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Pricing surrender risk in Ratchet equity-index annuities under regime-switching Lévy processes. (English) Zbl 1414.91414

Summary: This article presents a numerical method of pricing the surrender risk in Ratchet equity-index annuities (EIAs). We assume that log-returns of the underlying fund belong to a class of regime-switching models where the parameters are allowed to change randomly according to a hidden Markov chain. The defining feature of these models is the fact that in each regime the characteristic function of log-returns is assumed to have an analytical form. The presented method provides an unified pricing framework within this class and includes the recently developed COS method as a particular case. This aspect of the method is particularly useful when pricing Ratchet options embedded in EIAs, for which the COS method exhibits a low rate of convergence. Our numerical results confirm that for models considered in this article the proposed approach improves convergence of the COS method without increasing the computational burden.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
91G20 Derivative securities (option pricing, hedging, etc.)
91B30 Risk theory, insurance (MSC2010)
60G51 Processes with independent increments; Lévy processes
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