Does Actuarial Approach to Option Pricing Really Work?

This article explored the relation and difference between option pricing and actuarial pricing from thinking and technical level, with the result that such modern financial notations as fair pricing of contingent claim and the change of probability measure have been longstanding and common practice in actuarial science. However, discounted expectancy of actual loss under real-world P probability measure, the simple idea in actuarial science, ignored the role of financial market and failed to keep pace with modern financial economic, which differenciate itself from the option pricing based on no-arbitrage method. So, the traditional actuarial pricing method must be corrected by a covariance term which reflects the interaction between the insurance claim and the financial market. Nevertheless, after conducting the change from real-world probability measure to risk-neutral probability measure, the time-honored actuarial pricing method will be the same with option pricing. We started by giving a brief introduction to the actuarial approach to option pricing, and then investgated the structural similarity between option and insurance contracts like stop-loss ro excess loss and compared the differences between Bladt & Rydberg(1998) together with its subsequent articles and standard BS formula, which followed by analyzing their idiological roots. Then, we, with the modern asset pricing theory, discovered the essential discrepency between actuarial pricing which neglects the function of financial market and Black-Scholes method based on dynamic hedging strategy in market. Besides, we put forward the modified actuarial valuation method which is identical with the BS method in complete market and is also applicable to option pricing in incomplete market.