Modeling of Variable Annuity Economic Capital for Market Risk Using a Form of Path-Dependent Monte Carlo Scenarios and a 'Bump & Revalue' Approach on Greeks

Abstract:     
This paper introduces a simple yet powerful approach to risk-based economic capital computation covering against market risk for variable annuity (“VA”) products using a form of path-dependent Monte Carlo scenarios combined with a “bump and revalue” method where unhedged first and second-order Greeks are ex-ante valued for a set of perturbations over a few dimensions (e.g. moneyness and interest rates) and then properly employed according to the selected Monte Carlo scenario. The main advantage of this approach is to rely on a minimum amount of inputs thus making feasible the implementation of such a model in practice for insurance companies and large VA portfolios while ensuring an accurate estimate of economic capital. Carrying out that approach requires the derivation of matrices of Greeks derived based on a market consistent balance sheet. The key to this approach is the use of varying Greeks though multiple sets of Monte Carlo scenarios applied successively over the projection making this approach path-dependent such that Greeks that are not hedged are appropriately used to derive an economic capital according to the perturbation produced by the selected Monte Carlo scenario. Our in-sample tests show that the derivation of a continuous function for Greeks over two dimensions (i.e. level of equity index and interest rate levels) is best achieved using a cubic spline interpolation with linear extrapolation. This approach is of particular interest given the major changes observed in the VA market recently with the historically high level of implied volatility combined with very low risk-free interest rates that let VA writers with large blocks of in-force business with guaranteed benefits riders significantly in the money and therefore increased capital levels.

Number of Pages in PDF File: 12

Keywords: Economic capital, variable annuity (VA), market risk, Value-at-Risk (VaR), Monte Carlo, Solvency II, path-dependent scenarios, “bump & revalue” approach, multidimensional varying Greeks, matrix of Greeks, Taylor series expansion, nested simulation, Least-Square Monte Carlo (LSMC)

JEL Classification: C15, C60, C61, C63, G22

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