Study On The Pricing Methods Of American Basket Call Option With Dividend

A basket option is a derivative instrument on a portfolio of several underlying assets, the price of a basket option is determined by the weighted average of the prices of the underlying assets. According to the invest portfolio theory, the risk is reduced through diversification [6], therefore, the price of a basket option is lower than an option on a single variable. Theoretically speaking, in order to reduce the risk, any portfolio can be an underlying basket.This paper mainly research on regularly American basket call options. There are two basic hypotheses for regularly basket options: First, the risk-free interest rate is a constant. Second, the assets of the underlying portfolio are homogenous (the assets referred to in this paper are all stocks). In terms of the American call option with dividend, because of the property that it can be executed before expire, in very few special cases, closed form solutions can be found. More often, lattice method and Monte Carlo simulation method are necessary for pricing. But both of the two methods have a common limit that the computation requirements explode exponentially as the dimension of the problem increases called"dimension curse", which is the central problem that this paper tries to work out.So as to set forth the central work of this paper, the background and current state on basket options research are introduced at first. In the second chapter, the mathematical basis on American basket potions is set forth simply. There are two main tasks in the third chapter: first, achieve the transform from the mathematical average to geometrical average of the basket by Vorst [2], Gentle [3] and Merton [4,5] model. Second, deduce the approximate analytical solution of American basket call option with dividend based on the model of Barone-Adesi and Whaley [4] (BW in short). In the forth chapter, a new method is presented which is called Sum Least squares Monte Carlo simulation in this paper, aiming at the limit that the parameters of the fitting curve increase exponentially as the dimension of underlying assets increases by typical Least squares Monte Carlo simulation[6,7,8]. Finally, in the fifth chapter the methods which are presented in the third chapter and the forth chapter are tested, the results are satisfied.