Option Pricing Model Based On Actuarial Approach And Its Application In Medical Insurance

Option pricing model and actuarial approach essentially belong to the contingent claiming to a great extent, which has provided the possibility of mixing actuarial approach with option pricing model under the condition of uncertainty. But the two branches on behalf of uncertainty exist parallel at present and seem to have very little chance to integrate. However, on the basis of summarizing the related research of actuarial approach and option pricing methods, the author believes that option pricing model and actuarial fall into the unified research paradigm essentially. That is, the development of insurance actuarial depends on the contingent claim valuation, while the contingent claim valuation may also be derived from actuarial approach. Therefore, the author deduces option pricing model from actuarial approach and applies the option pricing model to the medical insurance domain, the main researching tasks carried out are as follows:First, the classic financial skills, such as duplicating, hedging and constructing investment portfolios universally used in modern finance approaches, are abandoned in the paper. Instead, the modern actuarial approach, from the viewpoint of evaluating latent losses and corresponding probability distribution, is applied to study the option pricing model in continuous-time. The classical Black-Scholes model is derived from this approach, which, on the one hand, clears away obstacles whether option pricing model should be applied to the insurance domain or not, on the other hand opens up a new way to apply the actuarial approach in option pricing model. Meanwhile, the paper modifies the formula put forward by Bladt and Rydberg as well. Then the validity of the method applied in this paper has been proved through the empirical analysis of Chicago S&P 500 stock index options.Second, grounded on Black-Scholes model and the actuarial approach, an American option pricing model in continuous-time state is deduced and an exact and explicit solution for the valuation of American put options is obtained. Contrasted with numerical methods, such as the Binomial Option Pricing model, GARCH model and the empirical analysis on Hong Kong stock options, this method advanced in the paper has proved its dependability and reliability.Third, through employing option operation pattern to transfer the risks undertaken by the government to those medical service suppliers, the author has designed a management pattern of national basic health service based on option idea. From evaluating the insurer's potential loss and corresponding probability, the option-pricing model based on actuarial approach is used to calculate the fair premium. The simulation calculation and example analysis by utilizing the data from Ministry of Public Health of China might provide consultations for the scientific policy-making of our government.Fourth, the author clarifies barrier option characteristics of major medical expense insurance from the viewpoint of option and believes that major medical expense insurance might be seen as an up-and-out call option. Through the actuarial approach of option pricing, the barrier option pricing formula of major medical expense insurance premium has been derived consequently. With the hospitalized expense distribution list of partial Enterprise Staff of Chengdu, the theoretical price of major medical expense insurance premium has been calculated by employing the paper's model. Furthermore, the rationality and reliability of the paper's models have been demonstrated through comparison with the actual premium level promulgated by the Bureau of Social Insurance and contrast with traditional insurance actuarial methods.