An Actuarial Approach To Some Kinds Of Pricing Option Under Vasicek Interest Rates Model

There are three traditional methods of option pricing: the Black-Scholes model, binomial tree method and martingale. All of them are based on the assumption of the financial market is arbitrage-free, equilibrium and complete, all of them are the application of replicating. But the formation of their theory can not explain the ture market really. Because of the weak efficiency of the domestic financial markets, if the market with arbitrage,nonequilibrium or in-complete under no economic considerations, options pricing is a valuble topic. In 1998 Mogens Bladt and Tina Hviid Rydberg put forward the actuarial approach option price, which is based on no economical considerations, In other words, The approach can also use in arbitrage, nonequilibrium or incomplete.In this paper, The first two chapters deal with the history of the development of option pricing,give the derivation of classic Black-Scholes formula under constant interest rate. The third chapter describes some random interest rate models which have the real economic significance, Vasicek interest rate model in theoretical study to solve practical problems is more superior, particularly in the calculation is relatively simple. Chapter IV gives European call options, Asian options and chooser options by insurance actuarial pricing methods under regular interest rates. The most important part of this paper is the fifth chapter, in the Vasicek interest rate model, insurance actuarial pricing method suppose risky assets and risk-free assets. Transform into bonds or cash also discount by the random rates, which also can be seen as risk, but it is not decided by people's expectations yield by the mathematical expectation of random interest rates. The pricing method becomes: risk assets (stocks) is discount by the return expectations, the other risk assets (bonds or cash) is discount according to the random interest rate expectations, and then the combination of this two assets will be in the stock prices of the actual probability measure from the mathematical expectation.we get the pricing formula of European call options, Asian options and chooser options under Vasicek interest rates model by the actuarial approach .