Efficient Valuation of Equity-Indexed Annuities Under Lévy Processes Using Fourier-Cosine Series
By: Geng Deng, Tim Dulaney, Craig McCann, and Mike Yan (Apr 2014)
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
annuity contracts.
