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

Autor: Antonio L. Martire, Emilio Russo, Alessandro Staino
Přispěvatelé: Martire, Antonio Luciano, Russo, Emilio, Staino, Alessandro
Rok vydání: 2023
Předmět:
Zdroj: Decisions in Economics and Finance. 46:177-220
ISSN: 1129-6569
1593-8883
DOI: 10.1007/s10203-022-00383-w
Popis: 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.
Databáze: OpenAIRE
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