Valuations of Mortality-Linked Structured Products

Pricing longevity derivatives via Fourier transforms

“…The valuation of longevity-linked derivatives with non-linear payoff structures (e.g., longevity options) has received little attention in the literature compared to that of longevity derivatives with a linear payoff but is attracting increasing interest. Some exceptions are Lin and Cox (2007), who study the pricing of a longevity call option linked to a population longevity index for older ages, Cui (2008), who discusses the valuation of longevity options (floors and caps) using the Equivalent Utility Pricing Principle, Dawson et al (2010), who derive closed-form Black-Scholes-Merton-type prices for European swaptions, Boyer and Stentoft (2013), who price European and American type survivor options using a risk neutral simulation approach, Wang and Yang (2013), who price survivor floors using an extension of the Lee-Carter model, Yueh et al (2016), who develop valuation models for mortality calls and puts-employing the jump-diffusion model developed by Cox et al (2006)-, Bravo andde Freitas (2018) and Bravo (2019Bravo ( , 2020, who discuss the valuation of longevity options embedded in longevity-linked life annuities, Fung et al (2019), who derive closed-form solutions for the price of longevity caps under a two-factor Gaussian mortality model resembling the Black-Scholes formula for option pricing when the underlying stock price follows a geometric Brownian motion, and Li et al (2019) as well as Cairns and Boukfaoui (2019), who discuss the valuation of K-options and call-spreads, respectively.…”