Research On The Pricing Of Some Options At Random Interest Rate

Options pricing has always been a hot topic in the field of financial research,it plays a significant role in hedging,risk aversion and speculative profit.As a financial product with the highest degree of derivation,the theory of option pricing developed rapidly.As the efficient market premise hypothesis of the classic Black-Scholes option pricing theory is always inconsistent with the real market,due to its condition is too strict and limitations in practical application,it cannot fully describe the needs of financial market.In order to better meet the needs of the financial market,this paper mainly studied the option pricing model under the Levy market,which has looser conditions and can be will be better describe the market characteristics.Thus,the limitation of pricing model in practical application can be overcome.The main purpose of this paper is to study the analytical formula of rainbow option in stochastic interest rate model,the traditional pricing model of European option and Compound option of Levy model.The main results of this paper are as follows:(1)We suppose that the underlying asset price process following the Ornstein-Uhlenbeck process,the stochastic interest rate submitting to Hull-White model.Further,we consider the mean reversion of underlying asset.Afterwards,we study the problem of pricing formulas of rainbow option under Ornstein-Unlenbeck process and stochastic rate by using the martingale theory and actuarial pricing method,and then give the pricing formulas of rainbow option.(2)Assuming that the interest rates and stock price process satisfy the Ho-Lee model and Levy process,then establishing a mathematical model of non-arbitrage financial market based on Levy-Laplace index and obtained the European option pricing formula with stochastic interest rates.With the help of mathematical tools such an Poisson process and Levy-Laplace index,research on the financial mathematic model of Levy pure jump process is further carried out and the European option pricing formula of Levy pure jump process in non-arbitrage financial market is finally derived.(3)Assuming that the interest rates and stock price process is subject to Ho-Lee model and Levy process,a mathematical model of option pricing in Levy market is established.Obtaining the European option pricing formula with stochastic interest rates.We study the compound option on the based of the European option pricing,with the help of mathematical tools such as measure transformation and martingale method,the Compound option pricing formula of Levy process in financial market is finally deduced.