Efficient Valuation of Equity-Indexed Annuities Under Lévy Processes Using Fourier-Cosine Series
Published in The Journal of Computational Finance, Vol 21, No. 2, September 2017.
Equity-Indexed Annuities (EIAs) are deferred annuities which accumulate value over time according to crediting formulas and realized equity index returns. We propose an efficient algorithm to value two popular crediting formulas found in EIAs - Annual Point-to-Point (APP) and Monthly Point-to-Point (MPP) - under general Lévy-process based index returns. APP contracts observe returns of referenced indexes annually and credit EIA accounts, subject to
minimum and maximum returns. MPP contracts incorporate both local/monthly caps and global/annual floors on index credits. MPP contracts have payoffs of a "cliquet" option.
Our algorithm, based on the COS method (Fang and Oosterlee, 2008), expands the present value of an EIA contract using Fourier-cosine series, expresses the value of the EIA contract
as a series of terms involving simple characteristic function evaluations. We present several
examples with different Lévy processes, including the Black-Scholes model and the CGMY
model. These examples illustrate the efficiency of our algorithm as well as its versatility
in computing annuity market sensitivities, which could facilitate the hedging and pricing of
Structured Product Based Variable Annuities
Published in the Journal of Retirement, Winter 2014, Vol. 1, No. 3: pp. 97-111.
Recently, a new type of variable annuity has been marketed to investors which is based on structured product-like investments instead of the mutual fund-like investments found in traditional variable annuities. Embedding a structured product into a variable annuity introduces substantial complexity into an investment typically considered conservative. In this paper, we describe structured product based variable annuity (spVA) crediting formulas and how they differ from traditional VAs, value the embedded derivative position for a range of example parameters, and calculate the fair cap levels required to fairly compensate investors for the derivative position. We also provide extensive backtests of spVA crediting formulas using our calculated cap levels and compare the results to their underlying indexes. Our findings suggest that the complexity of spVAs can be used to hide fees and reduce the comparability of variable annuities to other investments in the market.
An Economic Analysis of Equity-Indexed Annuities
At the request of the North American Securities Administrators Association, Dr. McCann authored a White Paper on equity-indexed annuities in support of the SEC's proposal to provide federal investor protections to purchasers of equity-indexed annuities.
Dr. McCann concluded that:
- Existing equity-indexed annuities are too complex for investors to understand.
- This complexity is designed to allow the true costs to be hidden
- The high hidden costs in equity-indexed annuities are sufficient to pay extraordinary commissions to a sales force that is not disciplined by sales practice abuse deterrents found in the market for regulated securities.
- Unsophisticated investors will continue to be victimized by issuers of equity indexed annuities until truthful disclosure and the absence of sales practice abuses is assured.
An Overview of Equity-Indexed Annuities
Equity-indexed annuities are complex investments sold by insurance companies that pay investors part of the capital appreciation in a stock index and guarantee a minimum return if the contract is held to maturity. Equity-indexed annuities to date have been regulated by state insurance commissions, rather than by the SEC and the NASD. We estimate that between 15% and 20% of the premium paid by investors in equity-indexed annuities is a transfer of wealth from unsophisticated investors to insurance companies and their sales forces and that the claimed benefits for EIAs can be had at a tiny fraction of the cost using stocks and Treasury securities.