金融数学期末测试.doc

金融数学期末测试 姓名：卞自成 学号：2012626630103 得分：一 计算题。1. given the following data compute the price of the associated European call option .(a) S0 : 80 X : 70 R 0.05 T 3mo Q 0.30解： V= 查正态分布表得： 代入公式可得： Then the price of the associated European call option is 11.84.2. using the data in Exercise 1 , compute the price of the associated European put option for h .(h) S0 : 25 X: 25 R 0.05 T 3mo Q 0.28解： 查正态分布表得： 代入公式得： Then the price of the associated European put option is 1.24.3. given the following information ,find the implied volatility for the associated European call option .(a) S0 40 K 40 R 0.05 T 3mo V 3.8解： 使用Maple软件计算 with (finance) solve(blackscholes(40,40,.25,x)=3.8,x); 解得： x=0.45 Then the implied volatility for the associated European call option is 0.45.4. Assume that a stock model has the parameter u = 1.7 d = 0.8 S0= 120 A European call option ,expiring at t =3 ,has an exercise price x =115 and the interest rate is 0.06 over each period . price this option at t= 0 using the chaining method .解： 二 英译汉。1. 7.2.1 Hedging with putsOne can simply purchase a put on a stock or purchase index option puts on a portfolio.This raises delicate questions as to what percent of the portfolio to hedge and how far out of the money to choose the put. The cost of the hedge wil vary widely depending on the selection.One could purchase puts on each stock in a portfolio,but it is much less expensive to purchase index option puts.采用看跌期权对冲 人们可以通过直接购买股票看跌期权或者指数看跌期权来对资产组合进行对冲。由此产生的问题是资产组合对冲的比例的确定以及选择看跌期权的数量。对冲方案选择不一样，对冲的成本将差异很大。你可以选择购买资产组合中每一个股票的看跌期权，但如果选择指数看跌期权成本就低多了。2. 7.2.2 Hedging with CollarsTo hedge a stock with a collar,one purchase an at-the-money put and sells an out-of-the-money call.Properly chosen,the cash is required from the investor.If the stock drops,the investor is protected.If the stock increases in price, then it will be called away. 采用双限对股票对冲 采用双限对股票进行对冲，是指一方面买进平值看跌期权，同时又卖出虚值看跌期权。通过适当的选择，使卖出期权的收入正好等于购买期权所需金额，这样投资者就无需额外支出了。如果股票下跌，投资者处于保护状态。如果股票价格上升了，则在股票上得益。3. 7.2.3 Hedging with Paired TradesSuppose that in the sane industrial group there are two companies: super good and hapless industries. It is agreed that the names accurately reflect the quality of the companies. Suppose we purchase 100 shares of super and short an equal dollar amount of hapless. If the economy surges strongly, both stocks should appreciate, but super should outperform hapless. If the economy falters, both stocks will drop, but hapless should fall faster and further than super. The same analysis holds if an exogenous or endogenous shock strikes the specific industrial niche occupied by super and hapless. Thus, no matter what the future holds, super should outperform hapless on a relative basis. At first glance, this approach seems too good to be true. We can not lose! That is true, but if the market appreciates, we would do much better by purchasing super alone and avoiding hapless. So we are giving up profits to protect ourselves on the downside. This is true for all hedges. 成对套期保值交易假设在同一产业中有两个公司：“超级商品”与“倒霉企业”。这两家公司的质量正如他们的名字一样。我们买进100股超级公司的股票，同时卖出相同市值的倒霉公司的股票。如果经济处于高涨周期，两家公司的股票都会上升，但超级公司的上升幅度会大一些。反过来如果经济处于萧条周期，两家公司的股票都会下跌，但倒霉公司的下跌幅度会大一些。如果外部的或者内在因素造成了对两家公司所在行业的一些冲击，则可以采用相同的方法进行分析。因此不管将来发生什么情况，超级公司的股票表现总是相对好于倒霉公司。一眼看来这种方法好像太好了，以至于不像真的，因为我们总是不输钱。但事实却是如此，但你应该知道如果市场走好，我们只购买超级公司而不进行对冲，我们利润会更多。因此我们在市场下跌时得到保护以市场上升的利润为代价的。所以对冲都是这一思路。三 小论文。1. 谈谈做股票时，如何用对冲的方法降低风险，提高收益（400字左右）。如何用对冲的方法降低风险，提高收益 浅谈我对对冲的理解对冲，是同一时间买入一外币，做买空。理论上，买空一种货币，要银码一样，这才是真正的对冲盘，否则两边大小不一样就做不到对冲的功能。那么股票对冲的方法是什么呢？ 股票对冲的方法和资金对冲。投资的股票，满仓时候的股价下跌，空仓时候的股价上涨。在股指期货没有推出前，若将股票和资金对冲，就能避免上述情况出现。股票与资金的对冲，就是折中的办法。在一般情况下，什么时候都不满仓，不空仓，任何时候都有股票又有资金。对于心态平和的投资者来说，在大盘和个股不同的位置时候，才能适当调整仓位的轻重。作为一般的投资者，均不宜采取满进满出法操作。 不同股票的对冲。某一点位、多少仓位确定之后，在具体选择时候应有多只股票可供选择的，在买入时机上要学会适时的等待。不同股票间对冲最大的好处是进可攻、退可