A Study On Several Exotic Options Pricing Under Jump-diffusion Model Using An Actuarial Approach

Recently, in addition to known European options and American options, there appear many new varieties which are changed, composed, derived by vanilla options in international financial market. How to pricing these exotic options is one of the kernel problems for financial community.Traditional methods of option pricing are based on the assumption that the financial market is arbitrage-free, equilibrium, and complete. However, if the market is arbitrage, non-equilibrium and incomplete, it is difficult to price options with traditional methods. Recently, option pricing theory has made great development in how to determine the option value under the imperfect market condition. One of the important methods is actuarial approach.This dissertation intends to study several exotic options pricing problems under jump-diffusion model by using actuarial approach, and gives the following main results:1. Firstly, we introduce the actuarial approach to option pricing. To European option for the stock process is driven by Poisson jump-diffusion, we give the deriving process of the pricing formula by using actuarial approach.2. Secondly, we study the reload option pricing (only consider the situation once again loaded) and the improved reload option pricing model which the long incentive and reload feature of executive stock option are included, and offer the pricing formulas.3. Thirdly, we study the four types of compound option pricing and offer the option pricing formulas by taking call option on call option as example.4. Finally, we study the pricing of chooser option by using actuarial approach and offer the option pricing formula.