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论文作者:meisishow论文属性:作业 Assignment登出时间:2014-09-02编辑:meisishow点击率:5982
论文字数:2882论文编号:org201409021407099834语种:英语 English地区:英国价格:免费论文
关键词:期权价值American OptionsFinanical Derivatives金融衍生品
摘要:美国期权是金融衍生品其价值来源于一个潜在的资产,通常一个股票。黑色和斯科尔斯(1973)描述了一个现像:“安全给予买入或卖出一种资产的权利,在一定的时间之内会受到一些条件的限制”。
In the case that it is optimal to exercise the option at a certain node, its price will be equal to the intrinsic value at that same node. Every node will be checked for the optimality of exercising the option or not, until we have reached the initial point where we want to price the option.
The model starts being built for a American option of a non dividend paying stock and after that the scenario of dividend payments and optimal early exercise strategy is considered.
As referenced before the stock goes up and down by a certain amount form one period to the next, if u is the up movement and d the down movement, then they can be calculated as, (3.3.1.1) and (3.3.1.2) as in Cox, Ross and Rubinstein (1979). In no arbitrage conditions it is possible to calculate the probability of the up and down movements, with the up being defined as, (3.3.1.3) where from the definition of probability and the down movement as (3.3.1.4).
The tree formed using these specifications from Cox, Ross and Rubinstein (1979), can have the following graphical representation。
The option is price is calculated from the asset price binomial tree. The maturity boundary condition for an American option, is that the payoff is equal to , we already have S at each maturity node from the asset price model, so we can calculate backwards the price of the option as the expectation of the future payoff of the option.
At each node we calculate the expectation of the future payoffs, where the price of the option will be a compound of expectations. These can be represented by the multi period case for a call as in Cox, Ross and Rubinstein (1979)。
The option prices are calculated as the expectation of the option's future payoffs using their respective weighted risk neutral probabilities of an up movement and a down movement and then discounted at the risk free rate r.
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