Option Pricing Research And Application Based On The Transaction Cost, The Volatility Of The Underlying Asset And The Strike Price

Option is an important derivative and the option pricing theory is an important branch of modern financial engineering. The purpose of the dissertation is to study the option pricing problem based on the transaction cost, the volatility of the underlying asset and the strike price.The first part of the dissertation discusses the influence that the underlying asset volatility has on the option pricing. Based on the study of the fixed volatility model, the stochastic volatility model, the diffusion-jump volatility model, he stochastic-jump volatility model and the Possion-jump model, the dissertation builds the mixed transition distribution option pricing model. This model, which is a modification of the Possion-jump model, can fit not only the stationary behavior, the bursts and the outliers, but the stretches of the time series.Strike price is a deterministic factor of the option pricing mechanism. The second part of the dissertation studies the executive basket stock option pricing with stochastic exercise date and fixed strike price. This part also studies the indexed stock option pricing with changeable strike price and variable exercise date. The third part studies the determination about the minimum level of the reload option strike price , and the pricing of reload stock option with variable strike price. The fourth part of the dissertation studies the option pricing model with variable and unfixed volatility, the volatility of this model is not a fixed value but a function of the time. What is more, the model is applied to analyze the debt-to-equity transformation ratio.Transaction cost also has great influence on option pricing. In the long run, the volatility of the underlying asset is mean reverting. The mean-reverting volatility option pricing model with transaction cost takes both changeable volatility and transaction cost into account, and modifies the portfolio replication option pricing model with transaction cost.The researches synthetically apply Martingale theory, Stochastic process,Uncertain programming theory, Financial engineering, Statistics and Computer science, as the embodiment of multi-subject combination characteristic, and try to get better results which can direct the financial practices.