Efficient Valuation of Equity-Indexed Annuities Under Lévy Processes Using Fourier-Cosine Series

Forthcoming Journal of Computational Finance

24 Pages Posted: 16 Feb 2014 Last revised: 6 Nov 2016

Geng Deng

Wells Fargo

Tim Dulaney

Securities and Exchange Commission

Craig J. McCann

Securities Litigation and Consulting Group

Mike Yan

Securities Litigation and Consulting Group

Date Written: January 14, 2015

Abstract

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.

Keywords: EIA, Lévy process, Fourier Method

JEL Classification: G12,G13

Suggested Citation

Deng, Geng and Dulaney, Tim and McCann, Craig J. and Yan, Mike, Efficient Valuation of Equity-Indexed Annuities Under Lévy Processes Using Fourier-Cosine Series (January 14, 2015). Forthcoming Journal of Computational Finance. Available at SSRN: https://ssrn.com/abstract=2396145 or http://dx.doi.org/10.2139/ssrn.2396145

Geng Deng (Contact Author)

Wells Fargo ( email )

1753 Pinnacle Dr
7th Floor
Mc Lean, VA Virginia 22102
United States

Tim Dulaney

Securities and Exchange Commission ( email )

100 F Street, NW
Washington, DC 20549-1105
United States

Craig J. McCann

Securities Litigation and Consulting Group ( email )

3998 Fair Ridge Drive, Suite 250
Fairfax, VA 22033
United States

Mike Yan

Securities Litigation and Consulting Group ( email )

3998 Fair Ridge Drive, Suite 250
Fairfax, VA 22033
United States
7035396780 (Phone)

Paper statistics

Downloads
74
Rank
258,668
Abstract Views
334