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|Hardy, Mary R.
|Dang, O., Feng, M. & Hardy, M. R. (2023). Two-stage nested simulation of tail risk measurement: a likelihood ratio approach. Insurance: Mathematics and Economics, 108, 1-24. https://dx.doi.org/10.1016/j.insmatheco.2022.10.002
|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.
|Insurance: Mathematics and Economics
|© 2022 Elsevier B.V. All rights reserved.
|Two-stage nested simulation of tail risk measurement: a likelihood ratio approach
|Nanyang Business School
|Likelihood Ratio Method
|We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada, funding reference number 03754 (Hardy) and 03755 (Feng). This work was also supported by the Society of Actuaries through a Center of Actuarial Excellence Research Grant and through the Hickman Scholarship held by Ou Dang. Ou Dang has also received support from the Ontario Graduate Scholarship.
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