also provide tables and plots of the classic designs versus the new design which show that the new ones are better than the old ones and also show how much better they are in terms of actual numbers for the participation rates for different prices.
Bostwick Wyman (Advisor)
94 p.

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