一种新的混合随机数生成器，用于更准确地评估保险负债

Anew hybrid Random NumberGeneratorformore accuratevaluation of insurance liabilities Hervé AndrèsPierre-Edouard ArrouyPaul BonnefoyAlexandre Boumezoued Valuing an insurance balance sheet is a complexexercisewhichrequires the use of stochastic economic scenarios. Various testsshould be performed to ensure such valuation is produced in areasonable manner,includingthemartingale testson the economicscenariosand theleakage teston the insuranceasset-liabilitymanagement (ALM)model,i.e.,initial market value of asset is equal tothe sum of the best estimate of liabilities (BEL) and the present value offuture profits (PVFP). In practice, giventherun time constraints of typicalALMmodels, the number of economic scenarios to beconsidered is limited. Hence,there is a need to develop techniques to ensurethatthe stochastic valuation of BELand PVFP converges towardstheirtrue valuesand thereforethatthe leakage is reasonable and stable betweendifferent valuation dates. One potentialsolutionis to enhance theRandom Number Generator(RNG)used togenerate thestochasticeconomic scenarios.In this paper, we present a new RNGand demonstrate its efficiencyover existing RNGs for the valuation ofstochastic BEL.We also discuss the need for universal and interpretablevalidation strategies for martingale tests for such types ofRNGs. The use of RNGsand theirrequirements The increasinguse ofstochastic economic scenariosforthe valuation of insurance liabilities—e.g.,Solvency II,International Financial Reporting Standard (IFRS)17,Long-Duration Targeted Improvements (LDTI), International Capital Standard, Risk-Based Capitalregimes in Asia—is puttingmorepressure on the operationalprocessesof insurance companies, with a particular focus on the ALM model run timewhen,for example,1,000or more stochasticeconomicscenarios are used forBEL and PVFPvaluation. Besides, there is an increasingneedto producereliableand stablevaluation estimates overtimeandfordifferent economic conditions. As oneofthe key inputs of the Economic Scenario Generator (ESG), the RNG playsacriticalrole in the qualityof theeconomic scenarios generatedandsubsequently on thequality oftheassessment of the interactions betweentheassets and liabilitiesof the insurer,and ultimately on theconvergence ofthe stochastic BEL and PVFP. At first,anyEconomic Scenario Generator (ESG)—hence the underlying RNG—shall satisfy the threefollowing conditions: Simulations consistently distributedaccording tothemathematicalspecification of themodelProperly correlated risk driversIndependent scenarios However, those conditions aretypicallynot sufficient to guaranteereasonablevalidation testsperformed on theeconomic scenarios(e.g.,martingale tests, repricing testsandcorrelation tests) if the number of simulations islimited, which is the case in practice. Intheworst-casescenario,validation tests may faileventhough anappropriate economic scenario generation process is in place.As a consequence, this could lead to asignificantleakageas well asissues withMonte Carlo repricingmis-estimation.To this extent, insurance and reinsuranceundertakings are required to demonstrate the quality of the RNGthey are using.This requirement isclearlymentioned underSolvency IIby the following guidelineregarding the valuation of the technical provisions: “Insurance and reinsurance undertakings should ensure that (pseudo)randomnumber generatorsused in an ESG are properly tested.”1 Besides, it is also an area of interest forregulators. In particular, in the second half of 2020,theFrench PrudentialSupervision and Resolution Authority(ACPR)carried out a review of theEconomicScenarioGenerators(ESGs)used bya sample of 15Frenchinsurancecompanies.This review was based on a series of on-site checksandthe key conclusions were set out ina paper2summarisingthe diversity of practices observed and providinginsights onsomeofthebest practices,with a particular focus ontheassessmentand validationoftheuncertaintyaroundthestochastic valuation. Thefollowing paragraphs discuss some of the more general market practices mentioned by the ACPR formakingand validating stochastic assessments. It is alsoworth noticing that such practices are also commonly used inother insurance markets across the world. Practitionershave typicallyobserved discrepancies between the”Monte Carlo”valuation estimateof the BEL andPVFPand theirtrue expected values, withthe exact gap changing from time to timedepending on economicconditions and/or stress tests performed. This discrepancyis referred to as”leakage.”Setting aside theALMmodel error as potential source of leakage, this gap isgenerallydue to the convergence error,given thata limitednumber ofrisk-neutraleconomicscenarios isproducedin practice, typicallybetween1,000and5,000.To try tomake this gap lower and/or more stable, some companieshaveinvestigateda fewmorepragmatic methods,such as: Seedoptimisationapproach.Becausemost of theRNGsdepend on a core parameter calleda ”seed,”it istempting to select the seed su