| Option pricing is one of the key problems in financial mathematics. The core princi-ple of traditional option pricing is dynamic-no arbitrage equilibrium analysis, such as B-S model, binomial tree model, martingale and so on. These methods are based on the as-sumption that the financial market is arbitrage-free, equilibrium and complete. However, this ideal market does not exist. Therefore, the traditional pricing methods are limited in application.In1998Mogens Blat and Tina Hviid Rydberg put forward the actuarial option pricing approach. In their paper, they turned the pricing problem into a equivalent fair premium determination. This approach does not involve in any economic assumption, and can be used in the arbitrage, not well balanced and incomplete market. So, we try to study the pricing problem by using the actuarial pricing approach.Firstly, through analysising the sensible execution condition under the actuarial ap-proach in terms of European call option, we modify the execution condition of Blat and Rydberg’s. Then we get the modified BS formula under actuarial approach. By analysis-ing numerical example we verify the effectiveness of the actuarial pricing approach and finish the sensitivity analysis.Secondly, we derive the pricing formula of European call options based on the Vasicek interest rate model by using the actuarial option approach. At the same time, we deduce the sensitivity analysis of the Vasicek interest rate model.Lastly, we derive the pricing formulas of path dependent options:Lookback option, Partial lookback option. The study of the pricing of Lookback option also verifies the effectiveness of this method. At the same time, we analysis the effect of expect rate of return to option price. The result of Partial lookback option contains Lookback option’s. Comparing the numerical results, we can deduce that by using the actuarial approach the Partial lookback option price is lower than Lookback option and the Partial lookback option under risk neutral method. |
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