Valuation of equity-linked insurance and annuity products with binomial models. (English) Zbl 1480.91204
Summary: In this paper we develop a valuation method for equity-linked insurance products. We assume that the premium information of term life insurances, pure endowment insurances, and endowment insurances at all maturities is obtainable within a company or from the insurance market. Using a method similar to that of R. Jarrow and S. Turnbull [“Pricing options on financial securities subject to default risk”, J. Finance 50, No. 1, 53–86 (1995)], we derive three martingale probability measures associated with these basic insurance products. These measures are age-dependent, include an adjustment for the mortality risk, and reproduce the premiums of the respective insurance products. We then extend the martingale measures to include the financial market information using copulas and use them to evaluate equity-linked insurance contracts and equity-indexed annuities in particular. This is different from the traditional approach under which diversification of mortality risk is assumed. A detailed numerical analysis is performed for various existing equity-indexed annuities in the North American market.
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