Two Kingds Of Variable Annuities Approximate Pricing Under The Stochastic Interest

Variable annuity is a insurance contract with the minimum guar-anteed interest,at the same time associated with the investment ac-count.Broadly speaking,it is a financial derivative products,and theminimum interest guarantee is equivalent to the put option.This in-surance product can make the policy holder in the gains while avoidingthe large losses caused by market volatility,with some securityFirstly,this paper introduces the concept of variable annuity andthe minimum interest guarantee,and introduces the form of the guar-anteed minimum benefits. Secondly,we assume the interest followingthe Vasicek model,and we dealt with it based on a new approximationmethod we had know about the stochastic interest rate.We give thepricing of the guaranteed minimum death benefit and the guaranteedminimum maturity benefit in the variable annuity under the inter-est rate model we have assumed,and do a sensitivity analysis for theguaranteed minimum death benefit.Finally,assuming death force obe-dience CIR model,we give the variable annuity pricing formula underthe death force,based on the variable annuity pricing formula we havesolved.