The Actuarial Approach To Option Pricing Under The Jump-Diffusion And The O-U Process

With the rapid development of global financial market,the status of options in financial derivatives is particularly important,and the option pricing is one of the core problems of financial mathematics.The traditional pricing methods include the partial differential equation method,the martingale method and the discrete model approximation method and so on.These methods are usually established under the assumption that the financial market is arbitrage-free,equilibrium and complete.However,the real financial market is arbitrage,non-equilibrium and incomplete.Bladt and Rydberg proposed the actuarial approach to solve the option pricing for the first time in 1998.The main idea is that risk-free asset is discounted by the risk-free rate,and the risk asset is discounted by the rate of expected return.Since there is no any economic assumptions in the actuarial approach,it is suitable for the real financial market.In addition,the occurrence of some important events(for example,economic crisis,earthquake,war,etc.)can also lead to intermittent jump in the stock price,while the mean reversion of return on asset and the stochastic interest rate have also an effect on the option price.Therefore,it is meaningful to study the option pricing under these circumstances by using the actuarial approach.In this paper,the pricing problem of the rainbow option and the chooser option under different conditions are studied by using the actuarial approach.The full text is divided into six parts.In Introduction,the option pricing theory and research status are introduced.In Chapter 1,the definition of actuarial price of the option is introduced,the definitions of Brownian movement and Poisson process and their properties are studied.In Chapter 2,we suppose that the underlying asset price follows the Jump-Diffusion process,the risk-free interest rate r(t)and the volatility of the stock ?(t)are the definite function of time .The pricing of rainbow options is obtained by using the actuarial approach.In Chapter 3,we suppose that the underlying asset price follows the O-U process of multi-dimensional Brownian motion model,the risk-free interest rate r(t)satisfies the Vasicek model.The pricing of rainbow options is obtained by using the actuarial approach.In Chapter 4,we suppose that the underlying asset price follows the O-U process,the risk-free interest rate r(t)satisfies the Vasicek model,one gets the pricing of chooser options by using the actuarial approach.In Chapter 5,we summarize the main results obtained in this paper and propose the problems that need to be solved in the further.