Research On Several Problems About Portfolio And Option Pricing

In this paper, the partial contents about portfolio theory and option theory are discussed. Markowitz's portfolio theory is tremendous achievement in modern finance, but in his theory, stock price yield obey to normal distribution which have windage with comparison to the fact. Later, many scholars extended and improved his theory. based on portfolio selection and Asset pricing Three-parameter Framework (Simaan(1993)), sectionⅡputs forward a new portfolio selection model with transaction cost , without short sale and with lower bound constrains. Besides, the author gives the optimal algorithm of the new optimization problem. Now barrier option numerical pricing is very significant to finance engineering and real option realm ,in the first part of sectionⅢ, The trinomial schemes of option pricing models are the extension of the binomial models. This section give the lattice method of barrier option pricing, based on the model of stock returns dependent on skewness and kurtosis. What's more, the section gives the algorithm of European double-barrier. In the second of sectionⅢ, under non-equilibrium, non-complete and arbitrage market situation, the paper extends the model of European call option pricing to Asian option pricing model by using merely probability measure of price process and actuarial considerations for pricing options, and obtain the approximately results. In the end, the paper gives an example, and the results illustrate the rationality of the Asian option pricing model. In the third of sectionⅢ, under continuous economic situation, based on barrier option pricing with curve boundary, this part clarified option characteristic of insurance contracts is substantively a put option, and compute insurance fee.