Pricing Equity-Linked Life Policies With Surrender Option

With the economic development of our country, all kinds of life insurance play a more and more position in the national economy. For each of us, the insurance allows us to make a long-term plan in our own economic well-off time. Planning ahead is positive for both individuals and society.Equity-linked life insurance combines the financial investment with the insurance. On one hand, people can enjoy the safety of insurance. On the other hand, people may obtain high returns brought by capital market. The equity-linked policies have two payment forms, which are single premium and periodical premium respectively. This article gives pricing proceeding of equity-linked insurance for two forms mentioned above.If the payment form of equity-linked policies is a single premium, we mainly use the least squares Monte Carlo simulation pricing equity-linked insurance. In the first place, we analyze the equity-linked insurance contract and its mathematical model. Here we give a pricing proceeding for a simple model of insurance. In the second place, we take consideration of the risk of death into pricing equity-linked insurance proceeding. And here gives computation result of insurance price respective for men and women in the same age. In the third place, there is no uniform pricing framework for computing this kind of policies. It depends on the historical data in a certain extent. In this case, we use the Monte Carlo simulation to obtain the paths those show the change of investment accounts in different paths, and then we can use MATLAB to compute the time when the surrender options should be executed. Furthermore, we get the prices of investment linked life insurance.To compute the periodical premium, we use the Cox-Ross-Rubinstein model to describe the change process of the value of investment account. An example is given to illustrate the reason why the value of the investment account is a non-recombinant binomial tree. Since the annual premium payment, the restructuring effect is damaged. The result is huge increase of the value of the reference fund. To overcome this problem, we use a part of the value of the investment account instead of all the possible value. Thus the computational complexity will be reduced. In the pricing process, we use backward process and linear interpolation.During the process of simulation for the value change of investment account, we find much bad value in the simulation path. That impacts the simulation results seriously, so we propose a method for this. We introduce a control parameter to reduce the number of bad value. Through simulation experiments, we get very good results. In addition, this control parameter introduced can be changed depending on the degree of risk that the insurer can endure. The equity-linked life insurance based variable parameter is suitable for more people.Usually equity-linked life insurance policies last a long period, so it is not always realistic to assume constant interest rates. We propose a method to make interest rate of policy random. In order to descript interest rate of equity-linked life insurance policies, we use both Gaussian and Poisson random number. This method can increase the credibility of the simulation process, reduce errors in the pricing process, and benefit both the insured and the insurer.