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

Antonio L. Martire (), Emilio Russo () and Alessandro Staino ()
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Antonio L. Martire: Rome Tre University
Emilio Russo: University of Calabria
Alessandro Staino: University of Calabria

Decisions in Economics and Finance, 2023, vol. 46, issue 1, No 6, 177-220

Abstract: 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.

Keywords: Variable annuity; Guaranteed minimum maturity/accumulation benefit; Volterra integral equation; Randomized trapezoidal quadrature; Lattice model; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10203-022-00383-w

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