Download or read book Efficient Valuation of Equity-Indexed Annuities Under Lévy Processes Using Fourier-Cosine Series written by Geng Deng and published by . This book was released on 2019 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.