Testing the least squares Monte Carlo method for the evaluation of capital requirements in life insu

Testing the least squares Monte Carlo method for the evaluation of capital requirements in life insu

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In Europe, the Solvency 2 directive prescribes that insurers must hold eligible own funds at least equal to their Solvency Capital Requirements (SCR) defined as the value at risk (VaR) of the basic own funds with a confidence level of 99:5% over a time horizion of one year. Evaluating VaR is complicated by the fact that it must be computed at the risk horizon and two probability measures have to be taken into account. This aspect implies that if one tries to determine VaR according to a straightforward application of the Monte Carlo method, a nested simulation problem arises which is extremely time consuming. In order to reduce the computational complexity of the evaluation problem, Bauer et al. [1] and Cathcart and Morrison [2] proposed to apply the least squares Monte Carlo method (LSMC). Our goal is to test the performance of LSMC in evaluating capital requirements. In order to have a solid benchmark, we restrict our attention to the case where an insurer sells just one kind of policy: an equity-linked with a maturity guarantee. Moreover, we will work in an extended Black-Scholes framework where two risk factors, a reference portfolio and the short interest rate, evolve according to a Gaussian model. To test the accuracy of LSMC, we have conducted extensive numerical experiments with different number and type of basis functions. By looking at numerical results it emerges that accurate results can be achieved only with a high computational effort, particularly for policies with long duration.

[1] Bauer, D., Bergmann, D. and Reuss, A. (2010), “Solvency II and nested simulations - a least-squares Monte Carlo approach.” Working paper.

[2] Cathcart, M., Morrison, M. (2009) “Variable annuity economic capital: the least- squares Monte Carlo approach.” Life & Pensions, July/August, pp. 44-48.

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