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.

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

Emilio Russo
;
Alessandro Staino
2023-01-01

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.
Variable annuity, guaranteed minimum maturity/accumulation benefit, Volterra integral equation, randomized trapezoidal quadrature, lattice model, Monte Carlo simulation.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/341202
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