随机波动率模型下一篮子期权的定价.pdfVIP

the difference of the income functions, basket options can be divided into two forms: the Geometric Basket Options and the Arithmetic Basket Options. Due to the more underlying assets, the pricing model become more complex. Therefore, this article focuses on the case of this two kinds of asset portfolio. Respectively, with the arithmetic and geometric income function forms of European and American basket options pricing. Chapter 1 provides simply an introduction on the academic literature for options pricing, especially for pricing the basket option, and the background of this article. In Chapter 2, under the stochastic volatility model the pricing of European bas- ket options are considered. By the derivation of the characteristic function under risk-neutral measure, the corresponding distribution function for the Geometric- style European call basket option by Shephard’s theorem is obtained with applying the method of partial differential equations. For the Arithmetic-style European call basket option, it’s difficult to derive the accuracy distribution function of the sum of two variables which are both log-normal distributed. The corresponding distribution function is obtained by approximating the solution of the arithmetic form of Euro- pean basket call options. And the MonteCarlo simulation method has been used in calculation and analysis. In Chapter 3, the pricing of American basket options are considered under the same assumption in Chapter 2. The value of American options and the reasonable- ness of implementation in advance have been analyzed. Deduced the best imple- mentation of the boundary of the American basket call options. Then using the Kim integral equation method in the price of European call option, we have obtained the approximated solution for the American basket call option price. Finally, the ef- fects of the option value and