An Actuarial Approach To Asian Option Pricing With Floating Striked Price

Options are important derivative securities. They are certain rights that enable their holders to buy or sell the underlying assets of certain quality and in certain quantity at a fixed time in the future after paying the cost of options. In 1973, F.Black and M.Scholes, the scholars from the Chicago University put forward their Black-Scholes Option Pricing Model, which has been hailed as a breakthrough in the research of options pricing theory, has laid the foundation for the establishment of the theory for pricing the options in various emerging derivative financial markets—the stock market, the bond market, the money market, and the commodity market. However, in recent years, with the increasing complexity of the demands of the financial markets, it is difficult to satisfy the specific needs of customers to use the standard option alone. In order to satisfy specific needs of customers, many financial companies devised a great deal of non-standard derivative securities. Being one of the typical non-standard derivative securities, Asian option is the most active one in financial derivative market.The main goal of this paper is to study the typical representative of strongly path -dependent option—Asian option. Because of strong path dependence, the pricing of Asian option is very complicated. Meanwhile, as an innovation of European option, it has close relationship with the standard European option. Therefore, the research of this paper should be based on the sympathetic, critical understanding of Black-Scholes Option Pricing Model.This paper contains two main research works: The first one is to establish a model for the pricing of target asset option on the presumption that the fluctuation of their price is subjected to the geometric Brownian Motion, and to procure, under the Black-Scholes environments, a closed form an actuarial approach to Asian option pricing analytic pricing formula of Asian option. The second one is to discuss the pricing formula of option on Asian option under the assumption that stocks price process driven by nonhmogeneous Poisson jump-diffusion process and striked price process driven by Ito process, we obtain the pricing formula of Asian option.