Pricing ratchet equity-indexed annuities with early surrender risk in a CIR\(++\) model. (English) Zbl 1412.91058

Summary: In this article we propose a lattice algorithm for pricing simple ratchet equity-indexed annuities (EIAs) with early surrender risk and global minimum contract value when the asset value depends on the CIR\(++\) stochastic interest rates. In addition we present an asymptotic expansion technique that permits us to obtain a first-order approximation formula for the price of simple ratchet EIAs without early surrender risk and without a global minimum contract value. Numerical comparisons show the reliability of the proposed methods.


91B30 Risk theory, insurance (MSC2010)
91G60 Numerical methods (including Monte Carlo methods)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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