Dynamic Importance Allocated Nested Simulation for Variable Annuity Risk Measurement

Abstract

involves projecting scenarios of key variables under the real world measure, while the inner stage is used to value payoffs under guarantees of varying complexity, under a risk neutral measure.

The computational burdens in nested simulation often hinders its practicality. In this paper we propose and analyse an efficient simulation approach that dynamically allocates the inner simulations to the specific outer scenarios that are most likely to generate larger losses. These scenarios are identified using a proxy calculation that is used only to rank the outer scenarios, not to estimate the tail risk measure directly.

As the proxy ranking will not generally provide a perfect match to the true ranking of outer scenarios, we calculate a measure based on concomitant order statistics to test whether further tail scenarios (by the proxy model) are required to ensure with given confidence that the true tail scenarios are captured. This procedure, which we call the Dynamic Importance Allocated Nested Simulation (DIANS) approach. The DIANS approach automatically adjusts for proxy calculations that are closer to, or farther away from the true valuations, and also signals when the proxy is not sufficiently accurate, which may be useful for ensuring that the valuation accuracy does not deteriorate over time as the proxy becomes outdated.

Keywords: Nested simulation, Expected Shortfall, Variable Annuities, Concomitants, Conditional Tail Expectation.

JEL Classification: C15,C53,G22