Studies from Macquarie University Add New Findings in the Area of Insurance Economics (Valuation of variable annuities with Guaranteed Minimum…

Studies from Macquarie University Add New Findings in the Area of Insurance Economics (Valuation of variable annuities with Guaranteed Minimum Withdrawal Benefit under stochastic interest rate)

By a News Reporter-Staff News Editor at Investment Weekly News -- Investigators publish new report on Economics - Insurance Economics. According to news reporting out of North Ryde, Australia, by VerticalNews editors, research stated, "This paper develops an efficient direct integration method for pricing of the variable annuity (VA) with guarantees in the case of stochastic interest rate. In particular, we focus on pricing VA with Guaranteed Minimum Withdrawal Benefit (GMWB) that promises to return the entire initial investment through withdrawals and the remaining account balance at maturity."

Funders for this research include CSIRO-Monash Superannuation Research Cluster, Australian Research Council.

Our news journalists obtained a quote from the research from Macquarie University, "Under the optimal (dynamic) withdrawal strategy of a policyholder, GMWB pricing becomes an optimal stochastic control problem that can be solved using backward recursion Bellman equation. Optimal decision becomes a function of not only the underlying asset but also interest rate. Presently our method is applied to the Vasicek interest rate model, but it is applicable to any model when transition density of the underlying asset and interest rate is known in closed-form or can be evaluated efficiently. Using bond price as a numeraire the required expectations in the backward recursion are reduced to two-dimensional integrals calculated through a high order Gauss-Hermite quadrature applied on a two-dimensional cubic spline interpolation. The quadrature is applied after a rotational transformation to the variables corresponding to the principal axes of the bivariate transition density, which empirically was observed to be more accurate than the use of Cholesky transformation. Numerical comparison demonstrates that the new algorithm is significantly faster than the partial differential equation or Monte Carlo methods. For pricing of GMWB with dynamic withdrawal strategy, we found that for positive correlation between the underlying asset and interest rate, the GMWB price under the stochastic interest rate is significantly higher compared to the case of deterministic interest rate, while for negative correlation the difference is less but still significant. In the case of GMWB with predefined (static) withdrawal strategy, for negative correlation, the difference in prices between stochastic and deterministic interest rate cases is not material while for positive correlation the difference is still significant. The algorithm can be easily adapted to solve similar stochastic control problems with two stochastic variables possibly affected by control."

According to the news editors, the research concluded: "Application to numerical pricing of Asian, barrier and other financial derivatives with a single risky asset under stochastic interest rate is also straightforward."

For more information on this research see: Valuation of variable annuities with Guaranteed Minimum Withdrawal Benefit under stochastic interest rate. Insurance Mathematics & Economics, 2017;76():104-117. Insurance Mathematics & Economics can be contacted at: Elsevier Science Bv, PO Box 211, 1000 Ae Amsterdam, Netherlands.

Our news journalists report that additional information may be obtained by contacting P.V. Shevchenko, Macquarie University, Appl Finance & Actuarial Studies, N Ryde, NSW, Australia.

The direct object identifier (DOI) for that additional information is: https://doi.org/10.1016/j.insmatheco.2017.06.008. This DOI is a link to an online electronic document that is either free or for purchase, and can be your direct source for a journal article and its citation.

Keywords for this news article include: North Ryde, Australia, Australia and New Zealand, Insurance Economics, Economics, Investment and Finance, Macquarie University.

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