The Study On Valuation Of Equity-linked Products With Guaranteed Minimum Death Benefits

In July 2010,China Insurance Regulatory Commission has issued two authoritative announcements on the commencement and management of variable annuities,which denotes the introduction of variable annuities into Chinese insurance market.Variable annuities were originated in last century in USA,and became sophisticated in the market.The products were broadly welcomed for its varieties of guaranteed minimum benefits which could be used for investment and retirement purposes.Besides,variable annuities could be a source of novel investment which are more profitable when compared to some traditional financial products.Different types of guaranteed minimum benefits can be provided in variable annuities,such as guaranteed minimum death benefits(GMDB),guaranteed minimum accumulation benefits(GMAB),guaranteed minimum income benefits(GMIB)and guaranteed minimum withdrawal benefits(GMWB).This thesis mainly focuses on the numerical valuation of guaranteed minimum death benefits,i.e.,GMDB.First,this thesis briefly introduces the development of variable annuities,summarizes the study on the valuation of GMDB as well as several other guarantees both domestically and overseas.Key formulae for valuing GMDB contracts are presented then.To value GMDB,this thesis has considered several aspects.From the distribution of the time-until-death of the insured,this thesis considers the Combination-of-Exponential distribution and the piecewise constant forces mortality assumption.Besides,as for asset processes,this thesis includes several Lévy stochastic processes such as Brownian motion,Kou model and Merton jump model and so on.Speaking of maturity,this thesis further considers the finite time maturity dates for GMDB.When it comes to the numerical methods,COS method,Laguerre method and PROJ method are well implemented.Various numerical examples are displayed,respectively,from which approximating results yield good performance.Finally,the conclusion is drawn that those methods are capable of handling calculations in this thesis and show potentials when it comes to complicated settings.Generally speaking,this thesis first present ideas and theoretical deductions on the numerical valuation for GMDB,then innovatively adopt auxiliary functions to simplify calculations while utilizing aforementioned methods.Moreover,to strengthen the connection with real industry,when piecewise constant forces mortality assumption is adopted,this thesis values GMDB contracts based on real life table data.