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.

Martire, A.L., Russo, E., Starino, A. (2023). Surrender and path-dependent guarantees in variable annuities: integral equation solutions and benchmark methods. DECISIONS IN ECONOMICS AND FINANCE [10.1007/s10203-022-00383-w].

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

Antonio Luciano Martire;
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.
Martire, A.L., Russo, E., Starino, A. (2023). Surrender and path-dependent guarantees in variable annuities: integral equation solutions and benchmark methods. DECISIONS IN ECONOMICS AND FINANCE [10.1007/s10203-022-00383-w].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/426294
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