Option Pricing Models Based on Levy Process and Entropy, and Applications

点击翻译按钮获取中文摘要

We have studied the option pricing problems in the incomplete asset market. In the previous research we have constructed the basic frameworks of the [GLP ＆ MEMM] pricing models, in which the geometric Levy processes are adopted as the underlying asset price processes and the MEMM (=minimal entropy martingale measure) is adopted as the equivalent martingale measure. So in this research we have investigated the fundamental properties of this model and have established the method how to apply this model to the practical option pricing problems.After that we have investigated the properties of this model by the computer simulation methods, and we have obtained a good result that this model has the possibility to realize the volatility smile/skew properties of the option prices in the markets.Next we have made empirical analysis on the market prices of the options, and we have obtained such a result that this model fits very well to the option prices in the market in the case that the underlying asset process moves very rapidly. Especially we could have seen that the [Geometric Stable Process ＆ MEMM] model is very desirable in the sense that this model has the possibility to fit to very wide class of the option price data in the market.