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Surrender and path-dependent guarantees in variable annuities: integral equation solutions and benchmark methods

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  • Antonio L. Martire

    (Rome Tre University)

  • Emilio Russo

    (University of Calabria)

  • Alessandro Staino

    (University of Calabria)

Abstract

We investigate the evaluation problem of variable annuities by considering guaranteed minimum maturity benefits, with constant or path-dependent guarantees of up-and-out barrier and lookback type, and guaranteed minimum accumulation benefit riders, with different forms of the surrender amount. We propose to solve the non-standard Volterra integral equations associated with the policy valuations through a randomized trapezoidal quadrature rule combined with an interpolation technique. Such a rule improves the converge rate with respect to the classical trapezoidal quadrature, while the interpolation technique allows us to obtain an efficient algorithm that produces a very accurate approximation of the early exercise boundary. The method accuracy is assessed by constructing two benchmarks: The first one, developed in a lattice framework, is characterized by a novel algorithm for the lookback path-dependent guarantee obtained thanks to the lattice convergence properties, while the application is straightforward in the other cases; the second one is based on the least-squares Monte Carlo simulations.

Suggested Citation

  • Antonio L. Martire & Emilio Russo & Alessandro Staino, 2023. "Surrender and path-dependent guarantees in variable annuities: integral equation solutions and benchmark methods," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 177-220, June.
    • Handle: RePEc:spr:decfin:v:46:y:2023:i:1:d:10.1007_s10203-022-00383-w
    DOI: 10.1007/s10203-022-00383-w
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