Two-stage nested simulation of tail risk measurement: A likelihood ratio approach

Ou Dang, Mingbin Feng and Mary R. Hardy

Insurance: Mathematics and Economics, 2023, vol. 108, issue C, 1-24

Abstract: Estimating tail risk measures is an important task in many financial and actuarial applications and often requires nested simulations, with the outer simulations representing real world scenarios, and the inner simulations typically used for risk neutral pricing or conditional risk measurement. The standard nested simulation method is highly flexible, able to incorporate complex asset models and exotic payoff structures, but it is also computationally highly burdensome, particularly in a multi-period setting, when inner simulation paths are required at each time step of each outer level scenario. In this study, we propose and analyze a two-stage simulation procedure that efficiently estimates the conditional tail expectation of cost of a dynamic hedging program for a Variable Annuity Guaranteed Minimum Withdrawal Benefit (GMWB), under a multi-period nested simulation. In each of the two stages, the method re-uses the same set of inner level simulation paths for each outer scenario at each time point, using a likelihood ratio method to re-weight the probabilities of each individual path for the different outer scenarios. Our numerical study shows that our two-stage, likelihood ratio weighted procedure can offer a very significant improvement in efficiency, of the order of 95% as measured by the RMSE, compared with a standard nested simulation with the same computational cost.

Keywords: Nested simulation; Likelihood ratio method; Importance sampling; Enterprise risk management; Conditional tail expectation; Tail value-at-risk; Expected shortfall; GMWB (search for similar items in EconPapers)
JEL-codes: C15 C53 C63 G22 G32 G52 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:108:y:2023:i:c:p:1-24

DOI: 10.1016/j.insmatheco.2022.10.002

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