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Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees

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Abstract

This paper proposes a paradigm shift in the valuation of long term cash-linked annuities and equity-linked annuities with cash-linked guarantees, away from classical no-arbitrage pricing towards pricing under the real world probability measure. In contrast to risk neutral pricing, which is a form of relative pricing, the long term average excess return of the equity market comes into play. Instead of the savings account, the numeraire portfolio is employed as the fundamental unit of value in the analysis. The numeraire portfolio is the strictly positive, tradable portfolio that when used as benchmark makes all benchmarked nonnegative portfolios supermartingales. Intuitively, benchmarked portfolios are in the mean downward trending or trendless. The benchmarked real world price of a benchmarked contingent claim equals its real world conditional expectation. This yields the minimal possible price for its hedgeable part and minimizes the variance for its hedge error. Classical actuarial and risk neutral pricing emerge as special cases of the proposed real world pricing. In long term liability and asset valuation, the proposed real world pricing can lead to significantly lower prices than suggested by classical approaches. The existence of an equivalent risk neutral probability measure is not required.

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  • Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:338
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    More about this item

    Keywords

    long term contracts; real world pricing; actuarial pricing; risk neutral pricing; numeraire portfolio; law of the minimal price; strong arbitrage; hedge error; diversification;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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