减少用于随机ALM估值的场景数量

MILLIMAN WHITE PAPER Reducing the number of scenariosused for stochastic ALM valuation Pierre-Edouard ArrouyJérémy BeaudetMohammed BennounaSteven FrancoisAlison Tonin The valuation of an insurance balance sheet is a complex exercise thatrequires the simulation of various stochastic variables, such as risk-neutral economic scenarios. In practice, given typical run-timeconstraints, the number of economic scenarios to beconsidered islimited and it is necessary to develop techniques to ensure that thestochastic valuation of the Best Estimate of Liabilities(BEL)and thePresent Value of Future Profits(PVFP)converge to their true values. In today's landscape, numerous insurance companies are actively working to reduce the computational timeassociated with stochasticasset-liability management(ALM) valuation, particularly under frameworks such asInternational Financial Reporting Standard (IFRS)17 or within Solvency II internal models,specifically forleastsquares Monte Carlo (LSMC)calibration. This paper focusses on exploring the reduction of the number of simulations as a means to achieve a reasonableobjective in terms of valuation accuracy while significantly decreasing the computational time required forstandard valuations.Additionally, efficiency, encompassing cost and energy considerations, has emerged as apressing concern for businesses of all magnitudes. The starting point of thisstudyisthe PrudentHarmonisedReduced Set of Scenarios(PHRSS) frameworkrecentlyintroduced bythe European Insurance and Occupational Pensions Authority (EIOPA)that aims to assistcompanies that relyon deterministic calculations for their technical provisions by enabling them to evaluate thetime value of their options and guarantees using a reduced set of economicscenarios.Nevertheless, scenarioreduction based on weighted MonteCarlo techniques have enjoyed enduring popularity for internal modelapplicationsthanks toESG Rebase.1 This research proposesarefined simulation reduction technique, centring on theoptimisationof critical choices.A key focus lies on enhancing the method for generating and selectingtrajectories, along with the reweightingoptimisationfunction.Thanks tocross-validation, we showcase the performance ofourproposed methodologyusing boththeMillimanEconomic Scenario Generator2and an ALM benchmark model. Notably,wedemonstratethat even with fewer than 200 simulations, our approach achieves a remarkably accurate replication, equivalentto employing 3,000 simulations through a best-in-class approach. The paperdiscusses thefollowing topics: 1.Analysis of the PHRSS frameworkand thereduced scenario set published by EIOPA.2.Implementation ofscenario reduction techniquesand study of trajectory selection approaches along withscenarioadjustments.3.Towards adaptativenumbers of scenariosin view ofdetermininganoptimisedscenario reduction approach. Analysis oftheEIOPAPHRSS Under Solvency II, insurers arerequiredto carry out an exhaustive stochastic assessment of their Best Estimatesof Liabilities (BELs) and their Valuesof In-Force (VIFs) using MonteCarlo techniques.Tothis extent theyuseastochasticcashflow model fed withthousands of risk-neutraleconomicscenariosgeneratedthroughaneconomic scenario generator (ESG).Nevertheless,manyEuropeaninsurancecompaniescurrently do notperform stochastic calculationsfor several reasons.Firstly, theymight lack therequiredcomputational resourcesor expertise to perform complex stochastic simulations. Secondly, some companies might have a business modelor risk profile that doesn'trequirestochastic valuation.Moreover, regulatory requirements or guidance might varyacross different jurisdictions, leading some companies to opt for simpler, non-stochastic approaches to valuation. For these reasons,EIOPA has introduced a new valuation method, called the PrudentHarmonisedReduced Setof Scenarios3(PHRSS) and aimed for”low-risk profile undertaking”companies that are not equipped to assessthe materiality of their time valuesof options and guarantees (TVOGs) and which solely perform deterministiccalculationsof their technical provisions.The objective of this approachis to provide insurers witha set ofstochastic economic scenarios containing only a few trajectories, so thatthe TVOG(as well as the VIF and theBEL)can be operationally estimatedbyrunning a deterministic modelseveral times.EIOPA has set theimplementation date for this framework in 2024. In January 2023,EIOPAdisclosedsixscenario sets4for the31December2021valuation date,each ofthemfeaturingnine scenarios.Thegeneral methodologyemployed by EIOPAfor creatingthese sixscenariosetsinvolvesthestepsdescribed inthe diagramin Figure 1. The first step of the approach consists ingenerating several thousands of stochasticrisk-neutraltrajectoriesincorporating variousfinancialrisk factorssuch as interest rates,equity indices5etc.Thisinitialpoolof scenariosis referredtoasthe“referencescenario set.”Secondly, based on this referencescenario set,EIOPA proposesthreemethodo